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DMS to Decimal Converter
Use this DMS to decimal converter to turn degrees, minutes and seconds into decimal degrees, the format maps and GPS apps use. Enter a latitude and a longitude, pick the hemisphere for each, and get the decimal result with a copy-ready "lat, lon" string — or switch to reverse mode to turn decimal degrees back into DMS.
Latitude
Longitude
Latitude degrees run 0–90 and longitude degrees run 0–180. Minutes and seconds run 0–59.999.
How it works
A position on Earth is written with two angles: latitude, the angle north or south of the equator, and longitude, the angle east or west of the prime meridian, which runs through Greenwich in London. The old way to write these angles is degrees, minutes and seconds (DMS). One degree is divided into 60 minutes, and one minute into 60 seconds — the same 60-based split used for time, because both come from the ancient Babylonian habit of counting in sixties.
Modern maps, GPS apps and mapping software prefer decimal degrees, where the whole angle is one plain number. Converting DMS to decimal is a matter of turning the minutes and seconds into fractions of a degree: divide the minutes by 60 and the seconds by 3600, then add both to the degrees. North and east stay positive; south and west become negative, so the letter is replaced by a minus sign.
Converting back works in reverse. The whole number in front of the decimal point is the degrees. Multiply what is left by 60: the whole number of that result is the minutes. Multiply what is left after that by 60 again, and you have the seconds. A positive latitude means north and a negative one means south; a positive longitude means east and a negative one means west.
Latitude can never be larger than 90 degrees — that is the North or South Pole — and longitude can never be larger than 180 degrees, which is the line opposite the prime meridian in the Pacific Ocean. Minutes and seconds must each be under 60, because 60 minutes make a whole degree. This converter checks all of those limits and tells you plainly if a value is out of range, instead of giving a wrong answer.
Worked example
The Statue of Liberty in New York stands at 40° 41′ 21″ N, 74° 2′ 40″ W. Convert that position to decimal degrees.
Step 1: Convert the latitude. 41 minutes ÷ 60 = 0.683333, and 21 seconds ÷ 3600 = 0.005833. Add them to 40 degrees: 40 + 0.683333 + 0.005833 = 40.689167. North stays positive.
Step 2: Convert the longitude. 2 minutes ÷ 60 = 0.033333, and 40 seconds ÷ 3600 = 0.011111. Add them to 74 degrees: 74 + 0.033333 + 0.011111 = 74.044444. West becomes negative, so the result is −74.044444.
Step 3: Write the pair as maps expect it, latitude first: 40.689167, -74.044444.
Step 4: Check the reverse. 40.689167 has 40 whole degrees; 0.689167 × 60 = 41.35, so 41 minutes; 0.35 × 60 = 21, so 21 seconds — back to 40° 41′ 21″ N.
Try it yourself: enter latitude 40° 41′ 21″ N and longitude 74° 2′ 40″ W, and press Calculate. The tool gives exactly the same answer — 40.689167, -74.044444. Switch to reverse mode and enter 40.689167 to see it turn back into 40° 41′ 21″ N.
FAQ
What is DMS in coordinates?
DMS stands for degrees, minutes and seconds, the traditional way of writing a position on Earth. One degree is split into 60 minutes, and one minute is split into 60 seconds, just like time. A latitude of 40 degrees, 41 minutes and 21 seconds north is written 40 degrees 41 minutes 21 seconds N. It is the format you see on paper maps, survey documents and older GPS devices.
How do you convert DMS to decimal degrees?
Divide the minutes by 60 and the seconds by 3600, then add both to the degrees. For 40 degrees, 41 minutes and 21 seconds: 41 divided by 60 is 0.683333, and 21 divided by 3600 is 0.005833, so the total is 40.689167 degrees. North and east stay positive, while south and west become negative, so 74 degrees, 2 minutes and 40 seconds west becomes -74.044444.
How do you convert decimal degrees back to DMS?
Take the whole number as the degrees, multiply the decimal part by 60 to get the minutes, then multiply the remaining decimal part by 60 again to get the seconds. For 40.689167, the degrees are 40, the decimal 0.689167 times 60 is 41.35, so the minutes are 41, and 0.35 times 60 is 21, so the seconds are 21. The result is 40 degrees, 41 minutes and 21 seconds, with N for a positive latitude or S for a negative one.
Why are west and south coordinates negative?
Decimal coordinates use a sign instead of a letter to show direction. Latitude is measured from the equator, so north is positive and south is negative. Longitude is measured from the prime meridian in Greenwich, so east is positive and west is negative. That is why New York, which is west of Greenwich, has a negative longitude, while London, which is just east of the prime meridian, has a small positive one.
How many decimal places do I need for an accurate location?
Six decimal places are enough for almost everything, and that is what this converter shows. Five decimal places pin a spot down to about 1 metre, and six decimal places to about 11 centimetres. More digits look more precise but do not help in practice, because consumer GPS is only accurate to a few metres. For a street address or a landmark, four or five decimal places are usually plenty.