Degrees Minutes Seconds (DMS) Converter
Paste a coordinate in almost any form into the DMS converter. It says how it read it, converts it to all three notations with exact arithmetic, and tells you how many decimals the input supports.
Decimal degrees
- How it was read Latitude, then longitude, as the letters say.
- 40° 26' 46", north (degrees, minutes and seconds); 79° 58' 56", west (degrees, minutes and seconds)
- Decimal degrees Signed: negative is south of the equator or west of Greenwich. This is the form mapping software and spreadsheets expect, latitude first. 6 decimal places of a degree is 11.1 cm at the equator.
- 40.446111, -79.982222
- 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.
- 40° 26' 46.00" N, 79° 58' 56.00" 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.
- 40° 26.7667' N, 79° 58.9333' W
- Latitude, exactly Degrees + minutes/60 + seconds/3600, done in exact fractions. An ellipsis means the decimal never ends, which is the usual case for anything with seconds.
- 40 + 26/60 + 46/3600 = 40.446111111111...
- Longitude, exactly Degrees + minutes/60 + seconds/3600, done in exact fractions. An ellipsis means the decimal never ends, which is the usual case for anything with seconds.
- 79 + 58/60 + 56/3600 = 79.982222222222...
- What the input can resolve Taken from the less precise of the two values. To keep that and invent nothing, write 4 decimal places of a degree, 0 of a second, or 2 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 1 second, about 30.92 m
- A degree here On the WGS 84 ellipsoid at this latitude. Lines of longitude converge toward the poles, so a degree of longitude shrinks with the cosine of the latitude while a degree of latitude stays near 111 km. At this latitude the 6th decimal of a longitude is 8.5 cm.
- 111.04 km north-south, 84.84 km east-west
| Decimal places | One step | At the equator | Same step in seconds | East-west at this latitude |
|---|---|---|---|---|
| 0 | 1° | 111.32 km | 3,600" | 84.84 km |
| 1 | 0.1° | 11.13 km | 360" | 8.48 km |
| 2 | 0.01° | 1.11 km | 36" | 848.36 m |
| 3 | 0.001° | 111.32 m | 3.6" | 84.84 m |
| 4 | 0.0001° | 11.13 m | 0.36" | 8.48 m |
| 5 | 0.00001° | 1.11 m | 0.036" | 84.8 cm |
| 6 | 0.000001° | 11.1 cm | 0.0036" | 8.5 cm |
| 7 | 0.0000001° | 1.1 cm | 0.00036" | 8.48 mm |
| 8 | 0.00000001° | 1.11 mm | 0.000036" | 0.85 mm |
- 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
The conversion is one formula in each direction.
DMS to decimal degrees: decimal = degrees + minutes / 60 + seconds / 3600. For 40° 26' 46" that is 40 + 26/60 + 46/3600 = 40 + 0.433333... + 0.012777... = 40.446111... degrees. Make it negative if the letter is S or W.
Decimal degrees to DMS: take the whole degrees, multiply the fraction by 60 for minutes, take the whole minutes, multiply what is left by 60 for seconds. For 79.982222: 79 degrees; 0.982222 x 60 = 58.93333 minutes, so 58 minutes; 0.93333 x 60 = 56.0 seconds. So 79° 58' 56", and W if the decimal was negative.
Degrees and decimal minutes (DDM) stops halfway: 40° 26.7667' is 40 degrees plus 26.7667 minutes. It is what most GPS units and chartplotters display, and to get there from DMS you divide the seconds by 60 and add them to the minutes.
That is the whole method, and it is base-60 arithmetic of the kind clocks use: a degree is split into 60 minutes of arc and a minute into 60 seconds of arc, exactly as an hour is split into minutes and seconds. What goes wrong in practice is three details around the formula.
The first is rounding. 40.446111 is itself a rounded number, and converting it back gives 45.9996 seconds, not 46. A converter that splits first and rounds the seconds afterward prints that as 46.00. Give it something like 10.9999999, though, and it prints 10° 59' 60.00", which is not a valid angle. This converter rounds the whole value once, in units of the last decimal of a second it is going to show, and only then splits it into degrees, minutes and seconds, so a carry rolls up into the minute and the degree the way it should. It also does the arithmetic in exact fractions on the digits you typed rather than in floating point, so 46/3600 is held exactly and not as the nearest binary approximation.
The second is the sign. In decimal degrees south and west are negative; in DMS they are letters. A value like -0.5 is half a degree south or west, and if a converter attaches the minus to the degrees part alone it writes 0° 30', because zero has no sign. That quietly moves the point to the other side of the equator or the prime meridian. Here the sign belongs to the whole value, and on a coordinate it becomes the letter. A minus sign together with S or W is read once, not as a double negative; a minus with N or E is refused, since one of them must be a typo.
The third is precision, and it is the one that matters most when the number is a place. Each decimal place of a degree is a tenth of the last, and one degree along the equator is 111,319 meters on the WGS 84 ellipsoid (2 x pi x 6,378,137 m / 360). So four decimals is about 11 meters, five about 1.1 m, six about 11 cm. A second of arc is about 31 m and a minute about 1,855 m. The table under the result lays that out, and the result tells you how precise your input was and how many decimals keep it. Writing a one-second DMS coordinate as eight decimal places does not make it more accurate; it makes it look as if it were surveyed to the millimeter.
Those east-west figures shrink away from the equator, because meridians converge: a degree of longitude is about 111 km at the equator, about 85 km at 40°, and nothing at the pole. A degree of latitude stays between about 110.6 and 111.7 km everywhere, slightly longer near the poles because the earth is flattened. When a latitude is known the result gives both for that latitude.
The input is read forgivingly: marks or no marks, spaces or colons, the hemisphere letter before or after, typographic primes pasted from a document, and degrees with a decimal part on their own. It is strict where a reading would otherwise be a guess. Minutes or seconds of 60 or more are refused rather than carried silently, a decimal part on anything but the last number is refused because 40.5° 30' has no single meaning, and a latitude past 90° or a longitude past 180° is refused with the reason. Two plain numbers separated only by a space are read as degrees and minutes, not as a pair; separate a latitude and longitude with a comma.
It also works for angles that are not positions: a bearing, a telescope setting, a cut on a miter saw. Choose plain angle and it drops the hemisphere letters, keeps the sign, gives radians, and reduces anything past a full turn.
Degrees Minutes Seconds (DMS) Converter FAQ
How do I convert degrees minutes seconds to decimal degrees?
Divide the minutes by 60, divide the seconds by 3600, and add both to the degrees. 40° 26' 46" is 40 + 26/60 + 46/3600 = 40.446111. If the letter is S or W, make the result negative: 79° 58' 56" W is -79.982222.
How many decimal places should a latitude or longitude have?
Enough to match how it was measured. Five places is about 1.1 m at the equator and six about 11 cm. GPS.gov puts a phone's typical accuracy at about 4.9 m under open sky, so for a phone reading five decimals already carries more precision than the fix had. Surveying-grade equipment justifies more. The result shows what your own input supports.
What is the difference between DMS and DDM?
Both start with whole degrees. DMS then gives whole minutes and seconds (40° 26' 46"); DDM gives minutes with a decimal part and no seconds (40° 26.7667'). They describe the same point. DDM is what most handheld GPS units and marine charts use; DMS is common on paper maps and in land records.
Why does my converter show 60 seconds?
Because it rounded the seconds after splitting the angle up. 10.9999999° is 10° 59' 59.99964", and rounding only the seconds to two places gives 60.00". The correct answer is 11° 00' 00.00": round the whole value once and then split it, so the carry moves up into the minutes and degrees.
Is a minute of latitude really a nautical mile?
Approximately, and historically by design: the nautical mile was based on one minute of latitude. It is now defined as exactly 1,852 m, while a minute of latitude on WGS 84 varies from about 1,843 m at the equator to about 1,862 m at the poles. A minute of longitude is a nautical mile only at the equator and shrinks toward the poles.