List of numbers
Encyclopedia
This is a list of articles about number
Number
A number is a mathematical object used to count and measure. In mathematics, the definition of number has been extended over the years to include such numbers as zero, negative numbers, rational numbers, irrational numbers, and complex numbers....

s
Number names
In linguistics, number names are specific words in a natural language that represent numbers.In writing, numerals are symbols also representing numbers...

).

Natural numberNatural numberIn mathematics, the natural numbers are the ordinary whole numbers used for counting and ordering . These purposes are related to the linguistic notions of cardinal and ordinal numbers, respectively...s

Notable integers

Other numbers that are notable for their mathematical properties or cultural meanings include:

• −40, the equal point in the Fahrenheit and Celsius scales.
• −1
• 0
0 (number)
0 is both a numberand the numerical digit used to represent that number in numerals.It fulfills a central role in mathematics as the additive identity of the integers, real numbers, and many other algebraic structures. As a digit, 0 is used as a placeholder in place value systems...

, a number which quantifies a count or an amount of null
Empty set
In mathematics, and more specifically set theory, the empty set is the unique set having no elements; its size or cardinality is zero. Some axiomatic set theories assure that the empty set exists by including an axiom of empty set; in other theories, its existence can be deduced...

size.
• 2, the smallest prime number and the only even prime.
• 42
42 (number)
42 is the natural number immediately following 41 and directly preceding 43. The number has received considerable attention in popular culture as a result of its central appearance in The Hitchhiker's Guide to the Galaxy as the "Answer to the Ultimate Question of Life, the Universe, and...

, "the Answer to the Ultimate Question of Life, the Universe, and Everything" according to the Hitchhikers Guide to the Galaxy
• 255
255 (number)
255 is the natural number following 254 and preceding 256.-In mathematics:Its factorization makes it a sphenic number. Since 255 = 28 - 1, it is a Mersenne number, and the fourth such number not to be a prime number...

, 28−1
• 496
496 (number)
Four hundred [and] ninety-six is the natural number following four hundred [and] ninety-five and preceding four hundred [and] ninety-seven.-In mathematics:...

, a perfect number
Perfect number
In number theory, a perfect number is a positive integer that is equal to the sum of its proper positive divisors, that is, the sum of its positive divisors excluding the number itself . Equivalently, a perfect number is a number that is half the sum of all of its positive divisors i.e...

.
• 786
786 (number)
786 is the integer coming after 785 and before 787.-In mathematics:786 is a sphenic number. 50 can be partitioned into powers of two in 786 different ways ....

, regarded as sacred in the Muslim Abjad numerology
The Abjad numerals are a decimal numeral system in which the 28 letters of the Arabic alphabet are assigned numerical values. They have been used in the Arabic-speaking world since before the 8th century Arabic numerals...

.
• 1729
1729 (number)
1729 is the natural number following 1728 and preceding 1730.1729 is known as the Hardy–Ramanujan number after a famous anecdote of the British mathematician G. H. Hardy regarding a hospital visit to the Indian mathematician Srinivasa Ramanujan...

, a taxicab number
Taxicab number
In mathematics, the nth taxicab number, typically denoted Ta or Taxicab, is defined as the smallest number that can be expressed as a sum of two positive algebraic cubes in n distinct ways. The concept was first mentioned in 1657 by Bernard Frénicle de Bessy, and was made famous in the early 20th...

; the smallest positive integer that can be written as the sum of two positive cubes in two different ways
• 65535, 216-1, the maximum number that a 16-bit
16-bit
-16-bit architecture:The HP BPC, introduced in 1975, was the world's first 16-bit microprocessor. Prominent 16-bit processors include the PDP-11, Intel 8086, Intel 80286 and the WDC 65C816. The Intel 8088 was program-compatible with the Intel 8086, and was 16-bit in that its registers were 16...

unsigned integer
Integer (computer science)
In computer science, an integer is a datum of integral data type, a data type which represents some finite subset of the mathematical integers. Integral data types may be of different sizes and may or may not be allowed to contain negative values....

can reach.
• 142857
142857 (number)
142857 is the six repeating digits of 1/7, 0., and is the best-known cyclic number in base 10. If it is multiplied by 2, 3, 4, 5, or 6, the answer will be a cyclic permutation of itself, and will correspond to the repeating digits of 2/7, 3/7, 4/7, 5/7, or 6/7, respectively.- Calculations :- 22/7...

, a base 10 cyclic number
Cyclic number
A cyclic number is an integer in which cyclic permutations of the digits are successive multiples of the number. The most widely known is 142857:For example:Multiples of these fractions exhibit cyclic permutation:...

.
• 2147483647
2147483647
The number 2,147,483,647 is the eighth Mersenne prime, equal to 231 − 1. It is one of only four known double Mersenne primes....

, 231−1, the maximum number that a 32-bit
32-bit
The range of integer values that can be stored in 32 bits is 0 through 4,294,967,295. Hence, a processor with 32-bit memory addresses can directly access 4 GB of byte-addressable memory....

signed integer
Integer (computer science)
In computer science, an integer is a datum of integral data type, a data type which represents some finite subset of the mathematical integers. Integral data types may be of different sizes and may or may not be allowed to contain negative values....

can reach.
• 9814072356
9814072356 (number)
9814072356 or 9,814,072,356 is 99066 squared, and is the eighty-seventh and largest square number using each of the digits 1, 2, 3, 4, 5, 6, 7, 8, 9, and 0 exactly once ....

, the largest perfect power that contains no repeated digits in base ten.

Named integers

• Googol
Googol
A googol is the large number 10100, that is, the digit 1 followed by 100 zeros:The term was coined in 1938 by 9-year-old Milton Sirotta , nephew of American mathematician Edward Kasner...

and googolplex
• Graham's number
Graham's number
Graham's number, named after Ronald Graham, is a large number that is an upper bound on the solution to a certain problem in Ramsey theory.The number gained a degree of popular attention when Martin Gardner described it in the "Mathematical Games" section of Scientific American in November 1977,...

• Moser's number
• Shannon number
Shannon number
The Shannon number, named after Claude Shannon, is an estimated lower bound on the game-tree complexity of chess. Shannon calculated it as an aside in his 1950 paper "Programming a Computer for Playing Chess"...

• Hardy-Ramanujan number
• Skewes' number
• Number of the Beast
Number of the Beast
The Number of the Beast is a term in the Book of Revelation, of the New Testament, that is associated with the first Beast of Revelation chapter 13, the Beast of the sea. In most manuscripts of the New Testament and in English translations of the Bible, the number of the Beast is...

• Leviathan number
Leviathan number
The Leviathan number in numerology is defined as the factorial of the 666th power of ten: !, which has approximately 6.65565705×10668 digits....

• Kaprekar's constant
6174 (number)
6174 is known as Kaprekar's constant after the Indian mathematician D. R. Kaprekar. This number is notable for the following property:#Take any four-digit number, using at least two different digits...

Prime numberPrime numberA prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. A natural number greater than 1 that is not a prime number is called a composite number. For example 5 is prime, as only 1 and 5 divide it, whereas 6 is composite, since it has the divisors 2...s

A prime number is a positive integer which has exactly two divisor
Divisor
In mathematics, a divisor of an integer n, also called a factor of n, is an integer which divides n without leaving a remainder.-Explanation:...

s: one and itself.

The first 100 prime numbers:
|  2 >
 3 5 7 1111 (number)11 is the natural number following 10 and preceding 12.Eleven is the first number which cannot be counted with a human's eight fingers and two thumbs additively. In English, it is the smallest positive integer requiring three syllables and the largest prime number with a single-morpheme name... 1313 (number)13 is the natural number after 12 and before 14. It is the smallest number with eight letters in its name spelled out in English. It is also the first of the teens – the numbers 13 through 19 – the ages of teenagers.... 1717 (number)17 is the natural number following 16 and preceding 18. It is prime.In spoken English, the numbers 17 and 70 are sometimes confused because they sound similar. When carefully enunciated, they differ in which syllable is stressed: 17 vs 70... 1919 (number)19 is the natural number following 18 and preceding 20. It is a prime number.In English speech, the numbers 19 and 90 are often confused. When carefully enunciated, they differ in which syllable is stressed: 19 vs 90... 2323 (number)23 is the natural number following 22 and preceding 24.- In mathematics :Twenty-three is the ninth prime number, the smallest odd prime that is not a twin prime. Twenty-three is also the fifth factorial prime, the third Woodall prime... 2929 (number)29 is the natural number following 28 and preceding 30.-In mathematics:It is the tenth prime number, and also the fourth primorial prime. It forms a twin prime pair with thirty-one, which is also a primorial prime. Twenty-nine is also the sixth Sophie Germain prime. It is also the sum of three... >- | 3131 (number)31 is the natural number following 30 and preceding 32.- In mathematics :Thirty-one is the third Mersenne prime as well as the fourth primorial prime, and together with twenty-nine, another primorial prime, it comprises a twin prime. As a Mersenne prime, 31 is related to the perfect number 496,... 3737 (number)37 is the natural number following 36 and preceding 38.-In mathematics:It is a prime number, the fifth lucky prime, the first irregular prime, the third unique prime and the third cuban prime of the form... 4141 (number)41 is the natural number following 40 and preceding 42.-In mathematics:Forty-one is the 13th smallest prime number. The next is forty-three, with which it comprises a twin prime... 4343 (number)43 is the natural number following 42 and preceding 44.- In mathematics :Forty-three is the 14th smallest prime number. The previous is forty-one, with which it comprises a twin prime, and the next is forty-seven. 43 is the smallest prime that is not a Chen prime... 4747 (number)47 is the natural number following 46 and preceding 48.-In mathematics:Forty-seven is the fifteenth prime number, a safe prime, the thirteenth supersingular prime, and the sixth Lucas prime. Forty-seven is a highly cototient number... 5353 (number)53 is the natural number following 52 and preceding 54.-In mathematics:Fifty-three is the 16th prime number. It is also an Eisenstein prime.... 5959 (number)59 is the natural number following 58 and preceding 60.-In mathematics:Fifty-nine is the 17th smallest prime number. The next is sixty-one, with which it comprises a twin prime. 59 is an irregular prime, a safe prime and the 14th supersingular prime. It is an Eisenstein prime with no imaginary... 6161 (number)61 is the natural number following 60 and preceding 62.-In mathematics:It is the 18th prime number. The previous is 59, with which it comprises a twin prime. Sixty-one is a cuban prime of the form p = / , x = y + 1.... 6767 (number)67 is the natural number following 66 and preceding 68. It is an odd number.-In mathematics:Sixty-seven is the 19th prime number , an irregular prime, a lucky prime, the sum of five consecutive primes , and a Heegner number.Since 18! + 1 is divisible by 67 but 67 is not one more than a multiple of... 7171 (number)71 is the natural number following 70 and preceding 72.-In mathematics:71 is the algebraic degree of Conway's constant, a remarkable number arising in the study of look-and-say sequences.... >- | 7373 (number)73 is the natural number following 72 and preceding 74. In English, it is the smallest integer with twelve letters in its spelled out name.- In mathematics :... 7979 (number)Seventy-nine is the natural number following 78 and preceding 80.79 may represent:-In mathematics:*An odd number*The smallest number that can't be represented as a sum of fewer than 19 fourth powers*A strictly non-palindromic number... 8383 (number)83 is the natural number following 82 and preceding 84.-In mathematics:Eighty-three is the sum of three consecutive primes as well as the sum of five consecutive primes .... 89 9797 (number)97 is the natural number following 96 and preceding 98.-In mathematics:97 is the 25th prime number , following 89 and preceding 101. 97 is a Proth prime as it is 3 × 25 + 1.The numbers 97, 907, 9007, 90007 and 900007 are happy primes... 101101 (number)101 is the natural number following 100 and preceding 102.It is variously pronounced "one hundred and one" / "a hundred and one", "one hundred one" / "a hundred one", and "one oh one"... 103103 (number)103 is the natural number following 102 and preceding 104.-In mathematics:One hundred [and] three is the 27th prime number. The previous prime is 101, making them both twin primes... 107107 (number)107 is the natural number following 106 and preceding 108.-In mathematics:One hundred [and] seven is the 28th prime number. The next prime is 109, with which it comprises a twin prime, making 107 a Chen prime.... 109109 (number)109 is the natural number following 108 and preceding 110.-In mathematics:One hundred [and] nine is the 29th prime number, and also a Chen prime. The previous prime is 107, making them both twin primes... 113113 (number)113 is the natural number following 112 and preceding 114.-In mathematics:One hundred [and] thirteen is the 30th prime number, following 109 and preceding 127, a Sophie Germain prime, a Chen prime and a Proth prime as it is a prime number of the form 7 × 24 + 1... >- |127127 (number)127 is the natural number following 126 and preceding 128.- In mathematics :*As a Mersenne prime, 127 is related to the perfect number 8128. 127 is also an exponent for the Mersenne prime 2127 - 1, making 127 a double Mersenne prime... 131131 (number)131 is the natural number following 130 and preceding 132.-In mathematics:131 is a Sophie Germain prime, the second 3-digit palindromic prime, and also a permutable prime with 113 and 311. It can be expressed as the sum of three consecutive primes, 131 = 41 + 43 + 47. 131 is an Eisenstein prime... 137137 (number)137 is the natural number following 136 and preceding 138.-In mathematics :One hundred [and] thirty-seven is the 33rd prime number; the next is 139, with which it comprises a twin prime, and thus 137 is a Chen prime. 137 is an Eisenstein prime with no imaginary part and a real part of the form 3n -... 139139 (number)139 is the natural number following 138 and preceding 140.-In mathematics:One hundred [and] thirty-nine is the 34th prime number, so it is divisible only by itself and 1. It is a twin prime with 137. Because 141 is a semiprime, 139 is a Chen prime... 149149 (number)149 is the natural number between 148 and 150. It is also a prime number.-In mathematics:*149 is the 35th prime number, and with the next prime number, 151, is a twin prime, thus 149 is a Chen prime. 149 is a strong prime in the sense that it is more than the arithmetic mean of its two neighboring... 151151 (number)151 is a natural number. It follows 150 and precedes 152.-In mathematics:151 is the 36th prime number, the previous is 149, with which it comprises a twin prime. 151 is also a palindromic prime. 151 is a centered decagonal number... 157157 (number)157 is the number equal to 100 + 50 + 7, following 156 and preceding 158.-In mathematics:* 157 is a prime number. The next prime is 163 and the previous prime is 151, which with 157 form a sexy prime triplet. Taking the arithmetic mean of those primes yields 157, thus it is a balanced prime.* In... 163163 (number)163 is the natural number following 162 and preceding 164.-In mathematics:163 is a strong prime in the sense that it is greater than the arithmetic mean of its two neighboring primes... 167167 (number)167 is the natural number following 166 and preceding 168.-In mathematics:* 167 is an odd number* 167 is a Chen prime, since the next odd number, 169, is a square of a prime... 173173 (number)173 is the natural number following 172 and preceding 174.-In mathematics:* 173 is an odd number* 173 is a balanced prime* 173 is a deficient number* 173 is an Eisenstein prime with no imaginary part* 173 is an Odious number* 173 is a prime number... >- |179179 (number)179 is the natural number following 178 and preceding 180.-In mathematics:* 179 is an odd number* 179 is a deficient number, as 1 is less than 179* 179 is a Gaussian number* 179 is an odious number* 179 is a square-free number... 181181 (number)181 is the natural number between 180 and 182.-In mathematics:* 181 is an odd number* 181 is a centered number** 181 is a centered pentagonal number** 181 is a centered 12-gonal number** 181 is a centered 18-gonal number... 191191 (number)191 is the natural number following 190 and preceding 192.-In mathematics:* 191 is an odd number* 191 is a centered 19-gonal number* 191 is a deficient number, as 1 is less than 191... 193193 (number)193 is the natural number following 192 and preceding 194.-In mathematics:* 193 is an odd number* 193 is a centered 32-gonal number* 193 is a deficient number, as 1 is less than 193* 193 is a happy number* 193 is a lucky number... 197197 (number)197 is the natural number following 196 and preceding 198.-In mathematics:* 197 is an odd number* 197 is a prime number** 197 is a Chen prime** 197 is an Eisenstein prime with no imaginary part** 197 is a strong prime** 197 is a twin prime with 199... 199199 (number)199 is the natural number following 198 and preceding 200.-In mathematics:* 199 is an odd number* 199 is a centered triangular number* 199 is a centered 33-gonal number* 199 is a deficient number, as 1 is less than 199* 199 is a Lucas number... 211211 (number)211 is the natural number between 210 and 212. It is also a prime number.-In mathematics:211 is an odd number.211 is a primorial prime, sum of three consecutive primes , Chen prime, centered decagonal prime, and self prime.... 223223 (number)223 is the natural number between 222 and 224. It is also a prime number.-In mathematics:223 is a long prime, a strong prime, a lucky prime and a sexy prime .223 is the fourth Carol number and the third to be prime.... 227227 (number)227 is the natural number between 226 and 228. It is also a prime number.-In mathematics:227 is a prime number, and a twin prime with 229 . 223 plus 4 is 227, so they are cousin primes... 229229 (number)229 is the natural number between 228 and 230. It is also a prime number.The North American telephone area code 229 is assigned to the area around the city of Albany in southwestern Georgia in North America.... >- |233233 (number)233 is the natural number between 232 and 234. It is also a prime number.-In mathematics:233 is an irregular prime, a full reptend prime, a cousin prime, a Chen prime, a Fibonacci prime and a sexy prime. It is the 13th Fibonacci number. It is an Eisenstein prime of the form 3n - 1 with no... 239239 (number)239 is the natural number following 238 and preceding 240.-In mathematics:It is a prime number. The next is 241, with which it forms a pair of twin primes. 239 is a Sophie Germain prime and a Newman–Shanks–Williams prime... 241241 (number)241 is the natural number between 240 and 242. It is also a prime number.-In mathematics:241 is the larger of the twin primes . Prime twins are always of the form , with n = 1, 2, 3, ...... 251251 (number)251 is the natural number between 250 and 252. It is also a prime number.-In mathematics:251 is a regular prime, an Eisenstein prime, a Chen prime, a Gaussian prime, a Sophie Germain prime, and a sexy prime.... 257 263263 (number)263 is the natural number between 262 and 264. It is also a prime number.-In mathematics:263 is an irregular prime, an Eisenstein prime, a long prime, a Chen prime, a Gaussian prime, a happy prime, a sexy prime, a safe prime, and a Higgs prime.... 269269 (number)269 is the natural number between 268 and 270. It is also a prime number.-In mathematics:269 is a regular prime, an Eisenstein prime with no imaginary part, a long prime, a Chen prime, a Pillai prime, a Pythagorean prime, a twin prime, a sexy prime, a Higgs prime, a strong prime, and a highly... 271 277277 (number)277 is the natural number following 276 and preceding 278.-In mathematics:277 is the fifty-ninth prime number, following 271 and preceding 281... >- |283 293 307 311311 (number)311 is the natural number after 310 and before 312.-In mathematics:311 is a twin prime with 313; an Eisenstein prime with no imaginary part and real part of the form 3n - 1; a Gaussian prime with no imaginary part and real part of the form 4n - 1; and a permutable prime with 113 and 131.It can be... 313313 (number)313 is an integer following 312 and preceding 314. 313 is a:* prime number* twin prime with 311* centered square number* long prime* pythagorean prime* regular prime* palindromic prime in both decimal and binary.* truncatable prime* happy number... 317 331 337 347 >- |353353 (number)353 is the natural number between 352 and 354. It is a prime number.-In mathematics:353 is a palindromic prime, a cousin prime with 349, and a sexy prime with both 347 and 359. It is the first multidigit palindromic prime with all prime digits. Also, it is the smallest number whose 4th power is... 359359 (number)Three hundred and fifty-nine is the number directly following 358 and directly preceding 360. 359 is a prime number.-359 in mathematics:359° is one degree less than a full revolution ; this makes it a reflex angle.... 367 373 379 383 389 397 401 >- |419419 (number)419 may refer to:*419, the year 419 C.E.*419 *Advance-fee fraud, also known as the 419 scam, the Nigerian scam, and the Nigerian money transfer fraud*Area code 419, which is the area code of the northwestern corner of Ohio... 421 431 433 439 443 449 457 461 >- |467 479 487 491 499 503 509 521 523

Perfect numberPerfect numberIn number theory, a perfect number is a positive integer that is equal to the sum of its proper positive divisors, that is, the sum of its positive divisors excluding the number itself . Equivalently, a perfect number is a number that is half the sum of all of its positive divisors i.e...s

A perfect number is an integer that is the sum of its positive proper divisors (all divisors except itself).

The first 10 perfect numbers:
 1 6 2828 (number)28 is the natural number following 27 and preceding 29.-In mathematics:It is a composite number, its proper divisors being 1, 2, 4, 7, and 14.... 496496 (number)Four hundred [and] ninety-six is the natural number following four hundred [and] ninety-five and preceding four hundred [and] ninety-seven.-In mathematics:... 8 1288128 (number)8128 is the natural number following 8127 and preceding 8129.It is most notable for being a perfect number, and one of the earliest numbers to be recognized as such. As a perfect number, it is tied to the Mersenne prime 127, 27 − 1, with 26 · yielding 8128... 33 550 336 8 589 869 056 137 438 691 328 2 305 843 008 139 952 128 2 658 455 991 569 831 744 654 692 615 953 842 176 191 561 942 608 236 107 294 793 378 084 303 638 130 997 321 548 169 216

Cardinal numberCardinal numberIn mathematics, cardinal numbers, or cardinals for short, are a generalization of the natural numbers used to measure the cardinality of sets. The cardinality of a finite set is a natural number – the number of elements in the set. The transfinite cardinal numbers describe the sizes of infinite...s

In the following tables, [and] indicates that the word and is used in some dialect
Dialect
The term dialect is used in two distinct ways, even by linguists. One usage refers to a variety of a language that is a characteristic of a particular group of the language's speakers. The term is applied most often to regional speech patterns, but a dialect may also be defined by other factors,...

s (such as British English
British English
British English, or English , is the broad term used to distinguish the forms of the English language used in the United Kingdom from forms used elsewhere...

), and omitted in other dialects (such as American English
American English
American English is a set of dialects of the English language used mostly in the United States. Approximately two-thirds of the world's native speakers of English live in the United States....

).

Small numbers

This table demonstrates the standard English construction of small cardinal numbers up to one hundred million—names for which all variants of English agree.
Value Name Alternate names, and names for sets of the given size
0 Zero
Names for the number 0
There are several names for the number 0 in English, and concomitant names for the decades where the tens column contains the number 0. Several names for the number 0 include "zero", "cipher", "naught", "nought", "love", "duck", "nil", "zilch", "zip", and "o"...

aught, cipher, cypher, goose egg, love, nada, naught, nil, none, nought, nowt, null, ought, oh, squat, zed, zilch, zip
1 One ace, single, singleton, unary, unit, unity
2 Two binary, brace, couple, couplet, distich, deuce, double, doubleton, duad, duality, duet, duo, dyad, pair, span, twain, twosome, yoke
3 Three deuce-ace, leash, set, tercet, ternary, ternion, terzetto, threesome, tierce, trey, triad, trine, trinity, trio, triplet, troika, hat-trick
4 Four foursome, quadruplet, quatern, quaternary, quaternion, quaternity, quartet, tetrad
5 Five cinque, fin, fivesome, pentad, quint, quintet, quintuplet
6 Six half dozen, hexad, sestet, sextet, sextuplet, sise
7 Seven heptad, septet, septuple
8 Eight octad, octave, octet, octonary, octuplet, ogdoad
10 Ten deca, decade
11 Eleven onze, ounze, ounce
12 Twelve dozen
13 Thirteen baker's dozen, long dozen
14 Fourteen
15 Fifteen
16 Sixteen
17 Seventeen
18 Eighteen
19 Nineteen
20 Twenty score
21 Twenty-one long score
22 Twenty-two Deuce-deuce
23 Twenty-three
24 Twenty-four two dozen
25 Twenty-five
26 Twenty-six
27 Twenty-seven
28 Twenty-eight
29 Twenty-nine
30 Thirty
31 Thirty-one
40 Forty
50 Fifty half-century
60 Sixty three-score
70 Seventy three-score and ten
80 Eighty four-score
87 Eighty-seven four-score and seven
The Gettysburg Address is a speech by U.S. President Abraham Lincoln and is one of the most well-known speeches in United States history. It was delivered by Lincoln during the American Civil War, on the afternoon of Thursday, November 19, 1863, at the dedication of the Soldiers' National Cemetery...

90 Ninety
100 One hundred centred, century, ton, short hundred
101 One hundred [and] one
110 One hundred [and] ten
111 One hundred [and] eleven
120 One hundred [and] twenty long hundred, great hundred, (obsolete) hundred
121 One hundred [and] twenty-one
144 One hundred [and] forty-four gross
Gross (unit)
A gross is equal to a dozen dozen, i.e. 12 × 12 = 144.It can be used in duodecimal counting. The use of gross likely originated from the fact that 144 can be counted on the fingers using the fingertips and first two joints of each finger when marked by the thumb of one hand. The other hand...

, dozen dozen, small gross
169 One hundred [and] sixty-nine baker's gross
200 Two hundred
300 Three hundred
666 Six Hundred [and] sixty-six Number of the Beast
Number of the Beast
The Number of the Beast is a term in the Book of Revelation, of the New Testament, that is associated with the first Beast of Revelation chapter 13, the Beast of the sea. In most manuscripts of the New Testament and in English translations of the Bible, the number of the Beast is...

1 000 One thousand chiliad, grand, G, thou, yard, kilo, k
1 001 One thousand [and] one
1 010 One thousand [and] ten
1 011 One thousand [and] eleven
1 024 One thousand [and] twenty-four kibi or kilo in computing
Computing
Computing is usually defined as the activity of using and improving computer hardware and software. It is the computer-specific part of information technology...

, see binary prefix
Binary prefix
In computing, a binary prefix is a specifier or mnemonic that is prepended to the units of digital information, the bit and the byte, to indicate multiplication by a power of 2...

(kilo is shortened to K, Kibi to Ki)
1 100 One thousand one hundred Eleven hundred
1 101 One thousand one hundred [and] one
1 728 One thousand seven hundred [and] twenty-eight great gross, long gross, dozen gross
2 000 Two thousand
10 000 Ten thousand myriad
Myriad , "numberlesscountless, infinite", is a classical Greek word for the number 10,000. In modern English, the word refers to an unspecified large quantity.-History and usage:...

, wan (China)
100 000 One hundred thousand lakh
Lakh
A lakh is a unit in the Indian numbering system equal to one hundred thousand . It is widely used both in official and other contexts in Pakistan, Bangladesh, India, Maldives, Nepal, Sri Lanka, Myanmar and is often used in Indian English.-Usage:...

500 000 Five hundred thousand crore
Crore
A crore is a unit in the Indian number system equal to ten million , or 100 lakhs. It is widely used in India, Bangladesh, Nepal, and Pakistan....

(Iranian)
1 000 000 One million Mega, meg, mil, (often shortened to M)
1 048 576 One million forty-eight thousand five hundred [and] seventy-six Mibi or Mega in computing
Computing
Computing is usually defined as the activity of using and improving computer hardware and software. It is the computer-specific part of information technology...

, see binary prefix
Binary prefix
In computing, a binary prefix is a specifier or mnemonic that is prepended to the units of digital information, the bit and the byte, to indicate multiplication by a power of 2...

(Mega is shortened to M, Mibi to Mi)
10 000 000 Ten million crore
Crore
A crore is a unit in the Indian number system equal to ten million , or 100 lakhs. It is widely used in India, Bangladesh, Nepal, and Pakistan....

(Bhartia)
100 000 000 One hundred million yi (China)

English names for powers of 10

This table compares the English names of cardinal numbers according to various American, British, and Continental European conventions. See English numerals or names of large numbers
Names of large numbers
This article lists and discusses the usage and derivation of names of large numbers, together with their possible extensions.The following table lists those names of large numbers which are found in many English dictionaries and thus have a special claim to being "real words"...

Short scale
Long and short scales
The long and short scales are two of several different large-number naming systems used throughout the world for integer powers of ten. Many countries, including most in continental Europe, use the long scale whereas most English-speaking countries use the short scale...

| Long scale
Long and short scales
The long and short scales are two of several different large-number naming systems used throughout the world for integer powers of ten. Many countries, including most in continental Europe, use the long scale whereas most English-speaking countries use the short scale...

| Power
Value American British
(Nicolas Chuquet
Nicolas Chuquet
Nicolas Chuquet was a French mathematician whose great work, Triparty en la science des nombres , was unpublished in his lifetime...

)
Continental European
(Jacques Peletier du Mans
Jacques Peletier du Mans
Jacques Pelletier du Mans, also spelled Peletier, in Latin: Peletarius , was a humanist, poet and mathematician of the French Renaissance....

)
of a thousand of a million
100 One 1000−1+1 10000000
101 Ten
102 Hundred
103 Thousand 10000+1 10000000.5
106 Million 10001+1 10000001
109 Billion Thousand million Milliard 10002+1 10000001.5
1012 Trillion Billion 10003+1 10000002
1015 Quadrillion Thousand billion Billiard 10004+1 10000002.5
1018 Quintillion Trillion 10005+1 10000003
1021 Sextillion Thousand trillion Trilliard 10006+1 10000003.5
1024 Septillion Quadrillion 10007+1 10000004
1027 Octillion Thousand quadrillion Quadrilliard 10008+1 10000004.5
1030 Nonillion Quintillion 10009+1 10000005
1033 Decillion Thousand quintillion Quintilliard 100010+1 10000005.5
1036 Undecillion Sextillion 100011+1 10000006
1039 Duodecillion Thousand sextillion Sextilliard 100012+1 10000006.5
1042 Tredecillion Septillion 100013+1 10000007
1045 Quattuordecillion Thousand septillion Septilliard 100014+1 10000007.5
1048 Quindecillion Octillion 100015+1 10000008
1051 Sexdecillion Thousand octillion Octilliard 100016+1 10000008.5
1054 Septendecillion Nonillion 100017+1 10000009
1057 Octodecillion Thousand nonillion Nonilliard 100018+1 10000009.5
1060 Novemdecillion Decillion 100019+1 100000010
1063 Vigintillion Thousand decillion Decilliard 100020+1 100000010.5
1066 Unvigintillion Undecillion 100021+1 100000011
1069 Duovigintillion Thousand undecillion Undecilliard 100022+1 100000011.5
1072 Trevigintillion Duodecillion 100023+1 100000012
1075 Quattuorvigintillion ... ... 100024+1 100000012.5
... ... ... ... ...
1093 Trigintillion Thousand quindecillion Quindecilliard 100030+1 100000015.5
... ... ... ... ...
10120 Novemtrigintillion Vigintillion 100039+1 100000020
10123 Quadragintillion Thousand vigintillion Vigintilliard 100040+1 100000020.5
... ... ... ... ...
10153 Quinquagintillion Thousand quinvigintillion Quinvigintilliard 100050+1 100000025.5
... ... ... ... ...
10180 Novemquinquagintillion Trigintillion 100059+1 100000030
10183 Sexagintillion Thousand trigintillion Trigintilliard 100060+1 100000030.5
... ... ... ... ...
10213 Septuagintillion Thousand quintrigintillion Quintrigintilliard 100070+1 100000035.5
... ... ... ... ...
10240 Novemseptuagintillion Quadragintillion 100079+1 100000040
10243 Octogintillion Thousand quadragintillion Quadragintilliard 100080+1 100000040.5
... ... ... ... ...
10273 Nonagintillion Thousand quinquadragintillion Quinquadragintilliard 100090+1 100000045.5
... ... ... ... ...
10300 Novemnonagintillion Quinquagintillion 100099+1 100000050
10303 Centillion
Centillion
Centillion is a big number. It refers to different quantities based on locality of usage.- North American system :* In Canadian and U.S. usage, two centillion is 10303+10303....

Thousand quinquagintillion Quinquagintilliard 1000100+1 100000050.5
... ... ... ...
10360 Sexagintillion 1000119+1 100000060
10420 Septuagintillion 1000139+1 100000070
10480 Octogintillion 1000159+1 100000080
10540 Nonagintillion 1000179+1 100000090
10600 Centillion
Centillion
Centillion is a big number. It refers to different quantities based on locality of usage.- North American system :* In Canadian and U.S. usage, two centillion is 10303+10303....

1000199+1 1000000100
10603 Ducentillion Thousand Centillion Centilliard  1000200+1 1000000100.5

There is no consistent and widely accepted way to extend cardinals beyond centillion
Centillion
Centillion is a big number. It refers to different quantities based on locality of usage.- North American system :* In Canadian and U.S. usage, two centillion is 10303+10303....

(centilliard).

Proposed systematic names for powers of 10

Proposed by Donald E. Knuth:
Value Name Notation
100 One 1
101 Ten 10
102 Hundred 100
103 Ten hundred 1000
105 Ten myriad 10,0000
106 Hundred myriad 100,0000
107 Ten hundred myriad 1000,0000
108 Myllion 1;0000,0000
1012 Myriad myllion 1,0000;0000,0000
1016 Byllion 1:0000,0000;0000,0000
1024 Myllion byllion 1;0000,0000:0000,0000;0000,0000
1032 Tryllion 1'0000,0000;0000,0000:0000,0000;0000,0000
10128 Quintyllion
10256 Sextyllion
10512 Septyllion
101024 Octyllion
102048 Nonyllion
104096 Decyllion
108192 Undecyllion
1016,384 Duodecyllion
1032,768 Tredecyllion
1065,536 Quattuordecyllion
10131,072 Quindecyllion
10262,144 Sexdecyllion
10524,288 Septendecyllion
101,048,576 Octodecyllion
102,097,152 Novemdecyllion
104,194,304 Vigintyllion
108,388,608 Cafarolion
1016,777,216 Saralion
Quinquagintyllion
Sexagintyllion
Septuagintyllion
Octogintyllion
Nonagintyllion
Centyllion
Millyllion
Myryllion

SI-derived
Value 1000m SI prefix
SI prefix
The International System of Units specifies a set of unit prefixes known as SI prefixes or metric prefixes. An SI prefix is a name that precedes a basic unit of measure to indicate a decadic multiple or fraction of the unit. Each prefix has a unique symbol that is prepended to the unit symbol...

Name Binary prefix
Binary prefix
In computing, a binary prefix is a specifier or mnemonic that is prepended to the units of digital information, the bit and the byte, to indicate multiplication by a power of 2...

1024m=210m Value
1 000 10001 k Kilo
Kilo
Kilo- is a unit prefix in the metric system denoting multiplication of the unit by one thousand.For example:* one kilogram is 1000 grams* one kilometre is 1000 metres* one kilojoule is 1000 joules...

Ki 10241 1 024
1 000 000 10002 M Mega
Mega
Mega- is an prefix in the metric system denoting a factor of million . Confirmed in 1960, it comes from the Greek μέγας, meaning great.-Other common examples of usage:* megapixel - 1 million pixels in a digital camera...

Mi 10242 1 048 576
1 000 000 000 10003 G Giga
Giga
Giga is a unit prefix in the metric system denoting a factor of billion . It has the symbol G.Giga is derived from the Greek γίγας, meaning 'giant'...

Gi 10243 1 073 741 824
1 000 000 000 000 10004 T Tera
Tera
Tera- is a prefix in the metric system denoting 1012 or .The prefix tera was was confirmed in 1960. In computer science tera can sometimes mean instead of , especially in the term terabyte. To avoid this ambiguity, the binary prefix tebi has been introduced to signify 240....

Ti 10244 1 099 511 627 776
1 000 000 000 000 000 10005 P Peta
Peta
Peta can refer to:* peta-, an SI prefix denoting a factor of 1015* Peta, Greece, a town in Greece* Peta, the Pāli word for a Preta, or hungry ghost in Buddhism* Peta Wilson, an Australian actress and model* Peta Todd, English glamour model...

Pi 10245 1 125 899 906 842 624
1 000 000 000 000 000 000 10006 E Exa
Exa
Exa- is a prefix in the metric system denoting 1018 or .Adopted in 1975, it comes from the Greek ἕξ, used as a prefix ἑξά-, meaning six , because it is equal to 10006.Examples:* 1 EeV = 1018 electronvolts = 0.1602 joule...

Ei 10246 1 152 921 504 606 846 976
1 000 000 000 000 000 000 000 10007 Z Zetta
Zetta
Zetta- is a prefix in the metric system denoting a factor of 1021 or .Added to the SI in 1991, it is evocative of the French numeral sept, meaning seven, because it is equal to 10007....

Zi 10247 1 180 591 620 717 411 303 424
1 000 000 000 000 000 000 000 000 10008 Y Yotta
Yotta
Yotta is the largest unit prefix in the International System of Units denoting a factor of 1024 or . It has the unit symbol Y.The prefix name is derived from the Greek , meaning eight, because it is equal to 10008...

Yi 10248 1 208 925 819 614 629 174 706 176

FractionalFraction (mathematics)A fraction represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, we specify how many parts of a certain size there are, for example, one-half, five-eighths and three-quarters.A common or "vulgar" fraction, such as 1/2, 5/8, 3/4, etc., consists... numbers

This is a table of English names for positive rational number
Rational number
In mathematics, a rational number is any number that can be expressed as the quotient or fraction a/b of two integers, with the denominator b not equal to zero. Since b may be equal to 1, every integer is a rational number...

s less than or equal to 1. It also lists alternative names, but there is no widespread convention for the names of extremely small positive numbers.

Keep in mind that rational numbers like 0.12 can be represented in infinitely many ways, e.g. zero-point-one-two (0.12), twelve percent (12%), three twenty-fifths , nine seventy-fifths , six fiftieths , twelve hundredths , twenty-four two-hundredths , etc.
Value Fraction Common names Alternative names
1 One 0.999...
0.999...
In mathematics, the repeating decimal 0.999... denotes a real number that can be shown to be the number one. In other words, the symbols 0.999... and 1 represent the same number...

0.9 Nine tenths, [zero] point nine
0.8 Four fifths, eight tenths, [zero] point eight
0.7 Seven tenths, [zero] point seven
0.6 Three fifths, six tenths, [zero] point six
0.5 One half, five tenths, [zero] point five
0.4 Two fifths, four tenths, [zero] point four
0.3 (333 333)... One third
0.3 Three tenths, [zero] point three
0.25 One quarter, one fourth, twenty-five hundredths, [zero] point two five
0.2 One fifth, two tenths, [zero] point two
0.16 (666 666)... One sixth
0.142 857 (142 857)... One seventh
0.125 One eighth, one-hundred-[and-]twenty-five thousandths, [zero] point one two five
0.1 (111 111)... One ninth
0.1 One tenth, [zero] point one One perdecime, one perdime
0.090 (909 090)... One eleventh
0.09 Nine hundredths, [zero] point zero nine
0.083 (333 333)... One twelfth
0.08 Two twenty-fifths, eight hundredths, [zero] point zero eight
0.0625 One sixteenth, six-hundred-[and-]twenty-five ten-thousandths, [zero] point zero six two five
0.05 One twentieth, [zero] point zero five
0.047 619 (047 619)... One twenty-first
0.045 (454 545)... One twenty-second
0.043 478 260 869 565 217 3913 (043 478)... One twenty-third
0.03 (333 333)... One thirtieth
0.016 (666 666)... One sixtieth One minute
Minute
A minute is a unit of measurement of time or of angle. The minute is a unit of time equal to 1/60th of an hour or 60 seconds. In the UTC time scale, a minute on rare occasions has 59 or 61 seconds; see leap second. The minute is not an SI unit; however, it is accepted for use with SI units...

0.012345679 (012345679)... One eighty-first
0.01 One hundredth, [zero] point zero one One percent
0.001 One thousandth, [zero] point zero zero one One permille
Permille
A per mil or per mille is a tenth of a percent or one part per thousand. It is written with the sign ‰ , which looks like a percent sign with an extra zero at the end...

0.000 27 (777 777)... One thirty-six hundredth One second
0.000 1 One ten-thousandth, [zero] point zero zero zero one One myriadth, one permyria, one permyriad, one basis point
Basis point
A basis point is a unit equal to 1/100 of a percentage point or one part per ten thousand...

0.000 01 One hundred-thousandth One lakhth, one perlakh
0.000 001 One millionth One perion, one ppm
0.000 000 1 One ten-millionth One crorth, one percrore
0.000 000 01 One hundred-millionth One awkth, one perawk
0.000 000 001 One billionth (in some dialects) One ppb
PPB
PPB can stand for:* Party political broadcast, a type of political programming in the United Kingdom* parts-per-billion, a unit of concentration* Portland Police Bureau, a police agency for the city of Portland...

0 Zero

Algebraic numberAlgebraic numberIn mathematics, an algebraic number is a number that is a root of a non-zero polynomial in one variable with rational coefficients. Numbers such as π that are not algebraic are said to be transcendental; almost all real numbers are transcendental...s

Expression Approximate value Notes
0.433 012 701 892 219 323 381 861 585 376 Area of a triangle with sides of length one and half its height.
0.618 033 988 749 894 848 204 586 834 366 Golden ratio conjugate , reciprocal
Multiplicative inverse
In mathematics, a multiplicative inverse or reciprocal for a number x, denoted by 1/x or x−1, is a number which when multiplied by x yields the multiplicative identity, 1. The multiplicative inverse of a fraction a/b is b/a. For the multiplicative inverse of a real number, divide 1 by the...

of and one less than the golden ratio
Golden ratio
In mathematics and the arts, two quantities are in the golden ratio if the ratio of the sum of the quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller one. The golden ratio is an irrational mathematical constant, approximately 1.61803398874989...

.
1.059 463 094 359 295 264 561 825 294 946 Twelfth root of two.
Proportion between the frequencies of adjacent semitone
Semitone
A semitone, also called a half step or a half tone, is the smallest musical interval commonly used in Western tonal music, and it is considered the most dissonant when sounded harmonically....

s in the equal temperament
Equal temperament
An equal temperament is a musical temperament, or a system of tuning, in which every pair of adjacent notes has an identical frequency ratio. As pitch is perceived roughly as the logarithm of frequency, this means that the perceived "distance" from every note to its nearest neighbor is the same for...

scale.
1.060 660 171 779 821 286 601 266 543 157 The size of the cube that satisfies Prince Rupert's cube
Prince Rupert's cube
In geometry, Prince Rupert's cube is the largest cube that can pass through a hole drilled through a unit cube, i.e. through a cube whose sides have length 1. Curiously, it is slightly larger than the unit cube, with a side length of...

.
1.259 921 049 894 873 164 767 210 607 278 Cube root of two.
Length of the edge of a cube
Cube
In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex. The cube can also be called a regular hexahedron and is one of the five Platonic solids. It is a special kind of square prism, of rectangular parallelepiped and...

with volume two. See doubling the cube
Doubling the cube
Doubling the cube is one of the three most famous geometric problems unsolvable by compass and straightedge construction...

for the significance of this number.
n/a 1.303 577 269 034 296 391 257 099 112 153 Conway's constant, defined as the unique positive real root of a certain polynomial of degree 71.

1.324 717 957 244 746 025 960 908 854 478 Plastic number
Plastic number
In mathematics, the plastic number ρ is a mathematical constant which is the unique real solution of the cubic equationx^3=x+1\, ....

, the unique real root of the cubic equation
1.414 213 562 373 095 048 801 688 724 210
Square root of two a.k.a. Pythagoras' constant.
Ratio of diagonal
Diagonal
A diagonal is a line joining two nonconsecutive vertices of a polygon or polyhedron. Informally, any sloping line is called diagonal. The word "diagonal" derives from the Greek διαγώνιος , from dia- and gonia ; it was used by both Strabo and Euclid to refer to a line connecting two vertices of a...

to side length in a square
Square (geometry)
In geometry, a square is a regular quadrilateral. This means that it has four equal sides and four equal angles...

.
Proportion between the sides of paper size
Paper size
Many paper size standards conventions have existed at different times and in different countries. Today there is one widespread international ISO standard and a localised standard used in North America . The paper sizes affect writing paper, stationery, cards, and some printed documents...

s in the ISO 216
ISO 216
ISO 216 specifies international standard paper sizes used in most countries in the world today. It defines the "A" and "B" series of paper sizes, including A4, the most commonly available size...

series (originally DIN
Din
DIN or Din or din can have several meanings:* A din is a loud noise.* Dīn, an Arabic term meaning "religion" or "way of life".* Din is one of the ten aspects of the Ein Sof in Kabbalah ....

476 series).
1.561 552 812 808 830 274 910 704 927 987 The Triangular root of 2.
1.618 033 988 749 894 848 204 586 834 366 Golden ratio
Golden ratio
In mathematics and the arts, two quantities are in the golden ratio if the ratio of the sum of the quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller one. The golden ratio is an irrational mathematical constant, approximately 1.61803398874989...

, the larger of the two real roots of
1.732 050 807 568 877 293 527 446 341 506
Square root of three a.k.a. the measure of the fish
Vesica piscis
The vesica piscis is a shape that is the intersection of two circles with the same radius, intersecting in such a way that the center of each circle lies on the circumference of the other. The name literally means the "bladder of a fish" in Latin...

.
Length of the space diagonal
Space diagonal
In a rectangular box or a magic cube, the four space diagonals are the lines that go from a corner of the box or cube, through the center of the box or cube, to the opposite corner...

of a cube
Cube
In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex. The cube can also be called a regular hexahedron and is one of the five Platonic solids. It is a special kind of square prism, of rectangular parallelepiped and...

with edge length 1.
Length of the diagonal of a rectangle
Rectangle
In Euclidean plane geometry, a rectangle is any quadrilateral with four right angles. The term "oblong" is occasionally used to refer to a non-square rectangle...

.
Altitude
Altitude (triangle)
In geometry, an altitude of a triangle is a straight line through a vertex and perpendicular to a line containing the base . This line containing the opposite side is called the extended base of the altitude. The intersection between the extended base and the altitude is called the foot of the...

of an equilateral triangle with side length 2.
Twice the altitude of an equilateral triangle with side length 1.
Altitude of a regular hexagon with side length 1 and diagonal length 2.
1.839 286 755 214 161 132 551 852 564 653 The Tribonacci constant.
Used in the formula for the volume of the snub cube
Snub cube
In geometry, the snub cube, or snub cuboctahedron, is an Archimedean solid.The snub cube has 38 faces, 6 of which are squares and the other 32 are equilateral triangles. It has 60 edges and 24 vertices. It is a chiral polyhedron, that is, it has two distinct forms, which are mirror images of each...

and properties of some of it's dual polyhedron
Dual polyhedron
In geometry, polyhedra are associated into pairs called duals, where the vertices of one correspond to the faces of the other. The dual of the dual is the original polyhedron. The dual of a polyhedron with equivalent vertices is one with equivalent faces, and of one with equivalent edges is another...

s.
It satisfies the equation x + x−3 = 2.
2.236 067 977 499 789 696 409 173 668 731 Square root of five.
Length of the diagonal
Diagonal
A diagonal is a line joining two nonconsecutive vertices of a polygon or polyhedron. Informally, any sloping line is called diagonal. The word "diagonal" derives from the Greek διαγώνιος , from dia- and gonia ; it was used by both Strabo and Euclid to refer to a line connecting two vertices of a...

of a rectangle
Rectangle
In Euclidean plane geometry, a rectangle is any quadrilateral with four right angles. The term "oblong" is occasionally used to refer to a non-square rectangle...

.
Length of the diagonal of a rectangle.
Length of the space diagonal of a rectangular box
Cuboid
In geometry, a cuboid is a solid figure bounded by six faces, forming a convex polyhedron. There are two competing definitions of a cuboid in mathematical literature...

.
2.414 213 562 373 095 048 801 688 724 210 Silver ratio
Silver ratio
In mathematics, two quantities are in the silver ratio if the ratio between the sum of the smaller plus twice the larger of those quantities and the larger one is the same as the ratio between the larger one and the smaller. This defines the silver ratio as an irrational mathematical constant,...

, the larger of the two real roots of
2.449 489 742 783 178 098 197 284 074 706 = area
Area
Area is a quantity that expresses the extent of a two-dimensional surface or shape in the plane. Area can be understood as the amount of material with a given thickness that would be necessary to fashion a model of the shape, or the amount of paint necessary to cover the surface with a single coat...

of a rectangle.
Length of the space diagonal
Space diagonal
In a rectangular box or a magic cube, the four space diagonals are the lines that go from a corner of the box or cube, through the center of the box or cube, to the opposite corner...

of a rectangular box
Cuboid
In geometry, a cuboid is a solid figure bounded by six faces, forming a convex polyhedron. There are two competing definitions of a cuboid in mathematical literature...

.
Length of the diagonal of a rectangle
Rectangle
In Euclidean plane geometry, a rectangle is any quadrilateral with four right angles. The term "oblong" is occasionally used to refer to a non-square rectangle...

.
Length of the diagonal of a rectangle.
Length of the diagonal
Diagonal
A diagonal is a line joining two nonconsecutive vertices of a polygon or polyhedron. Informally, any sloping line is called diagonal. The word "diagonal" derives from the Greek διαγώνιος , from dia- and gonia ; it was used by both Strabo and Euclid to refer to a line connecting two vertices of a...

of a square
Square (geometry)
In geometry, a square is a regular quadrilateral. This means that it has four equal sides and four equal angles...

with side length .
2.645 751 311 064 590 590 501 615 753 639 Length of the space diagonal
Space diagonal
In a rectangular box or a magic cube, the four space diagonals are the lines that go from a corner of the box or cube, through the center of the box or cube, to the opposite corner...

of a rectangular box
Cuboid
In geometry, a cuboid is a solid figure bounded by six faces, forming a convex polyhedron. There are two competing definitions of a cuboid in mathematical literature...

.
Length of the diagonal of a rectangle
Rectangle
In Euclidean plane geometry, a rectangle is any quadrilateral with four right angles. The term "oblong" is occasionally used to refer to a non-square rectangle...

.
Length of the diagonal of a rectangle.
Length of the diagonal of a rectangle.
2.828 427 124 746 190 097 603 377 448 419
Volume
Volume
Volume is the quantity of three-dimensional space enclosed by some closed boundary, for example, the space that a substance or shape occupies or contains....

of a cube
Cube
In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex. The cube can also be called a regular hexahedron and is one of the five Platonic solids. It is a special kind of square prism, of rectangular parallelepiped and...

with edge length .
Length of the diagonal
Diagonal
A diagonal is a line joining two nonconsecutive vertices of a polygon or polyhedron. Informally, any sloping line is called diagonal. The word "diagonal" derives from the Greek διαγώνιος , from dia- and gonia ; it was used by both Strabo and Euclid to refer to a line connecting two vertices of a...

of a square
Square (geometry)
In geometry, a square is a regular quadrilateral. This means that it has four equal sides and four equal angles...

with side length 2.
Length of the diagonal of a rectangle.
Length of the diagonal of a rectangle.
Length of the diagonal of a rectangle.
3.162 277 660 168 379 331 998 893 544 433 = area
Area
Area is a quantity that expresses the extent of a two-dimensional surface or shape in the plane. Area can be understood as the amount of material with a given thickness that would be necessary to fashion a model of the shape, or the amount of paint necessary to cover the surface with a single coat...

of a rectangle.
Length of the diagonal
Diagonal
A diagonal is a line joining two nonconsecutive vertices of a polygon or polyhedron. Informally, any sloping line is called diagonal. The word "diagonal" derives from the Greek διαγώνιος , from dia- and gonia ; it was used by both Strabo and Euclid to refer to a line connecting two vertices of a...

of a rectangle
Rectangle
In Euclidean plane geometry, a rectangle is any quadrilateral with four right angles. The term "oblong" is occasionally used to refer to a non-square rectangle...

.
Length of the diagonal of a rectangle.
Length of the diagonal of a rectangle.
Length of the diagonal
Diagonal
A diagonal is a line joining two nonconsecutive vertices of a polygon or polyhedron. Informally, any sloping line is called diagonal. The word "diagonal" derives from the Greek διαγώνιος , from dia- and gonia ; it was used by both Strabo and Euclid to refer to a line connecting two vertices of a...

of a square
Square (geometry)
In geometry, a square is a regular quadrilateral. This means that it has four equal sides and four equal angles...

with side length .
3.316 624 790 355 399 849 114 932 736 671 Length of the space diagonal
Space diagonal
In a rectangular box or a magic cube, the four space diagonals are the lines that go from a corner of the box or cube, through the center of the box or cube, to the opposite corner...

of a rectangular box
Cuboid
In geometry, a cuboid is a solid figure bounded by six faces, forming a convex polyhedron. There are two competing definitions of a cuboid in mathematical literature...

.
Length of the diagonal of a rectangle
Rectangle
In Euclidean plane geometry, a rectangle is any quadrilateral with four right angles. The term "oblong" is occasionally used to refer to a non-square rectangle...

.
Length of the diagonal of a rectangle.
Length of the diagonal of a rectangle.
Length of the diagonal of a rectangle.
Length of the diagonal of a rectangle.
3.464 101 615 137 754 587 054 892 683 012
Length of the space diagonal
Space diagonal
In a rectangular box or a magic cube, the four space diagonals are the lines that go from a corner of the box or cube, through the center of the box or cube, to the opposite corner...

of a cube
Cube
In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex. The cube can also be called a regular hexahedron and is one of the five Platonic solids. It is a special kind of square prism, of rectangular parallelepiped and...

with edge length 2.
Length of the diagonal of a rectangle
Rectangle
In Euclidean plane geometry, a rectangle is any quadrilateral with four right angles. The term "oblong" is occasionally used to refer to a non-square rectangle...

.
Length of the diagonal of a rectangle.
Length of the diagonal of a rectangle.
Length of the diagonal of a rectangle.
Length of the diagonal of a rectangle.
Length of the diagonal
Diagonal
A diagonal is a line joining two nonconsecutive vertices of a polygon or polyhedron. Informally, any sloping line is called diagonal. The word "diagonal" derives from the Greek διαγώνιος , from dia- and gonia ; it was used by both Strabo and Euclid to refer to a line connecting two vertices of a...

of a square
Square (geometry)
In geometry, a square is a regular quadrilateral. This means that it has four equal sides and four equal angles...

with side length .

Transcendental numberTranscendental numberIn mathematics, a transcendental number is a number that is not algebraic—that is, it is not a root of a non-constant polynomial equation with rational coefficients. The most prominent examples of transcendental numbers are π and e...s

• (−1)i
Imaginary unit
In mathematics, the imaginary unit allows the real number system ℝ to be extended to the complex number system ℂ, which in turn provides at least one root for every polynomial . The imaginary unit is denoted by , , or the Greek...

= e−π = 0.0432139183...
• Liouville constant: c = 0.110001000000000000000001000...
• Champernowne constant
Champernowne constant
In mathematics, the Champernowne constant C10 is a transcendental real constant whose decimal expansion has important properties. It is named after mathematician D. G...

: C10 = 0.12345678910111213141516...
• ii = √(e−π) = 0.207879576...
• Copeland–Erdős constant: 0.235711131719232931374143...
• The logarithm
Logarithm
The logarithm of a number is the exponent by which another fixed value, the base, has to be raised to produce that number. For example, the logarithm of 1000 to base 10 is 3, because 1000 is 10 to the power 3: More generally, if x = by, then y is the logarithm of x to base b, and is written...

of 2 to base 10, used to find the number of digits in a power of 2: 0.301029995663981...
• The inverse of π: 0.318309886183790671537767526745028724068919291480...
• The inverse of e: 0.367879441171442321595523770161460867445811131031...
• Prouhet–Thue–Morse constant: τ = 0.412454033640...
• Omega constant: Ω = 0.5671432904097838729999686622...
• Cahen's constant: c = 0.64341054629...
• ln 2: 0.693147180559945309417232121458...
• π/√18 = 0.7404... the maximum density of sphere packing in three dimensional Euclidean space according to the Kepler conjecture
Kepler conjecture
The Kepler conjecture, named after the 17th-century German astronomer Johannes Kepler, is a mathematical conjecture about sphere packing in three-dimensional Euclidean space. It says that no arrangement of equally sized spheres filling space has a greater average density than that of the cubic...

• Gauss's constant
Gauss's constant
In mathematics, Gauss's constant, denoted by G, is defined as the reciprocal of the arithmetic-geometric mean of 1 and the square root of 2:The constant is named after Carl Friedrich Gauss, who on May 30, 1799 discovered thatso that...

: G = 0.8346268...
• π/√12 = 0.9086..., the fraction of the plane covered in circle packing
• ei+e-i = 2cos(1)
Cosine similarity
Cosine similarity is a measure of similarity between two vectors by measuring the cosine of the angle between them. The cosine of 0 is 1, and less than 1 for any other angle. The cosine of the angle between two vectors thus determines whether two vectors are pointing in roughly the same...

= 1.08060461...
• π4/90 = ζ(4) = 1.082323...
• Khinchin–Lévy constant: 1.1865691104...http://mathworld.wolfram.com/Khinchin-LevyConstant.html
• √2s: 1.559610469...
• Favard constant: K1 = 1.57079633...
• log2 3: 1.584962501..., in fact, the logarithm of any positive integer to any integer base greater than one is either rational or transcendental.
• √2√2: 1.6325269...
• Komornik–Loreti constant: q = 1.787231650...
• Universal parabolic constant
Universal parabolic constant
The universal parabolic constant is a mathematical constant.It is defined as the ratio, for any parabola, of the arc length of the parabolic segment formed by the latus rectum to the focal parameter...

: P2 = 2.29558714939...
• Gelfond–Schneider constant: 2.665144143...
• Euler's number: e = 2.718281828459045235360287471353...
• Pi
Pi
' is a mathematical constant that is the ratio of any circle's circumference to its diameter. is approximately equal to 3.14. Many formulae in mathematics, science, and engineering involve , which makes it one of the most important mathematical constants...

: π = 3.141592653589793238462643383279...
• Van der Pauw's constant: pi/ln(2) = 4.53236014182719380962...
• i√i
Imaginary unit
In mathematics, the imaginary unit allows the real number system ℝ to be extended to the complex number system ℂ, which in turn provides at least one root for every polynomial . The imaginary unit is denoted by , , or the Greek...

: 4.81047738..., √eπ
Gelfond's constant
In mathematics, Gelfond's constant, named after Aleksandr Gelfond, is eπ, that is, e to the power of π. Like both e and π, this constant is a transcendental number. This can be proven by the Gelfond–Schneider theorem and noting the fact that...

• Tau
Tau
Tau is the 19th letter of the Greek alphabet. In the system of Greek numerals it has a value of 300.The name in English is pronounced , but in modern Greek it is...

, or 2π: τ = 6.283185307179586..., The ratio of the circumference
Circumference
The circumference is the distance around a closed curve. Circumference is a special perimeter.-Circumference of a circle:The circumference of a circle is the length around it....

In classical geometry, a radius of a circle or sphere is any line segment from its center to its perimeter. By extension, the radius of a circle or sphere is the length of any such segment, which is half the diameter. If the object does not have an obvious center, the term may refer to its...

, and the number of radians in a complete circle
• Gelfond's constant
Gelfond's constant
In mathematics, Gelfond's constant, named after Aleksandr Gelfond, is eπ, that is, e to the power of π. Like both e and π, this constant is a transcendental number. This can be proven by the Gelfond–Schneider theorem and noting the fact that...

: 23.14069263277925...
• Ramanujan's constant: e(π√163) = 262537412640768743.99999999999925...

Suspected transcendentals

• -2W (½) = -0.703467422498391652049818601859902130..., the real solution to exp(x) = x2.
• Z(1)
Riemann–Siegel formula
In mathematics, the Riemann–Siegel formula is an asymptotic formula for the error of the approximate functional equation of the Riemann zeta function, an approximation of the zeta function by a sum of two finite Dirichlet series. It was found by in unpublished manuscripts of Bernhard Riemann...

: -0.736305462867317734677899828925614672...
• Heath-Brown–Moroz constant: C = 0.001317641...
• Kepler–Bouwkamp constant: 0.1149420448...
• MRB constant
MRB constant
The MRB constant, named after Marvin Ray Burns, is a mathematical constant for which no closed-form expression is known. It is not known whether the MRB constant is algebraic, transcendental, or even irrational....

: 0.187859...
• Meissel–Mertens constant: M = 0.2614972128476427837554268386086958590516...
• Bernstein's constant
Bernstein's constant
Bernstein's constant, usually denoted by the Greek letter β , is a mathematical constant named after Sergei Natanovich Bernstein and is approximately equal to 0.2801694990.- Definition :...

: β = 0.2801694990...
• Strongly carefree constant: 0.286747...
• Gauss–Kuzmin–Wirsing constant: λ1 = 0.3036630029...http://mathworld.wolfram.com/Gauss-Kuzmin-WirsingConstant.html
• Hafner–Sarnak–McCurley constant: 0.3532363719...
• Artin's constant
Artin's conjecture on primitive roots
In number theory, Artin's conjecture on primitive roots states that a given integer a which is not a perfect square and not −1 is a primitive root modulo infinitely many primes p. The conjecture also ascribes an asymptotic density to these primes...

: 0.3739558136...
• Prime constant
Prime constant
The prime constant is the real number \rho whose nth binary digit is 1 if n is prime and 0 if n is composite or 1.In other words, \rho is simply the number whose binary expansion corresponds to the indicator function of the set of prime numbers...

: ρ = 0.414682509851111660248109622...
• Carefree constant: 0.428249...
• The Logarithm
Logarithm
The logarithm of a number is the exponent by which another fixed value, the base, has to be raised to produce that number. For example, the logarithm of 1000 to base 10 is 3, because 1000 is 10 to the power 3: More generally, if x = by, then y is the logarithm of x to base b, and is written...

of e to base 10: 0.434294481903251827651128918916605082294397005803...
• S(1)
Fresnel integral
250px|thumb|S and C The maximum of C is about 0.977451424. If πt²/2 were used instead of t², then the image would be scaled vertically and horizontally ....

: 0.438259147390354766076756696625152...
• F(1): 0.538079506912768419136387420407556...
• Stephens' constant: 0.575959...
• Euler–Mascheroni constant
Euler–Mascheroni constant
The Euler–Mascheroni constant is a mathematical constant recurring in analysis and number theory, usually denoted by the lowercase Greek letter ....

: γ = 0.577215664901532860606512090082...
• Golomb–Dickman constant: λ = 0.62432998854355087099293638310083724...
• Twin prime constant: C2 = 0.660161815846869573927812110014...
• Feller-Tornier constant: 0.661317...
• Laplace limit
Laplace limit
In mathematics, the Laplace limit is the maximum value of the eccentricity for which the series solution to Kepler's equation converges. It is approximately...

: ε = 0.6627434193...http://mathworld.wolfram.com/LaplaceLimit.html
• Taniguchi's constant: 0.678234...
• Continued Fraction Constant: C = 0.697774657964007982006790592551...
• Embree–Trefethen constant: β* = 0.70258...
• Sarnak's constant: 0.723648...
• Landau–Ramanujan constant: 0.76422365358922066299069873125...
• C(1)
Fresnel integral
250px|thumb|S and C The maximum of C is about 0.977451424. If πt²/2 were used instead of t², then the image would be scaled vertically and horizontally ....

: 0.77989340037682282947420641365...
• ζ(3)−1 = 0.831907..., the probability that three random numbers have no common factor.
• Brun's constant for prime quadruplets: B2 = 0.8705883800...
• Quadratic class number constant: 0.881513...
• Catalan's constant: G = 0.915965594177219015054603514932384110774...
• Viswanath's constant: σ(1) = 1.13198824...
• ζ(3) = 1.202056903159594285399738161511449990764986292..., also known as Apéry's constant
Apéry's constant
In mathematics, Apéry's constant is a number that occurs in a variety of situations. It arises naturally in a number of physical problems, including in the second- and third-order terms of the electron's gyromagnetic ratio using quantum electrodynamics...

, known to be irrational, but not known whether or not it is transcendental
Transcendental function
A transcendental function is a function that does not satisfy a polynomial equation whose coefficients are themselves polynomials, in contrast to an algebraic function, which does satisfy such an equation...

.
• Vardi's constant: E = 1.264084735305...
• Glaisher–Kinkelin constant: A = 1.28242712...
• Mills' constant: A = 1.30637788386308069046...
• Totient summatory constant: 1.339784...
• Ramanujan–Soldner constant: μ = 1.451369234883381050283968485892027449493…
• Backhouse's constant
Backhouse's constant
Backhouse's constant is a mathematical constant founded by N. Backhouse and is approximately 1.456 074 948.It is defined by using the power series such that the coefficients of successive terms are the prime numbers:and whereThen:...

: 1.456074948...
• Lieb's square ice constant
Lieb's square ice constant
Lieb's square ice constant is a mathematical constant used in the field of combinatorics. It was introduced by Elliott H. Lieb in 1967.-Definition:...

: 1.5396007...
• Erdős–Borwein constant: E = 1.606695152415291763...
• Somos' quadratic recurrence constant: σ = 1.661687949633594121296...
• Niven's constant
Niven's constant
In number theory, Niven's constant, named after Ivan Niven, is the largest exponent appearing in the prime factorization of any natural number n "on average"...

: c = 1.705211...
• Brun's constant: B2 = 1.902160583104...
• Landau's totient constant: 1.943596...
• exp(-W 0(-ln(3))) = 2.47805268028830..., the smaller solution to 3x = x3 and what, when put to the root of itself, is equal to 3 put to the root of itself.
• Second Feigenbaum constant: α = 2.5029...
• Sierpiński's constant: K = 2.5849817595792532170658936...
• Barban's constant: 2.596536...
• Khinchin's constant: K0 = 2.685452001...http://mathworld.wolfram.com/KhinchinsConstant.html
• Fransén–Robinson constant: F = 2.8077702420...
• Murata's constant: 2.826419...
• Lévy's constant
Lévy's constant
In mathematics Lévy's constant occurs in an expression for the asymptotic behaviour of the denominators of the convergents of continued fractions....

: γ = 3.275822918721811159787681882...
• Reciprocal Fibonacci constant: ψ = 3.359885666243177553172011302918927179688905133731...
• First Feigenbaum constant: δ = 4.6692...

Numbers not known with high precision

• Landau's constant
Landau's constants
In complex analysis, a branch of mathematics, Landau's constants are certain mathematical constants that describe the behaviour of holomorphic functions defined on the unit disk...

: 0.4330 < B < 0.472
• Bloch's constant: 0.4332 < B < 0.4719
• Landau's constant
Landau's constants
In complex analysis, a branch of mathematics, Landau's constants are certain mathematical constants that describe the behaviour of holomorphic functions defined on the unit disk...

: 0.5 < L < 0.544
• Landau's constant
Landau's constants
In complex analysis, a branch of mathematics, Landau's constants are certain mathematical constants that describe the behaviour of holomorphic functions defined on the unit disk...

: 0.5 < A < 0.7853
• Grothendieck constant: 1.67 < k < 1.79

Algebraic complex numberComplex numberA complex number is a number consisting of a real part and an imaginary part. Complex numbers extend the idea of the one-dimensional number line to the two-dimensional complex plane by using the number line for the real part and adding a vertical axis to plot the imaginary part...s

• Imaginary unit
Imaginary unit
In mathematics, the imaginary unit allows the real number system ℝ to be extended to the complex number system ℂ, which in turn provides at least one root for every polynomial . The imaginary unit is denoted by , , or the Greek...

:
• nth roots of unity:

Other hypercomplex numbers

• The quaternion
Quaternion
In mathematics, the quaternions are a number system that extends the complex numbers. They were first described by Irish mathematician Sir William Rowan Hamilton in 1843 and applied to mechanics in three-dimensional space...

s
• The octonion
Octonion
In mathematics, the octonions are a normed division algebra over the real numbers, usually represented by the capital letter O, using boldface O or blackboard bold \mathbb O. There are only four such algebras, the other three being the real numbers R, the complex numbers C, and the quaternions H...

s
• The sedenion
Sedenion
In abstract algebra, sedenions form a 16-dimensional non-associative algebra over the reals obtained by applying the Cayley–Dickson construction to the octonions...

s
• The dual number
Dual number
In linear algebra, the dual numbers extend the real numbers by adjoining one new element ε with the property ε2 = 0 . The collection of dual numbers forms a particular two-dimensional commutative unital associative algebra over the real numbers. Every dual number has the form z = a + bε with a and...

s (with an infinitesimal
Infinitesimal
Infinitesimals have been used to express the idea of objects so small that there is no way to see them or to measure them. The word infinitesimal comes from a 17th century Modern Latin coinage infinitesimus, which originally referred to the "infinite-th" item in a series.In common speech, an...

)

Transfinite numberTransfinite numberTransfinite numbers are numbers that are "infinite" in the sense that they are larger than all finite numbers, yet not necessarily absolutely infinite. The term transfinite was coined by Georg Cantor, who wished to avoid some of the implications of the word infinite in connection with these...s

• Infinity
Infinity
Infinity is a concept in many fields, most predominantly mathematics and physics, that refers to a quantity without bound or end. People have developed various ideas throughout history about the nature of infinity...

in general:
• Aleph-null:
• Aleph-one:
• Beth-one: () is the cardinality of the continuum
Cardinality of the continuum
In set theory, the cardinality of the continuum is the cardinality or “size” of the set of real numbers \mathbb R, sometimes called the continuum. It is an infinite cardinal number and is denoted by |\mathbb R| or \mathfrak c ....

:

Numbers representing measured quantities

• Pair: 2 (the base of the binary numeral system
Binary numeral system
The binary numeral system, or base-2 number system, represents numeric values using two symbols, 0 and 1. More specifically, the usual base-2 system is a positional notation with a radix of 2...

)
• Dozen
Dozen
A dozen is a grouping of approximately twelve. The dozen may be one of the earliest primitive groupings, perhaps because there are approximately a dozen cycles of the moon or months in a cycle of the sun or year...

: 12 (the base of the duodecimal
Duodecimal
The duodecimal system is a positional notation numeral system using twelve as its base. In this system, the number ten may be written as 'A', 'T' or 'X', and the number eleven as 'B' or 'E'...

numeral system)
• Baker's dozen: 13
• Score
20 (number)
20 is the natural number following 19 and preceding 21. A group of twenty units may also be referred to as a score.-In mathematics:*20 is the basis for vigesimal number systems....

: 20 (the base of the vigesimal
Vigesimal
The vigesimal or base 20 numeral system is based on twenty .- Places :...

numeral system)
• Gross
Gross (unit)
A gross is equal to a dozen dozen, i.e. 12 × 12 = 144.It can be used in duodecimal counting. The use of gross likely originated from the fact that 144 can be counted on the fingers using the fingertips and first two joints of each finger when marked by the thumb of one hand. The other hand...

: 144 (= 122)
• Great gross: 1728 (= 123)

Numbers representing scientific quantities

• Avogadro constant: N = 6.0221417930... mol−1
• Electronvolt
Electronvolt
In physics, the electron volt is a unit of energy equal to approximately joule . By definition, it is equal to the amount of kinetic energy gained by a single unbound electron when it accelerates through an electric potential difference of one volt...

: eV = 1.60217648740... J
• Electron relative atomic mass: A(e) = 0.0005485799094323...
• Fine structure constant: α = 0.007297352537650...
• Molar mass constant
Molar mass constant
The molar mass constant, symbol Mu, is a physical constant which relates atomic weight and molar mass. Its value is defined to be 1 g/mol in SI units....

: M = 0.001 kg/mol
• Planck constant
Planck constant
The Planck constant , also called Planck's constant, is a physical constant reflecting the sizes of energy quanta in quantum mechanics. It is named after Max Planck, one of the founders of quantum theory, who discovered it in 1899...

: h = 6.6260689633... Js
• Rydberg constant
Rydberg constant
The Rydberg constant, symbol R∞, named after the Swedish physicist Johannes Rydberg, is a physical constant relating to atomic spectra in the science of spectroscopy. Rydberg initially determined its value empirically from spectroscopy, but Niels Bohr later showed that its value could be calculated...

: R = 10973731.56852773... m−1
• Speed of light in vacuum
Speed of light
The speed of light in vacuum, usually denoted by c, is a physical constant important in many areas of physics. Its value is 299,792,458 metres per second, a figure that is exact since the length of the metre is defined from this constant and the international standard for time...

: c = 299792458 m/s
• Stefan-Boltzmann constant
Stefan-Boltzmann constant
The Stefan–Boltzmann constant , a physical constant denoted by the Greek letter σ, is the constant of proportionality in the Stefan–Boltzmann law: the total energy radiated per unit surface area of a black body in unit time is proportional to the fourth power of the thermodynamic temperature.The...

: σ = 5.670400 W • m−2 • K−4