How to convert degrees, minutes and seconds to decimal
A DMS coordinate splits each degree into 60 minutes and each minute into 60 seconds, like a clock. To get decimal degrees, add the parts back together:
Decimal = Degrees + Minutes ÷ 60 + Seconds ÷ 3600, then make it negative for S or W.
Worked example
- Start with 40°42′46.08″N.
- Minutes: 42 ÷ 60 = 0.700000.
- Seconds: 46.08 ÷ 3600 = 0.012800.
- Add them: 40 + 0.7 + 0.0128 = 40.7128. North stays positive.
- For 74°00′21.60″W: 74 + 0 + 0.006 = 74.006, and West makes it −74.006.
Ways of writing DMS this converter understands
- Symbols: 40°42′46.08″N 74°00′21.60″W (prime marks or straight quotes)
- Letters: 40d 42m 46.08s N, 74d 0m 21.6s W
- Hemisphere first: N 40 42 46.08 W 74 0 21.6
- Signed numbers without letters: 40 42 46.08, -74 0 21.6
- Longitude written first, as long as it carries an E or W letter
Common mistakes
Minutes or seconds of 60 or more are not valid; the converter flags them instead of guessing. A missing hemisphere letter makes a western or southern point land on the wrong side of the world — check the marker on the map. Rounding seconds to whole numbers costs up to 15 metres; keep one or two decimals if the source has them.
Frequently asked questions
What is the formula for DMS to decimal degrees?
Decimal degrees = degrees + minutes/60 + seconds/3600. Use a negative sign for south latitudes and west longitudes.
Do I have to type the degree symbol?
No. Spaces, straight quotes, prime marks or the letters d, m and s all work, for example 40 42 46 N 74 0 22 W.
How many decimal places should I keep?
Five decimal places are about one metre on the ground, which is enough for most uses. Six or more only make sense for survey-grade data.