Decimal degrees (DD) is a notation for expressing
latitude
In geography, latitude is a coordinate that specifies the north– south position of a point on the surface of the Earth or another celestial body. Latitude is given as an angle that ranges from –90° at the south pole to 90° at the north pol ...
and
longitude
Longitude (, ) is a geographic coordinate that specifies the east– west position of a point on the surface of the Earth, or another celestial body. It is an angular measurement, usually expressed in degrees and denoted by the Greek lette ...
geographic coordinates
The geographic coordinate system (GCS) is a spherical or ellipsoidal coordinate system for measuring and communicating positions directly on the Earth as latitude and longitude. It is the simplest, oldest and most widely used of the various ...
as
decimal fractions
The decimal numeral system (also called the base-ten positional numeral system and denary or decanary) is the standard system for denoting integer and non-integer numbers. It is the extension to non-integer numbers of the Hindu–Arabic numeral ...
of a
degree. DD are used in many
geographic information systems (GIS),
web mapping
Web mapping or an online mapping is the process of using maps, usually created through geographic information systems (GIS), on the Internet, more specifically in the World Wide Web (WWW). A web map or an online map is both served and consumed, ...
applications such as
OpenStreetMap, and
GPS
The Global Positioning System (GPS), originally Navstar GPS, is a satellite-based radionavigation system owned by the United States government and operated by the United States Space Force. It is one of the global navigation satellite sy ...
devices. Decimal degrees are an alternative to using
sexagesimal degrees (degrees, minutes, and seconds - ''DMS notation''). 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 the
Prime Meridian
A prime meridian is an arbitrary meridian (a line of longitude) in a geographic coordinate system at which longitude is defined to be 0°. Together, a prime meridian and its anti-meridian (the 180th meridian in a 360°-system) form a great ...
; negative longitudes are west of the Prime Meridian. Latitude and longitude are usually expressed in that sequence, latitude before longitude. The abbreviation dLL has been used in the scientific literature with locations in texts being identified as a tuple within square brackets, for example
4.5798,-3.5820 The appropriate decimal places are used.
Precision
The radius of the
semi-major axis of the
Earth
Earth is the third planet from the Sun and the only astronomical object known to harbor life. While large volumes of water can be found throughout the Solar System, only Earth sustains liquid surface water. About 71% of Earth's surfa ...
at the
equator is resulting in a
circumference
In geometry, the circumference (from Latin ''circumferens'', meaning "carrying around") is the perimeter of a circle or ellipse. That is, the circumference would be the arc length of the circle, as if it were opened up and straightened out t ...
of .
World Geodetic System
The World Geodetic System (WGS) is a standard used in cartography, geodesy, and satellite navigation including GPS. The current version, WGS 84, defines an Earth-centered, Earth-fixed coordinate system and a geodetic datum, and also descr ...
(''WGS-84'')
Available online
from National Geospatial-Intelligence Agency
The National Geospatial-Intelligence Agency (NGA) is a combat support agency within the United States Department of Defense whose primary mission is collecting, analyzing, and distributing geospatial intelligence (GEOINT) in support of natio ...
. The equator is divided into 360 degrees of longitude, so each degree at the equator represents . As one moves away from the equator towards a pole, however, one degree of longitude is multiplied by the cosine of the latitude, decreasing the distance, approaching zero at the pole. The number of decimal places required for a particular precision at the equator is:
A value in decimal degrees to a precision of 4 decimal places is precise to at the
equator. A value in decimal degrees to 5 decimal places is precise to at the equator. Elevation also introduces a small error: at elevation, the radius and surface distance is increased by 0.001 or 0.1%. Because the
earth
Earth is the third planet from the Sun and the only astronomical object known to harbor life. While large volumes of water can be found throughout the Solar System, only Earth sustains liquid surface water. About 71% of Earth's surfa ...
is not flat, the precision of the longitude part of the coordinates increases the further from the equator you get. The precision of the latitude part does not increase so much, more strictly however, a
meridian arc length per 1 second depends on the latitude at the point in question. The discrepancy of 1 second meridian arc length between equator and pole is about because the earth is an
oblate spheroid.
Example
A
DMS value is converted to decimal degrees using the formula:
:
For instance, the decimal degree representation for
:38° 53′ 23″ N, 77° 00′ 32″ W
(the location of the
United States Capitol
The United States Capitol, often called The Capitol or the Capitol Building, is the seat of the legislative branch of the United States federal government, which is formally known as the United States Congress. It is located on Capitol Hill ...
) is
:38.8897°, -77.0089°
In most systems, such as
OpenStreetMap, the degree symbols are omitted, reducing the representation to
38.8897,-77.0089
To calculate the D, M and S components, the following formulas can be used:
:
where
is the
absolute value of
and
is the
truncation function. Note that with this formula only
can be negative and only
may have a fractional value.
See also
*
ISO 6709 ''Standard representation of geographic point location by coordinates''
*
geo URI scheme
References
{{DEFAULTSORT:Decimal Degrees
Geographic data and information
Geographic coordinate systems