Latitude and longitude
Latitude measures north or south of the equator, from 0° at the equator to 90° at each pole. Lines of equal latitude run east to west around the globe. Longitude measures east or west of the prime meridian through Greenwich, England, from 0° to 180°. Lines of equal longitude run from pole to pole.
By convention latitude is written first. So 40.7128, -74.0060 means 40.7128° north and 74.0060° west, which is lower Manhattan. One exception catches programmers: GeoJSON and some mapping libraries write longitude first.
The three formats
In decimal degrees, south latitudes and west longitudes are negative. In the other two formats, the letters N, S, E and W carry the direction and the numbers stay positive. Mixing the two, such as writing -74° W, is a common way to end up on the other side of the world.
| Format | Example | Where you see it |
|---|---|---|
| Decimal degrees (DD) | 40.71280, -74.00600 | Google Maps, apps, spreadsheets, web forms |
| Degrees, minutes, seconds (DMS) | 40°42'46.1" N, 74°00'21.6" W | Paper maps, aviation, property deeds |
| Degrees, decimal minutes (DDM) | 40°42.768' N, 74°00.360' W | Boating, geocaching, many handheld GPS units |
Converting decimal degrees to DMS
Take 40.71280. The whole number, 40, is the degrees. Multiply the decimal part by 60: 0.71280 × 60 = 42.768. The whole number, 42, is the minutes. Multiply the remaining decimal by 60 again: 0.768 × 60 = 46.08, which rounds to 46.1 seconds. Result: 40°42'46.1".
For DDM, stop after the first step: 40°42.768'. For a negative decimal, do the arithmetic on the positive number and add S or W at the end.
Converting DMS to decimal degrees
Divide the minutes by 60 and the seconds by 3,600, then add them to the degrees. For 74°00'21.6" W: 0 ÷ 60 = 0, 21.6 ÷ 3,600 = 0.006, so 74.006. Because it is west, write -74.00600.
Our coordinates tool shows your position in both DD and DMS, so you can check your working against a known point.
How precise do the numbers need to be?
One degree of latitude is about 111 kilometres. Each extra decimal place divides that by ten, so five decimal places is about 1.1 metres, already finer than a phone can measure. In DMS, one second of latitude is about 31 metres, and a tenth of a second about 3 metres.
Longitude degrees shrink towards the poles, because the meridians converge. At the latitude of the US-Canada border, a degree of longitude is about 73 kilometres rather than 111.
Other systems you may meet
- UTM divides the world into 60 zones and gives positions in metres east and north within a zone. Common on topographic maps and in search and rescue.
- MGRS is the military grid built on UTM, used by the US armed forces and NATO.
- Plus Codes are short letter-and-number codes with a plus sign in the middle, from Google's Open Location Code, used where streets have no addresses.
- Datums: GPS and web maps use WGS 84. Older US maps may use NAD 27, which can put the same coordinates tens of metres away.