This articleneeds additional citations forverification. Please helpimprove this article byadding citations to reliable sources. Unsourced material may be challenged and removed. Find sources: "Decimal degrees" – news ·newspapers ·books ·scholar ·JSTOR(July 2017) (Learn how and when to remove this message)

Decimal degrees (DD) is a notation for expressinglatitude andlongitudegeographic coordinates asdecimal fractions of adegree. DD are used in manygeographic information systems (GIS),web mapping applications such asOpenStreetMap, andGPS devices. Decimal degrees are an alternative to using degrees-minutes-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 thePrime Meridian; 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 [54.5798, −3.5820]. The appropriate decimal places are used,^[1] negative values are given using ahyphen-minus character.^[2] The designation of a location as, for example [54.1855, −2.9857] means that it is potentially computer searchable and that it can be located by a generally (open) referencing system such asGoogle Earth orOpenStreetMap. Four decimal places is usually sufficient for most locations, although for some sites, for examplesurface exposure dating, five or even six decimal places should be used.

The [dLL] format can be used within publications to specify points or features of interest and withinremote sensing to identifyground truth locations withinDigital Earth and complying within theFAIR data principles. The format can also be used as a starting point for a traverse or transect.^[3] With the increase in scientific papers needing to be searched for words, terms, phrases, authors and data, the [dLL] format can be used to link terms to author name (and byORCID), place-label location and journal or publication.^[4]

The radius of thesemi-major axis of theEarth at theequator is 6,378,137.0 metres (20,925,646.3 ft) resulting in acircumference of 40,075,016.7 metres (131,479,714 ft).^[5] The equator is divided into 360 degrees of longitude, so each degree at the equator represents 111,319.5 metres (365,221 ft). 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 11.1 metres (36 ft) at theequator. A value in decimal degrees to 5 decimal places is precise to 1.11 metres (3 ft 8 in) at the equator. Elevation also introduces a small error: at 6,378 metres (20,925 ft) elevation, the radius and surface distance is increased by 0.001 or 0.1%. Because theearth 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, ameridian 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 0.3 metres (1 ft 0 in) because the earth is anoblate spheroid.

A DMS value is converted to decimal degrees using the formula:

${\displaystyle {\mathrm{D}}_{\text{dec}}=\mathrm{D}+\frac{\mathrm{M}}{60}+\frac{\mathrm{S}}{3600}}$

For instance, the decimal degree representation for

38° 53′ 23″ N, 77° 00′ 32″ W

(the location of theUnited States Capitol) is

38.8897°, −77.0089°

In most systems, such asOpenStreetMap, 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$\left|{\mathrm{D}}_{\mathrm{d}\mathrm{e}\mathrm{c}}-\mathrm{D}\right|$ is theabsolute value of${\mathrm{D}}_{\mathrm{d}\mathrm{e}\mathrm{c}}-\mathrm{D}$ and$\mathrm{t}\mathrm{r}\mathrm{u}\mathrm{n}\mathrm{c}$ is thetruncation function. Note that with this formula only$\mathrm{D}$ can be negative and only$\mathrm{S}$ may have a fractional value.

• ISO 6709Standard representation of geographic point location by coordinates
• geo URI scheme

• Geographic data and information
• Geographic coordinate systems

• Articles with short description
• Short description is different from Wikidata
• Articles needing additional references from July 2017
• All articles needing additional references