Decimal degrees
Encyclopedia
Decimal degrees express latitude
and longitude
geographic coordinates
as decimal fractions and are used in many Geographic Information Systems
(GIS), web mapping
applications such as Google Maps
, and GPS
devices. Decimal degrees are an alternative to using degrees, minutes, and seconds (DMS). As with latitude and longitude, the values are bounded by ±90° and ±180° respectively.
Positive latitudes are north of the equator, negative latitudes are south of the equator. Positive longitudes are east of Prime Meridian
, negative longitudes are west of the Prime Meridian. Latitude and longitude are usually expressed in that sequence, latitude before longitude.
at the equator
is 6,378,160.0 meters resulting in a circumference of 40,075,161.2 meters. The equator is divided into 360 degrees of longitude, so each degree at the equator represents 111,319.9 metres or approximately 111 km. As one moves away from the equator towards a pole, however, one degree of longitude represents a diminishing number of meters, approaching zero at the pole. The number of decimal places required for a particular accuracy at the equator is:
A value in decimal degrees to an accuracy of 4 decimal places is accurate to 11.1 meters (± 5.55 m) at the equator
. A value in decimal degrees to 5 decimal places is accurate to 1.11 meter at the equator. Because the earth
is not flat, the accuracy of the longitude part of the coordinates increases the further from the equator you get. The accuracy of the latitude part does not increase so much, more strictly however, a meridian arc
length per 1 second depends on latitude at point concerned. The discrepancy of 1 second meridian arc length between equator and pole is about 0.3 metres because the earth is an oblate spheroid.
is:
In most systems, such as Google Maps, the degree symbol is omitted and thus the coordinates are expressed as "38.889722, -77.008889".
A DMS value is converted to decimal degrees using the formula:
The decimal degree representation for the location of the United States Capitol of
is:
To calculate the D, M and S components, the following formulas can be used:
where |DD| is the absolute value
of DD, trunc is the truncation
function, and mod is the modulo operator
. Note that with this formula, only S may have a fractional value.
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...
and 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 ....
geographic coordinates
Geographic coordinate system
A geographic coordinate system is a coordinate system that enables every location on the Earth to be specified by a set of numbers. The coordinates are often chosen such that one of the numbers represent vertical position, and two or three of the numbers represent horizontal position...
as decimal fractions and are used in many Geographic Information Systems
Geographic Information System
A geographic information system, geographical information science, or geospatial information studies is a system designed to capture, store, manipulate, analyze, manage, and present all types of geographically referenced data...
(GIS), web mapping
Web mapping
Web mapping is the process of designing, implementing, generating and delivering maps on the World Wide Web and its product. While web mapping primarily deals with technological issues, web cartography additionally studies theoretic aspects: the use of web maps, the evaluation and optimization of...
applications such as Google Maps
Google Maps
Google Maps is a web mapping service application and technology provided by Google, free , that powers many map-based services, including the Google Maps website, Google Ride Finder, Google Transit, and maps embedded on third-party websites via the Google Maps API...
, and 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...
devices. Decimal degrees are an alternative to using degrees, minutes, and seconds (DMS). As with latitude and longitude, the values are bounded by ±90° and ±180° respectively.
Positive latitudes are north of the equator, negative latitudes are south of the equator. Positive longitudes are east of Prime Meridian
Prime Meridian
The Prime Meridian is the meridian at which the longitude is defined to be 0°.The Prime Meridian and its opposite the 180th meridian , which the International Date Line generally follows, form a great circle that divides the Earth into the Eastern and Western Hemispheres.An international...
, negative longitudes are west of the Prime Meridian. Latitude and longitude are usually expressed in that sequence, latitude before longitude.
Accuracy
The radius of the semi major axis of the EarthEarth
Earth is the third planet from the Sun, and the densest and fifth-largest of the eight planets in the Solar System. It is also the largest of the Solar System's four terrestrial planets...
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....
is 6,378,160.0 meters resulting in a circumference of 40,075,161.2 meters. The equator is divided into 360 degrees of longitude, so each degree at the equator represents 111,319.9 metres or approximately 111 km. As one moves away from the equator towards a pole, however, one degree of longitude represents a diminishing number of meters, approaching zero at the pole. The number of decimal places required for a particular accuracy at the equator is:
| decimal places | degrees | distance |
|---|---|---|
| 0 | 1.0 | 111 km |
| 1 | 0.1 | 11.1 km |
| 2 | 0.01 | 1.11 km |
| 3 | 0.001 | 111 m |
| 4 | 0.0001 | 11.1 m |
| 5 | 0.00001 | 1.11 m |
| 6 | 0.000001 | 0.111 m |
| 7 | 0.0000001 | 1.11 cm |
| 8 | 0.00000001 | 1.11 mm |
A value in decimal degrees to an accuracy of 4 decimal places is accurate to 11.1 meters (± 5.55 m) 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....
. A value in decimal degrees to 5 decimal places is accurate to 1.11 meter at the equator. Because the earth
Earth
Earth is the third planet from the Sun, and the densest and fifth-largest of the eight planets in the Solar System. It is also the largest of the Solar System's four terrestrial planets...
is not flat, the accuracy of the longitude part of the coordinates increases the further from the equator you get. The accuracy of the latitude part does not increase so much, more strictly however, a 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...
length per 1 second depends on latitude at point concerned. The discrepancy of 1 second meridian arc length between equator and pole is about 0.3 metres because the earth is an oblate spheroid.
Example
The decimal degree representation of the location of the United States CapitolUnited States Capitol
The United States Capitol is the meeting place of the United States Congress, the legislature of the federal government of the United States. Located in Washington, D.C., it sits atop Capitol Hill at the eastern end of the National Mall...
is:
- 38.889722°, -77.008889°
In most systems, such as Google Maps, the degree symbol is omitted and thus the coordinates are expressed as "38.889722, -77.008889".
A DMS value is converted to decimal degrees using the formula:
The decimal degree representation for the location of the United States Capitol of
- 38° 53′ 23″ N, 77° 00′ 32″ W
is:
- 38.889722°, -77.008889°
To calculate the D, M and S components, the following formulas can be used:
where |DD| is the absolute value
Absolute value
In mathematics, the absolute value |a| of a real number a is the numerical value of a without regard to its sign. So, for example, the absolute value of 3 is 3, and the absolute value of -3 is also 3...
of DD, trunc is the truncation
Truncation
In mathematics and computer science, truncation is the term for limiting the number of digits right of the decimal point, by discarding the least significant ones.For example, consider the real numbersThe result would be:- Truncation and floor function :...
function, and mod is the modulo operator
Modulo operation
In computing, the modulo operation finds the remainder of division of one number by another.Given two positive numbers, and , a modulo n can be thought of as the remainder, on division of a by n...
. Note that with this formula, only S may have a fractional value.