Rho (letter)
Encyclopedia
Rho is the 17th letter of the Greek alphabet
Greek alphabet
The Greek alphabet is the script that has been used to write the Greek language since at least 730 BC . The alphabet in its classical and modern form consists of 24 letters ordered in sequence from alpha to omega...

. In the system of Greek numerals
Greek numerals
Greek numerals are a system of representing numbers using letters of the Greek alphabet. They are also known by the names Ionian numerals, Milesian numerals , Alexandrian numerals, or alphabetic numerals...

, it has a value of 100. It is derived from Semitic
Semitic
In linguistics and ethnology, Semitic was first used to refer to a language family of largely Middle Eastern origin, now called the Semitic languages...

resh
Resh
Resh is the twentieth letter of many Semitic alphabets, including Phoenician, Aramaic, Hebrew and Arabic alphabet . Its sound value is one of a number of rhotic consonants: usually or , but also or in Hebrew....

"head". Its uppercase form is not to be confused with the Latin
Latin alphabet
The Latin alphabet, also called the Roman alphabet, is the most recognized alphabet used in the world today. It evolved from a western variety of the Greek alphabet called the Cumaean alphabet, which was adopted and modified by the Etruscans who ruled early Rome...

letter P
P
P is the sixteenth letter of the basic modern Latin alphabet.-Usage:In English and most other European languages, P is a voiceless bilabial plosive. Both initial and final Ps can be combined with many other discrete consonants in English words...

, although both are typeset using the same glyph
Glyph
A glyph is an element of writing: an individual mark on a written medium that contributes to the meaning of what is written. A glyph is made up of one or more graphemes....

.

## Uses

### Greek

Rho is classed as a liquid consonant
Liquid consonant
In phonetics, liquids or liquid consonants are a class of consonants consisting of lateral consonants together with rhotics.-Description:...

(together with lambda and sometimes the nasals mu
Mu (letter)
Carlos Alberto Vives Restrepo is a Grammy Award and three-time Latin Grammy Award winning-Colombian singer, composer and actor.-Biography:...

and nu
Nu (letter)
Nu , is the 13th letter of the Greek alphabet. In the system of Greek numerals it has a value of 50...

), which has important implications for morphology
Morphology (linguistics)
In linguistics, morphology is the identification, analysis and description, in a language, of the structure of morphemes and other linguistic units, such as words, affixes, parts of speech, intonation/stress, or implied context...

. In both Ancient
Ancient Greek
Ancient Greek is the stage of the Greek language in the periods spanning the times c. 9th–6th centuries BC, , c. 5th–4th centuries BC , and the c. 3rd century BC – 6th century AD of ancient Greece and the ancient world; being predated in the 2nd millennium BC by Mycenaean Greek...

and Modern Greek
Modern Greek
Modern Greek refers to the varieties of the Greek language spoken in the modern era. The beginning of the "modern" period of the language is often symbolically assigned to the fall of the Byzantine Empire in 1453, even though that date marks no clear linguistic boundary and many characteristic...

, it represents a trilled
Alveolar trill
The alveolar trill is a type of consonantal sound, used in some spoken languages. The symbol in the International Phonetic Alphabet that represents dental, alveolar, and postalveolar trills is , and the equivalent X-SAMPA symbol is r. It is commonly called the rolled R, rolling R, or trilled R...

or tapped r.

In polytonic orthography a rho at the beginning of a word is written with a rough breathing (equivalent to h) — rh — and a double
Gemination
In phonetics, gemination happens when a spoken consonant is pronounced for an audibly longer period of time than a short consonant. Gemination is distinct from stress and may appear independently of it....

rho within a word is written with a smooth breathing over the first rho and a rough breathing over the second — rrh — apparently reflecting an aspirated
Aspiration
Aspiration may refer to:In linguistics:*Aspirated consonant, a plosive pronounced with a strong burst of air*Debuccalization, the conversion of a consonant to [h] or [ʔ]*Voiceless glottal fricative In engine technology:...

or voiceless
Voiceless
In linguistics, voicelessness is the property of sounds being pronounced without the larynx vibrating. Phonologically, this is a type of phonation, which contrasts with other states of the larynx, but some object that the word "phonation" implies voicing, and that voicelessness is the lack of...

pronunciation in Ancient Greek
Ancient Greek
Ancient Greek is the stage of the Greek language in the periods spanning the times c. 9th–6th centuries BC, , c. 5th–4th centuries BC , and the c. 3rd century BC – 6th century AD of ancient Greece and the ancient world; being predated in the 2nd millennium BC by Mycenaean Greek...

, hence the various Greek-derived English words which start with rh or contain rrh.

The name of the letter is written in Greek as (polytonic) or ρω/ρο (monotonic).

### Other alphabets

Letters that arose from rho include Roman R
R
R is the eighteenth letter of the basic modern Latin alphabet.-History:The original Semitic letter may have been inspired by an Egyptian hieroglyph for tp, "head". It was used for by Semites because in their language, the word for "head" was rêš . It developed into Greek Ρ and Latin R...

and Cyrillic Er
Er (Cyrillic)
Er is a letter of the Cyrillic alphabet.It commonly represents the alveolar trill , like the "rolled" sound in the Scottish pronunciation of ⟨r⟩ in "curd".-History:...

(Р).

### Math and science

The characters Ρ, ρ and are also used outside its Greek alphabetical context in science
Science
Science is a systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe...

and mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

.
• In physics
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...

to represent:
• Density
Density
The mass density or density of a material is defined as its mass per unit volume. The symbol most often used for density is ρ . In some cases , density is also defined as its weight per unit volume; although, this quantity is more properly called specific weight...

(ρ)
• Resistivity
Resistivity
Electrical resistivity is a measure of how strongly a material opposes the flow of electric current. A low resistivity indicates a material that readily allows the movement of electric charge. The SI unit of electrical resistivity is the ohm metre...

(ρ)
• Charge density
Charge density
The linear, surface, or volume charge density is the amount of electric charge in a line, surface, or volume, respectively. It is measured in coulombs per meter , square meter , or cubic meter , respectively, and represented by the lowercase Greek letter Rho . Since there are positive as well as...

(ρ)
• Rho meson
Rho meson
In particle physics, a rho meson is a short-lived hadronic particle that is an isospin triplet whose three states are denoted as , and . After the pions and kaons, the rho mesons are the lightest strongly interacting particle with a mass of roughly for all three states...

(ρ+, ρ-, ρ0)

• In mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

to represent:
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...

in the spherical coordinate system
Spherical coordinate system
In mathematics, a spherical coordinate system is a coordinate system for three-dimensional space where the position of a point is specified by three numbers: the radial distance of that point from a fixed origin, its inclination angle measured from a fixed zenith direction, and the azimuth angle of...

• The correlation coefficient
Pearson product-moment correlation coefficient
In statistics, the Pearson product-moment correlation coefficient is a measure of the correlation between two variables X and Y, giving a value between +1 and −1 inclusive...

of a population parameter
In mathematics, the spectral radius of a square matrix or a bounded linear operator is the supremum among the absolute values of the elements in its spectrum, which is sometimes denoted by ρ.-Matrices:...

of a matrix denoted as
• The 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 sensitivity to interest rates of a pricing function

• In economics
Economics
Economics is the social science that analyzes the production, distribution, and consumption of goods and services. The term economics comes from the Ancient Greek from + , hence "rules of the house"...

to represent the discount rate of future pence cash flows

• In molecular biology
Molecular biology
Molecular biology is the branch of biology that deals with the molecular basis of biological activity. This field overlaps with other areas of biology and chemistry, particularly genetics and biochemistry...

to represent the Rho protein responsible for termination of RNA synthesis. In such occasions, it is often represented as ("rho symbol" U+03F1), to avoid confusion with the Latin letter p

• In ecology
Ecology
Ecology is the scientific study of the relations that living organisms have with respect to each other and their natural environment. Variables of interest to ecologists include the composition, distribution, amount , number, and changing states of organisms within and among ecosystems...

to represent the population damping ratio where ρ = λ1 / |λ2|.

• In programming
• For LaTeX
LaTeX
LaTeX is a document markup language and document preparation system for the TeX typesetting program. Within the typesetting system, its name is styled as . The term LaTeX refers only to the language in which documents are written, not to the editor used to write those documents. In order to...

, the symbols are P (Ρ), \rho (), and \varrho ()
• The lower-case rho ρ has a special meaning in the APL programming language
APL programming language
APL is an interactive array-oriented language and integrated development environment, which is available from a number of commercial and noncommercial vendors and for most computer platforms. It is based on a mathematical notation developed by Kenneth E...

• In statistics
Statistics
Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....

to represent Spearman's rank correlation coefficient
Spearman's rank correlation coefficient
In statistics, Spearman's rank correlation coefficient or Spearman's rho, named after Charles Spearman and often denoted by the Greek letter \rho or as r_s, is a non-parametric measure of statistical dependence between two variables. It assesses how well the relationship between two variables can...

, commonly known as Spearman's rho

• In options
Option (finance)
In finance, an option is a derivative financial instrument that specifies a contract between two parties for a future transaction on an asset at a reference price. The buyer of the option gains the right, but not the obligation, to engage in that transaction, while the seller incurs the...

theory to represent the rate of change of a portfolio with respect to interest rates

### Chi Rho

The letter rho overlaid with chi
Chi (letter)
Chi is the 22nd letter of the Greek alphabet, pronounced as in English.-Greek:-Ancient Greek:Its value in Ancient Greek was an aspirated velar stop .-Koine Greek:...

forms the Chi Rho
Chi Rho
The Chi Rho is one of the earliest forms of christogram, and is used by Christians. It is formed by superimposing the first two letters chi and rho of the Greek word "ΧΡΙΣΤΟΣ" =Christ in such a way to produce the monogram ☧...

symbol, used to represent Jesus Christ.

### Rhodes Scholars

Former Rhodes Scholars are entitled to use the Greek letter rho as a designation of their status. When used, the symbol should precede the name.

## Unicode

 description character Unicode HTML GREEKLETTERRHO Ρ U+03A1 Ρ ρ U+03C1 ρ GREEKRHO SYMBOL ϱ U+03F1 ϱ GREEKRHO WITH STROKEBar (diacritic)A bar or stroke is a modification consisting of a line drawn through a grapheme. It may be used as a diacritic to derive new letters from old ones, or simply as an addition to make a grapheme more distinct from others....SYMBOL ϼ U+03FC ϼ GREEK LETTERSMALL CAPITALRHO ᴩ U+1D29 ᴩ GREEK SUBSCRIPTSubscript and superscriptA subscript or superscript is a number, figure, symbol, or indicator that appears smaller than the normal line of type and is set slightly below or above it – subscripts appear at or below the baseline, while superscripts are above...SMALL LETTERRHO ◌ᵨ U+1D68 ᵨ GREEKLETTER RHOWITH DASIA Ῥ U+1FEC Ῥ ῥ U+1FE5 ῥ GREEKSMALL LETTER RHOWITH PSILI ῤ U+1FE4 ῤ APLFUNCTIONAL SYMBOLRHO ⍴ U+2374 ⍴ CHI RHOChi RhoThe Chi Rho is one of the earliest forms of christogram, and is used by Christians. It is formed by superimposing the first two letters chi and rho of the Greek word "ΧΡΙΣΤΟΣ" =Christ in such a way to produce the monogram ☧... ☧ U+2627 ☧