Decimal to DMS Converter
Decimal to DMS takes a signed coordinate into degrees, minutes and seconds, with the minus turned into a hemisphere letter and every rounding carried properly.
Degrees, minutes, seconds
- How it was read Read as a longitude, with the minus sign meaning west.
- -73.9857°, west, from the minus sign (decimal degrees)
- Decimal degrees Signed: negative is south of the equator or west of Greenwich. This is the form mapping software and spreadsheets expect, with no letter. 6 decimal places of a degree is 11.1 cm at the equator.
- -73.985700
- Degrees, minutes, seconds Rounded once, in units of the last second shown, and split afterward, so a value just under a whole minute carries into the minute instead of printing as 60". The letter carries the sign; a minus is not written as well.
- 73° 59' 08.52" W
- Degrees and decimal minutes The form most GPS receivers, chartplotters and marine charts use. A minute of latitude is about one nautical mile, which is why navigators keep the minutes.
- 73° 59.1420' W
- The arithmetic Already in degrees. Minutes are the fractional part times 60; seconds are the fractional minutes times 60.
- 73.9857
- What the input can resolve To keep that and invent nothing, write 4 decimal places of a degree, 1 of a second, or 3 of a minute. The 6 decimals shown above are exact arithmetic on what you typed, not extra accuracy. The digits past the 4th place describe nothing you measured.
- the nearest 0.0001 degrees, about 11.13 m
| Decimal places | One step | At the equator | Same step in seconds |
|---|---|---|---|
| 0 | 1° | 111.32 km | 3,600" |
| 1 | 0.1° | 11.13 km | 360" |
| 2 | 0.01° | 1.11 km | 36" |
| 3 | 0.001° | 111.32 m | 3.6" |
| 4 | 0.0001° | 11.13 m | 0.36" |
| 5 | 0.00001° | 1.11 m | 0.036" |
| 6 | 0.000001° | 11.1 cm | 0.0036" |
| 7 | 0.0000001° | 1.1 cm | 0.00036" |
| 8 | 0.00000001° | 1.11 mm | 0.000036" |
- Distances use the WGS 84 ellipsoid (EPSG::7030): equatorial radius 6,378,137 m exactly, inverse flattening 298.257223563. One degree along the equator is 2 x pi x 6,378,137 / 360 = 111,319.49 m.
- GPS.gov states that GPS-enabled smartphones are typically accurate to within a 4.9 m radius under open sky, so past the fifth decimal of a degree a phone reading is reporting digits, not position.
- Marks are written with the ASCII apostrophe and double quote rather than the prime symbols, because that is what pastes cleanly into mapping software and spreadsheets.
How the Degrees Minutes Seconds (DMS) Converter works
Going from decimal degrees to DMS is two multiplications by 60. Take -73.9857 as a longitude:
The sign says west, so set it aside and work with 73.9857. The whole part, 73, is the degrees. The fraction, 0.9857, times 60 is 59.142 minutes; the whole part, 59, is the minutes. What is left, 0.142, times 60 is 8.52 seconds. So the answer is 73° 59' 08.52" W.
The step that goes wrong is the last one: rounding the seconds. Seconds produced this way are usually a long decimal, and if a converter rounds them on their own after the split, any value that lands just under 60 rounds up to 60. That gives something like 73° 59' 60.00", which is not a valid angle and which some software rejects outright. The right way is to round the whole value once, in units of the smallest second you mean to show, and split afterward. Then 59.996" to two places carries correctly into the next minute, and if that minute was 59, into the next degree. This converter does exactly that, with exact fractions rather than floating point, so the carry is decided by the digits you typed and not by a binary approximation of them.
The sign needs the same care. A latitude of -0.25 is a quarter of a degree south. Put the minus on the degrees part and it disappears, because the degrees part is zero; written correctly it is 0° 15' 00.00" S. Once the coordinate has a letter there is no minus sign at all, and writing both (-73° 59' 08.52" W) is read by some people as a double negative. For a value with no letter, such as a bare -73.9857, you have to say whether it is a latitude or a longitude, because the same number would be S in one case and W in the other. If it is neither, choose plain angle and the sign stays on the front.
How many decimals of a second to show depends on the input, not on taste. -73.9857 has four decimal places, so it was rounded to the nearest 0.0001°, about 11 m at the equator. That is 0.36 of a second, so one decimal place of a second (0.1", about 3.1 m) is the fewest that preserve it, and two places invent a little. The result works this out for whatever you enter.
The same input also gives degrees and decimal minutes (73° 59.1420' W), which is what to type into most handheld GPS units and chartplotters.
Degrees Minutes Seconds (DMS) Converter FAQ
What is -73.9857 in degrees, minutes and seconds?
As a longitude, 73° 59' 08.52" W. 0.9857 x 60 = 59.142 minutes, and 0.142 x 60 = 8.52 seconds. The minus sign becomes the W.
Why should a converter never show 60 seconds?
Because seconds run from 0 up to but not including 60, exactly as on a clock. A 60 appears only when the seconds are rounded after the split. Rounding the total first and then splitting carries it into the minutes instead.
Does a negative decimal mean south or west?
It means south for a latitude and west for a longitude. The number alone does not say which it is, so the converter needs to know, or it can only give the angle with its sign.
How many decimal places of a second should I keep?
Match the input. Four decimal places of a degree is about 0.36 of a second, so one decimal place of a second keeps it. Six decimal places of a degree (about 0.0036 of a second) justifies two or three.