Decimal degrees

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Decimal degrees (DD) 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° each.

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.

Contents 1 Accuracy 2 Example 3 Conversion from DMS 4 References

[edit] Accuracy

The radius of the semi major axis of the earth ie at the equator is 6,378,160.0 meters^[1] resulting in a circumference of 40,075,161.2 metres. The equator is divided into 360 degrees of longitude, so each degree represents 111,319.9 metres or approximately 111 km. Consequently the number of decimal places required for a particular accuracy at the equator is:

Accuracy versus decimal places

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. A value in decimal degrees to 5 decimal places is accurate to 1.11 meter at the equator. Because the earth is a spheroid and 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.

[edit] Example

The decimal degree representation of the location of the United States Capitol 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".

[edit] Conversion from DMS

With DMS, the location of the United States Capitol is "38° 53' 23" N, 77° 00' 32" W". A DMS value is converted to decimal degrees using the formula (D + M/60 + S/3600). Thus the decimal degree representation of "38° 53' 23" N, 77° 00' 32" W" is "38.889722°, -77.008889°", as shown above in the example.

[edit] References