Nautical mile
Encyclopedia
The nautical mile is a unit
Units of measurement
A unit of measurement is a definite magnitude of a physical quantity, defined and adopted by convention and/or by law, that is used as a standard for measurement of the same physical quantity. Any other value of the physical quantity can be expressed as a simple multiple of the unit of...

of length
Length
In geometric measurements, length most commonly refers to the longest dimension of an object.In certain contexts, the term "length" is reserved for a certain dimension of an object along which the length is measured. For example it is possible to cut a length of a wire which is shorter than wire...

that is about one minute of arc
Minute of arc
A minute of arc, arcminute, or minute of angle , is a unit of angular measurement equal to one sixtieth of one degree. In turn, a second of arc or arcsecond is one sixtieth of one minute of arc....

of latitude
Latitude
In geography, the latitude of a location on the Earth is the angular distance of that location south or north of the Equator. The latitude is an angle, and is usually measured in degrees . The equator has a latitude of 0°, the North pole has a latitude of 90° north , and the South pole has a...

along any meridian
Meridian (geography)
A meridian is an imaginary line on the Earth's surface from the North Pole to the South Pole that connects all locations along it with a given longitude. The position of a point along the meridian is given by its latitude. Each meridian is perpendicular to all circles of latitude...

, but is approximately one minute of arc of longitude
Longitude
Longitude is a geographic coordinate that specifies the east-west position of a point on the Earth's surface. It is an angular measurement, usually expressed in degrees, minutes and seconds, and denoted by the Greek letter lambda ....

only at the equator
Equator
An equator is the intersection of a sphere's surface with the plane perpendicular to the sphere's axis of rotation and containing the sphere's center of mass....

. By international agreement it is exactly 1,852 metre
Metre
The metre , symbol m, is the base unit of length in the International System of Units . Originally intended to be one ten-millionth of the distance from the Earth's equator to the North Pole , its definition has been periodically refined to reflect growing knowledge of metrology...

s (approximately 6,076 feet).

It is a non-SI
International System of Units
The International System of Units is the modern form of the metric system and is generally a system of units of measurement devised around seven base units and the convenience of the number ten. The older metric system included several groups of units...

unit (although accepted for use in the International System of Units by the BIPM
International Bureau of Weights and Measures
The International Bureau of Weights and Measures , is an international standards organisation, one of three such organisations established to maintain the International System of Units under the terms of the Metre Convention...

) used especially by navigator
Navigator
A navigator is the person on board a ship or aircraft responsible for its navigation. The navigator's primary responsibility is to be aware of ship or aircraft position at all times. Responsibilities include planning the journey, advising the Captain or aircraft Commander of estimated timing to...

s in the shipping
Shipping
Shipping has multiple meanings. It can be a physical process of transporting commodities and merchandise goods and cargo, by land, air, and sea. It also can describe the movement of objects by ship.Land or "ground" shipping can be by train or by truck...

and aviation
Aviation
Aviation is the design, development, production, operation, and use of aircraft, especially heavier-than-air aircraft. Aviation is derived from avis, the Latin word for bird.-History:...

industries, and also in polar exploration
Arctic exploration
Arctic exploration is the physical exploration of the Arctic region of the Earth. The region that surrounds the North Pole. It refers to the historical period during which mankind has explored the region north of the Arctic Circle...

. It is commonly used in international law
International law
Public international law concerns the structure and conduct of sovereign states; analogous entities, such as the Holy See; and intergovernmental organizations. To a lesser degree, international law also may affect multinational corporations and individuals, an impact increasingly evolving beyond...

and treaties
Treaty
A treaty is an express agreement under international law entered into by actors in international law, namely sovereign states and international organizations. A treaty may also be known as an agreement, protocol, covenant, convention or exchange of letters, among other terms...

, especially regarding the limits of territorial waters
Territorial waters
Territorial waters, or a territorial sea, as defined by the 1982 United Nations Convention on the Law of the Sea, is a belt of coastal waters extending at most from the baseline of a coastal state...

. It developed from the sea mile and the related geographical mile
Geographical mile
The geographical mile is a unit of length determined by 1 minute of arc along the Earth's equator. For the 1924 International Spheroid this equalled 1855.4 metres...

.

The nautical mile remains in use by sea and air navigators worldwide because of its convenience when working with charts. Most nautical charts are constructed on the Mercator projection
Mercator projection
The Mercator projection is a cylindrical map projection presented by the Belgian geographer and cartographer Gerardus Mercator, in 1569. It became the standard map projection for nautical purposes because of its ability to represent lines of constant course, known as rhumb lines or loxodromes, as...

whose scale varies by approximately a factor of six from the equator to 80° north or south latitude. It is, therefore, impossible to show a single linear scale
Linear scale
A linear scale, also called a bar scale, scale bar, graphic scale, or graphical scale, is a means of visually showing the scale of a map, nautical chart, engineering drawing, or architectural drawing....

for use on charts on scales smaller than about 1/80,000. Since a nautical mile is, for practical navigation, the same as a minute of latitude, it is easy to measure a distance on a chart with dividers, using the latitude scale on the side of the chart directly to the east or west of the distance being measured.

Definition

The international nautical mile was defined by the First International Extraordinary Hydrographic Conference, Monaco (1929) as exactly 1852 metre
Metre
The metre , symbol m, is the base unit of length in the International System of Units . Originally intended to be one ten-millionth of the distance from the Earth's equator to the North Pole , its definition has been periodically refined to reflect growing knowledge of metrology...

s. This is the only definition in widespread current use, and is the one accepted by the International Hydrographic Organization
International Hydrographic Organization
The International Hydrographic Organization is the inter-governmental organisation representing the hydrographic community. It enjoys observer status at the UN and is the recognised competent authority on hydrographic surveying and nautical charting...

and by the International Bureau of Weights and Measures
International Bureau of Weights and Measures
The International Bureau of Weights and Measures , is an international standards organisation, one of three such organisations established to maintain the International System of Units under the terms of the Metre Convention...

(BIPM). Before 1929, different countries had different definitions, and the Soviet Union, the United Kingdom and the United States did not immediately accept the international value.

Both the Imperial and U.S. definitions
United States customary units
United States customary units are a system of measurements commonly used in the United States. Many U.S. units are virtually identical to their imperial counterparts, but the U.S. customary system developed from English units used in the British Empire before the system of imperial units was...

of the nautical mile were based on the Clarke (1866) Spheroid: they were different approximations to the length of one minute of arc along a great circle
Great circle
A great circle, also known as a Riemannian circle, of a sphere is the intersection of the sphere and a plane which passes through the center point of the sphere, as opposed to a general circle of a sphere where the plane is not required to pass through the center...

of a sphere having the same surface area as the Clarke Spheroid. The United States nautical mile was defined as 1853.248 metres (6080.20 U.S. feet, based on the definition of the foot in the Mendenhall Order
Mendenhall Order
The Mendenhall Order marked a decision to change the fundamental standards of length and mass of the United States from the customary standards based on those of England to metric standards. It was issued on April 5, 1893 by Thomas Corwin Mendenhall, superintendent of the U.S...

of 1893): it was abandoned in favour of the international nautical mile in 1954. The Imperial (UK) nautical mile, also known as the Admiralty mile, was defined in terms of the knot such that one nautical mile was exactly 6080 feet (1853.184 m): it was abandoned in 1970 and, for legal purposes, old references to the obsolete unit are now converted to 1853 metres exactly.

Sea mile

In English usage, a sea mile is, for any latitude, the length of one minute of latitude at that latitude. It varies from about 1842.9 metres (6,046.3 ft) at the equator
Equator
An equator is the intersection of a sphere's surface with the plane perpendicular to the sphere's axis of rotation and containing the sphere's center of mass....

to about 1861.7 metres (6,107.9 ft) at the poles, with a mean value of 1852.3 metres (6,077.1 ft). The international nautical mile was chosen as the integer number of metres closest to the mean sea mile.

American use has changed recently. The glossary in the 1966 edition of Bowditch
Bowditch's American Practical Navigator
The American Practical Navigator , originally written by Nathaniel Bowditch, is an encyclopedia of navigation. It serves as a valuable handbook on oceanography and meteorology, and contains useful tables and a maritime glossary...

defines a "sea mile" as a "nautical mile". In the 2002 edition, the glossary says: "An approximate mean value of the nautical mile equal to 6,080 feet; the length of a minute of arc along the meridian at latitude 48°."

The sea mile has also been defined as 6000 feet or 1000 fathoms, for example in Dresner's Units of Measurement. Dresner includes a remark to the effect that this must not be confused with the nautical mile.

Geographical mile

The geographical mile is the length of one minute of longitude
Longitude
Longitude is a geographic coordinate that specifies the east-west position of a point on the Earth's surface. It is an angular measurement, usually expressed in degrees, minutes and seconds, and denoted by the Greek letter lambda ....

along the Equator, about 1855.4 m on the International (1924) Spheroid
Hayford ellipsoid
The Hayford ellipsoid is a geodetic reference ellipsoid, named after the US geodesist John Fillmore Hayford , which was introduced in 1910. The Hayford ellipsoid was also referred to as the International ellipsoid 1924 after it had been adopted by the International Union of Geodesy and Geophysics...

or about 1855.325 m on the WGS 84 ellipsoid. Bowditch defines it as 6,087.08 feet, which is 1,855.34 metres. The term "geographical mile" has also been used to refer to the mean sea mile, which would later become the international nautical mile.

Do not confuse this with the similar-sounding unit the geografische Meile, seen in historical German measurements. This unit was intended to be the length of four minutes of arc along the equator and is standardized as 7421.6 metres. In Germany, the Mile, Uhr or Stunde typically refers to 24,000 of the local foot. This is the distance one might walk in an hour (Stunde).

Telegraphic mile

A telegraphic mile is the rounded length of a minute of arc along the Equator.

Tactical mile or data mile

As an approximation, designers of radar systems for ballistic, cruise
Cruise missile
A cruise missile is a guided missile that carries an explosive payload and is propelled, usually by a jet engine, towards a land-based or sea-based target. Cruise missiles are designed to deliver a large warhead over long distances with high accuracy...

and anti-ship missiles used by NATO navies use as their equivalent of a nautical mile. In the Royal Navy
Royal Navy
The Royal Navy is the naval warfare service branch of the British Armed Forces. Founded in the 16th century, it is the oldest service branch and is known as the Senior Service...

, this is also known as a data mile
Data mile
In radar-related subjects and in JTIDS, a data mile is a unit of distance equal to 6000 feet , or 0.987 nautical miles. An international mile is exactly 0.88 of a data mile....

.

Radar is an object-detection system which uses radio waves to determine the range, altitude, direction, or speed of objects. It can be used to detect aircraft, ships, spacecraft, guided missiles, motor vehicles, weather formations, and terrain. The radar dish or antenna transmits pulses of radio...

theory, the data mile (6,000 feet) is the length unit. A radar mile is the time it takes a radar pulse to travel one datamile forth and a data mile back again, which equals 12.277 μs. This value corresponds with the speed of light (c. 3 m/s). A radar's range can be determined by dividing the listening time (pulse repetition time
PRF
PRF is an acronym and can stand for:* Platelet Rich Fibrin, A combination of platelets and fibrin used to regenerate tissue* PRF-3, the call letters of the now defunct TV Tupi, Brazil's first television station* Pain Relief Foundation...

minus pulsewidth) by a radar mile.

Unit symbol

The International Hydrographic Organization
International Hydrographic Organization
The International Hydrographic Organization is the inter-governmental organisation representing the hydrographic community. It enjoys observer status at the UN and is the recognised competent authority on hydrographic surveying and nautical charting...

, whose membership includes essentially all seafaring nations, and the International Bureau of Weights and Measures
International Bureau of Weights and Measures
The International Bureau of Weights and Measures , is an international standards organisation, one of three such organisations established to maintain the International System of Units under the terms of the Metre Convention...

use M as the abbreviation for the nautical mile. The preferred abbreviation of the International Civil Aviation Organization
International Civil Aviation Organization
The International Civil Aviation Organization , pronounced , , is a specialized agency of the United Nations. It codifies the principles and techniques of international air navigation and fosters the planning and development of international air transport to ensure safe and orderly growth...

is nm. The abbreviation nm, though conflicting with the SI
International System of Units
The International System of Units is the modern form of the metric system and is generally a system of units of measurement devised around seven base units and the convenience of the number ten. The older metric system included several groups of units...

symbol for the nanometre
Nanometre
A nanometre is a unit of length in the metric system, equal to one billionth of a metre. The name combines the SI prefix nano- with the parent unit name metre .The nanometre is often used to express dimensions on the atomic scale: the diameter...

, is also widely used. The SI symbol for the newton metre
Newton metre
A newton metre is a unit of torque in the SI system. The symbolic form is N m or N·m, and sometimes hyphenated newton-metre...

is (with a space) or n·m, not nm, because only prefixes may abut a unit symbol.

History

The nautical mile was historically defined as a minute of arc
Minute of arc
A minute of arc, arcminute, or minute of angle , is a unit of angular measurement equal to one sixtieth of one degree. In turn, a second of arc or arcsecond is one sixtieth of one minute of arc....

along a meridian
Meridian (geography)
A meridian is an imaginary line on the Earth's surface from the North Pole to the South Pole that connects all locations along it with a given longitude. The position of a point along the meridian is given by its latitude. Each meridian is perpendicular to all circles of latitude...

of the Earth (north-south), making a meridian exactly 180×60 = historical nautical miles. It can therefore be used for approximate measures on a meridian as change of latitude
Latitude
In geography, the latitude of a location on the Earth is the angular distance of that location south or north of the Equator. The latitude is an angle, and is usually measured in degrees . The equator has a latitude of 0°, the North pole has a latitude of 90° north , and the South pole has a...

on a nautical chart
Nautical chart
A nautical chart is a graphic representation of a maritime area and adjacent coastal regions. Depending on the scale of the chart, it may show depths of water and heights of land , natural features of the seabed, details of the coastline, navigational hazards, locations of natural and man-made aids...

. The originally intended definition of the metre as 10−7 of a half-meridian arc
Meridian arc
In geodesy, a meridian arc measurement is a highly accurate determination of the distance between two points with the same longitude. Two or more such determinations at different locations then specify the shape of the reference ellipsoid which best approximates the shape of the geoid. This...

makes the mean historical nautical mile exactly (2)/ = historical metres. Based on the current IUGG meridian of (standard) metres the mean historical nautical mile is .

The historical definition differs from the length-based standard in that a minute of arc, and hence a nautical mile, is not a constant length at the surface of the Earth but gradually lengthens in the north-south direction with increasing distance from the equator, as a corollary of the Earth's oblateness, hence the need for "mean" in the last sentence of the previous paragraph. This length equals about at the poles and at the Equator.

Other nations had different definitions of the nautical mile. This variety in combination with the complexity of angular measure described above along with the intrinsic uncertainty of geodetically derived units mitigated against the extant definitions in favor of a simple unit of pure length. International agreement was achieved in 1929 when the International Extraordinary Hydrographic Conference
International Hydrographic Organization
The International Hydrographic Organization is the inter-governmental organisation representing the hydrographic community. It enjoys observer status at the UN and is the recognised competent authority on hydrographic surveying and nautical charting...

held in Monaco
Monaco
Monaco , officially the Principality of Monaco , is a sovereign city state on the French Riviera. It is bordered on three sides by its neighbour, France, and its centre is about from Italy. Its area is with a population of 35,986 as of 2011 and is the most densely populated country in the...

adopted a definition of one international nautical mile as being equal to 1,852 metres
1 E3 m
To help compare different orders of magnitude this page lists lengths between 1 kilometre and 10 kilometres .Distances shorter than 1 kilometre-Conversions:1 kilometre is equal to:* 1,000 metres...

exactly, in excellent agreement (for an integer) with both the above-mentioned values of historical metres and standard metres.

Use of angle-based length was first suggested by E. Gunter (of Gunter's chain
Gunter's chain
Gunter's chain is a measuring device used for land survey. It was designed and introduced in 1620 by English clergyman and mathematician Edmund Gunter long before the development of the theodolite and other more sophisticated equipment, enabling plots of land to be accurately surveyed and plotted,...

fame). During the 18th century, the relation of a mile of 6000 (geometric) feet, or a minute of arc on the earth surface had been advanced as a universal measure for land and sea. The metric kilometre was selected to represent a centisimal minute of arc, on the same basis, with the circle divided into 400 degrees of 100 minutes.

Conversions to other units

One international nautical mile converts to:
• 1.852 kilometre
Kilometre
The kilometre is a unit of length in the metric system, equal to one thousand metres and is therefore exactly equal to the distance travelled by light in free space in of a second...

s (exact)
• 1.150779 miles (statute)
Mile
A mile is a unit of length, most commonly 5,280 feet . The mile of 5,280 feet is sometimes called the statute mile or land mile to distinguish it from the nautical mile...

(exact: 57,875/50,292 miles)
• 2,025.372 yard
Yard
A yard is a unit of length in several different systems including English units, Imperial units and United States customary units. It is equal to 3 feet or 36 inches...

s (exact:
• 6,076.1155 feet (exact: 2,315,000/381 feet or 1,822,831/300 survey feet)
• 1,012.6859 fathom
Fathom
A fathom is a unit of length in the imperial and the U.S. customary systems, used especially for measuring the depth of water.There are 2 yards in an imperial or U.S. fathom...

s (exact: 1,157,500/1,143 fathoms)
• 10 international cables
Cable length
A cable length or cable's length is a nautical unit of measure equal to one tenth of a nautical mile or 100 fathoms, or sometimes 120 fathoms. The unit is named after the length of a ship's anchor cable in the age of sail...

(exact)
• 10.126859 imperial (100-fathom) cables
Cable length
A cable length or cable's length is a nautical unit of measure equal to one tenth of a nautical mile or 100 fathoms, or sometimes 120 fathoms. The unit is named after the length of a ship's anchor cable in the age of sail...

(exact: 11,575/1,143 imperial cables)
• 8.439049 U.S. customary (120-fathom) cables
Cable length
A cable length or cable's length is a nautical unit of measure equal to one tenth of a nautical mile or 100 fathoms, or sometimes 120 fathoms. The unit is named after the length of a ship's anchor cable in the age of sail...

(exact: 57,875/6,858 U.S. customary cables)
• 0.998383 equatorial arc minutes (traditional geographical mile
Geographical mile
The geographical mile is a unit of length determined by 1 minute of arc along the Earth's equator. For the 1924 International Spheroid this equalled 1855.4 metres...

s)
• 0.9998834 mean meridian arc minutes (mean historical nautical miles)

Associated units

The derived unit of speed
Speed
In kinematics, the speed of an object is the magnitude of its velocity ; it is thus a scalar quantity. The average speed of an object in an interval of time is the distance traveled by the object divided by the duration of the interval; the instantaneous speed is the limit of the average speed as...

is the knot, defined as one nautical mile per hour
Hour
The hour is a unit of measurement of time. In modern usage, an hour comprises 60 minutes, or 3,600 seconds...

. The term "log" is used to measure the distance a vessel has moved through the water. This term can also be used to measure the speed through the water (see chip log
Chip log
A chip log, also called common log, ship log or just log, is a navigation tool used by mariners to estimate the speed of a vessel through water.-Construction:...

), as the speed and distance are directly related.

The terms "knot" and "log" are derived from the practice of using a "log" tied to a knotted rope as a method of gauging the speed of a ship. A log attached to a knotted rope was thrown into the water, trailing behind the ship. The number of knots that passed off the ship and into the water in a given time would determine the speed in "knots". The present day measurement of knots and log are determined using a mechanical tow, electronic tow, hull-mounted units (which may or may not be retractable), Doppler
Doppler effect
The Doppler effect , named after Austrian physicist Christian Doppler who proposed it in 1842 in Prague, is the change in frequency of a wave for an observer moving relative to the source of the wave. It is commonly heard when a vehicle sounding a siren or horn approaches, passes, and recedes from...

(either ultrasonic
Ultrasound
Ultrasound is cyclic sound pressure with a frequency greater than the upper limit of human hearing. Ultrasound is thus not separated from "normal" sound based on differences in physical properties, only the fact that humans cannot hear it. Although this limit varies from person to person, it is...

Radar is an object-detection system which uses radio waves to determine the range, altitude, direction, or speed of objects. It can be used to detect aircraft, ships, spacecraft, guided missiles, motor vehicles, weather formations, and terrain. The radar dish or antenna transmits pulses of radio...

), or GPS
Global Positioning System
The Global Positioning System is a space-based global navigation satellite system that provides location and time information in all weather, anywhere on or near the Earth, where there is an unobstructed line of sight to four or more GPS satellites...

. Speeds measured with a GPS differ from those measured by other means in that they are Speed Over Ground (accounting for the effect of current) while the others are Speed Through the Water, which does not account for current.

• Conversion of units
Conversion of units
Conversion of units is the conversion between different units of measurement for the same quantity, typically through multiplicative conversion factors.- Process :...

• Knot (unit) for the unit of speed
• Mile
Mile
A mile is a unit of length, most commonly 5,280 feet . The mile of 5,280 feet is sometimes called the statute mile or land mile to distinguish it from the nautical mile...

for other types of mile
• Orders of magnitude (length)
• Units of measurement
Units of measurement
A unit of measurement is a definite magnitude of a physical quantity, defined and adopted by convention and/or by law, that is used as a standard for measurement of the same physical quantity. Any other value of the physical quantity can be expressed as a simple multiple of the unit of...