Decimal degrees

The radius of the semi-major axis of the Earth at the equator is 6,378,137.0 metres (20,925,646.3 ft) resulting in a circumference of 40,075,016.7 metres (131,479,714 ft).^[3] 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 the equator. 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 the earth 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 0.3 metres (1 ft 0 in) because the earth is an oblate 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 the United States Capitol) 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:

${\displaystyle {\begin{aligned}\mathrm {D} &=\operatorname {trunc} (\mathrm {D} _{\text{dec}},0)\\\mathrm {M} &=\operatorname {trunc} (60\times |\mathrm {D} _{\text{dec}}-\mathrm {D} |,0)\\\mathrm {S} &=3600\times |\mathrm {D} _{\text{dec}}-\mathrm {D} |-60\times \mathrm {M} \end{aligned}}}$ 

where ${\textstyle \mathrm {\left\vert D_{dec}-D\right\vert } }$  is the absolute value of ${\textstyle \mathrm {D_{dec}-D} }$  and ${\textstyle \mathrm {trunc} }$  is the truncation function. Note that with this formula only ${\textstyle \mathrm {D} }$  can be negative and only ${\textstyle \mathrm {S} }$  may have a fractional value.

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