Degrees Minutes Seconds to Decimal Degrees Calculator
MathConvert an angle from degrees, minutes, and seconds (DMS) format to decimal degrees.
Decimal Degrees
The angle as a single decimal degree value. South and west come out negative.
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SponsoredTo convert DMS to decimal degrees, add the degrees, the minutes divided by 60, and the seconds divided by 3,600 (decimal = degrees + minutes/60 + seconds/3,600). This calculator does it instantly: 30° 30′ 36″ becomes 30.51°.
Decimal degrees put each coordinate in one number, which spreadsheets and most formulas need, while latitude and longitude are traditionally written in degrees, minutes, and seconds. The minutes box also accepts decimals, so degrees and decimal minutes (DDM) such as 41° 24.2028′ convert too. For a coordinate, pick N, S, E, or W as the direction: south latitudes and west longitudes come out negative, so 33° 52′ 7.68″ S becomes -33.8688.
Quick answer: 0° 30′ 0″ = 0.5°, 1° 15′ 0″ = 1.25°, 12° 20′ 42″ = 12.345°, and 45° 45′ 45″ = 45.7625°.
This page covers DMS to decimal degrees only. The related converters below handle the reverse direction and single unit conversions such as arcminutes to degrees.
DMS to Decimal Formula
The formula is: decimal degrees = degrees + minutes ÷ 60 + seconds ÷ 3,600. The sign applies to the whole value, not just the degrees: -30° 30′ 36″ is -(30 + 0.5 + 0.01) = -30.51°.
Worked example: 40° 42′ 46.08″ N = 40 + 42/60 + 46.08/3,600 = 40.7128°.
Most calculators take one decimal angle, not three DMS parts: the Sine Calculator, the Cosine Calculator, and the Rotation Calculator each take a single decimal angle, so convert here first.
How to Convert DMS to Decimal Degrees
- Divide the minutes by 60: 42′ ÷ 60 = 0.7.
- Divide the seconds by 3,600: 46.08″ ÷ 3,600 = 0.0128.
- Add both to the whole degrees: 40 + 0.7 + 0.0128 = 40.7128.
- Make the result negative for S or W: 74° 0′ 21.6″ W becomes -74.006.
Degrees and Decimal Minutes (DDM) to Decimal Degrees
Coordinates are sometimes written as degrees and decimal minutes, such as 41 24.2028, and Google Maps accepts that format, calling it DMM. Enter 41 as the degrees, 24.2028 as the minutes, and 0 as the seconds: 41 + 24.2028/60 = 41.40338. The same formula works because the seconds are already folded into the decimal minutes.
Converting DMS Coordinates in a Spreadsheet
With degrees, minutes, and seconds in cells A1, B1, and C1, the formula =A1+B1/60+C1/3600 returns decimal degrees. Wrap it as =-(ABS(A1)+B1/60+C1/3600) for a south or west coordinate so the sign applies to the whole value.
DMS to Decimal Degrees Table
Common DMS values and their decimal equivalents:
| DMS | Decimal Degrees |
|---|---|
| 0° 30′ 0″ | 0.5° |
| 1° 15′ 0″ | 1.25° |
| 12° 20′ 42″ | 12.345° |
| 30° 30′ 36″ | 30.51° |
| 45° 45′ 45″ | 45.7625° |
| 40° 42′ 46.08″ N | 40.7128° |
| 74° 0′ 21.6″ W | -74.006° |
| 33° 52′ 7.68″ S | -33.8688° |
Converting GPS Coordinates to Decimal Degrees
Google Maps accepts decimal degrees, DMS, and DDM, but spreadsheets, GIS files, and most formulas need one decimal number per coordinate, so a coordinate copied from a printed source is usually converted to decimal first. Keep latitude first, between -90 and 90, and longitude second, between -180 and 180. A converter with no direction setting will put a western longitude in the wrong hemisphere unless the minus sign is typed.
The Sector Area Calculator also takes its angle in decimal degrees, and the Scientific Calculator is handy for checking the minutes ÷ 60 and seconds ÷ 3,600 steps by hand.
Frequently Asked Questions
How do you convert DMS to decimal degrees?
Add the degrees, the minutes divided by 60, and the seconds divided by 3,600. For example, 30° 30′ 36″ = 30 + 0.5 + 0.01 = 30.51°.
How do I handle south and west coordinates?
Convert the positive value, then make the whole result negative. 33° 52′ 7.68″ S is -33.8688, not -33 plus the minutes and seconds. Choose S or W as the direction above and enter positive numbers: the letter sets the sign, so a minus sign is not needed as well.
How do I enter a negative angle smaller than 1 degree?
Enter 0 degrees and put the minus sign on the minutes or seconds instead, for example 0, -30, 0 for -0° 30′ 0″, which gives -0.5. Any minus sign makes the whole value negative.
Why did my conversion give the wrong answer for a negative degree?
Adding positive minutes and seconds to a negative degree value shrinks it instead of growing it: -30 + 0.51 = -29.49, which is wrong. The minutes and seconds belong to the same side as the degrees, so the correct result is -30.51.
Can minutes or seconds be 60 or more?
Not in standard notation. Minutes and seconds each run from 0 to 59.99, and 60 of them roll over into the next unit, just like minutes on a clock.
Can I convert decimal degrees back to DMS?
Yes. Use the Decimal Degrees to DMS Calculator, which also shows the N, S, E, or W direction for coordinates.
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