Three ways to write one place
| Format | Latitude | Longitude | Used by |
|---|---|---|---|
| Degrees, minutes, seconds (DMS) | 40° 44′ 54.36″ N | 73° 59′ 8.36″ W | Paper charts, surveying, signs and plaques |
| Degrees and decimal minutes (DDM) | 40° 44.906′ N | 73° 59.139′ W | Marine and aviation GPS, geocaching |
| Decimal degrees (DD) | 40.748433 | -73.985656 | Web maps, software, data files, URLs |
A degree is split into 60 minutes of arc and each minute into 60 seconds, the same sexagesimal habit as a clock. Decimal degrees drop the subdivisions and carry the fraction after the point, with the hemisphere as a sign: north and east positive, south and west negative. The angle converter converts between degrees, minutes and seconds and decimal degrees for any angle, which is exactly this operation.
Converting by hand
Decimal = degrees + minutes ÷ 60 + seconds ÷ 3,600. Negative for S and W.
DMS from decimal: the whole number is the degrees; the fraction × 60 gives the minutes; the fraction of that × 60 gives the seconds.
Forward: 40° 44′ 54.36″ = 40 + 44 ÷ 60 + 54.36 ÷ 3,600 = 40.748433. Back: 40.748433 has 40 whole degrees; 0.748433 × 60 = 44.9060 minutes, so 44 minutes; 0.9060 × 60 = 54.36 seconds. The most common slip is treating minutes as hundredths: 40° 30′ is 40.5, not 40.3.
Order, signs and the swapped-pair trap
By convention latitude is written first. Latitude runs from −90° at the South Pole to +90° at the North Pole and longitude from −180° to +180° from the Greenwich meridian, so any value beyond ±90 must be a longitude, which exposes most swapped pairs. Software disagrees on order more than people do: most mapping sites take latitude, longitude, while some data formats store longitude, latitude as x, y. The distance between cities calculator and the sunrise and sunset calculator accept pasted decimal coordinates in the latitude, longitude order; the time zone converter is the next step once a longitude has told you roughly which zone a place is in.
What each decimal place is worth
A nautical mile is one minute of latitude, exactly 1,852 metres by NOAA's definition, so a degree of latitude is 111,120 metres and each decimal place of a decimal-degree latitude is worth a tenth of the previous one:
| Decimal places | Latitude step | Locates |
|---|---|---|
| 0 | 111 km | A country or large state |
| 1 | 11 km | A city |
| 2 | 1.11 km | A town or district |
| 3 | 111 m | A street |
| 4 | 11 m | A building |
| 5 | 1.11 m | A doorway |
| 6 | 0.11 m | A person |
USGS gives the same picture in DMS: one second of latitude is about 101 feet. Longitude is different, because the meridians converge: USGS puts a degree of longitude at 54.6 miles at 38° north against 69 miles for a degree of latitude, and a second of longitude at 80 feet there, shrinking further toward the poles. Six decimal places is as much as any consumer GPS can justify; more digits are copied noise.
Coordinates inside photos
A phone writes the location of a photo into its EXIF metadata as degrees, minutes and seconds stored as fractions, with separate N/S and E/W reference fields, which viewers then show in whichever format they prefer. The EXIF viewer and remover shows those fields, converts them to decimal degrees for a map link, and strips them before a photo is shared, which is the one case where the precision of the sixth decimal place is a liability rather than a feature.
Frequently asked questions
What is the difference between DMS and decimal degrees?
They are two ways of writing the same angle. Degrees, minutes and seconds split each degree into 60 minutes and each minute into 60 seconds, like a clock; decimal degrees write the fraction of a degree after a decimal point. 40° 44′ 54.36″ N and 40.748433 are the same latitude. Charts, surveying and older GPS units favour DMS; software and web maps use decimal degrees.
How do I convert degrees, minutes and seconds to decimal?
Degrees plus minutes divided by 60 plus seconds divided by 3,600. For 40° 44′ 54.36″: 40 + 44 ÷ 60 + 54.36 ÷ 3,600 = 40.748433. For south latitudes and west longitudes the decimal value is negative.
Which number is latitude and which is longitude?
Latitude comes first by convention and runs from −90 at the South Pole to +90 at the North Pole; longitude runs from −180 to +180, measured from the Greenwich meridian, west negative. A value above 90 can only be a longitude, which catches most swapped pairs. In DMS the letters N, S, E and W make it explicit.
How accurate is a coordinate with five decimal places?
About a metre in latitude. One degree of latitude is 60 nautical miles, 111,120 metres, so each decimal place divides that by ten: the fifth place is worth 1.11 metres. USGS gives one second of latitude as about 101 feet, and the sixth decimal place as the one that locates to a few inches.
Why are longitude distances shorter than latitude distances?
Because the meridians converge toward the poles. USGS gives one degree of latitude as about 69 miles everywhere, but one degree of longitude as 54.6 miles at 38° north and shrinking to nothing at the pole. A coordinate's precision in metres therefore depends on where it is, for the east-west part.
Sources
- USGS: How much distance does a degree, minute, and second cover on your maps? (one degree of latitude about 69 miles, one minute about 1.15 miles, one second 101 feet; one degree of longitude 54.6 miles at 38° north, one second 80 feet; longitude distances vary greatly toward the poles)
- NOAA National Ocean Service: nautical mile and knot (one nautical mile equals one minute of latitude, exactly 1.852 km)