What this calculator does
Coordinates come in two forms and mapping tools disagree about which to use. Degrees, minutes and seconds is the traditional form, dividing each degree into 60 minutes and each minute into 60 seconds. Decimal degrees puts the whole thing after one decimal point, which is what most software and APIs expect.
Converting to decimal is straightforward: divide the minutes by 60, the seconds by 3,600, and add both to the degrees. Going back is a division with remainders. The part to watch is the sign, which belongs to the degrees alone: in a southern or western coordinate the whole value is negative, not just the degrees part.
The formula
To decimal degrees, the minutes are divided by 60 and the seconds by 3,600 and both added to the whole degrees, with the sign taken from the degrees. To DMS, the whole part of the absolute value gives the degrees, the fractional part multiplied by 60 gives the minutes, and what remains multiplied by 60 again gives the seconds. The radian equivalent is included because that is what trigonometric functions need.
| Term | Meaning |
|---|---|
| DMS | Degrees, minutes and seconds, written like 40° 42′ 46.08″. |
| Decimal degrees | The same angle as a single number, 40.7128, which is what most software expects. |
| Arcminute | A sixtieth of a degree. One arcminute of latitude is one nautical mile. |
| Arcsecond | A sixtieth of an arcminute. About 31 metres of latitude on the ground. |
The inputs explained
| Field | What to enter |
|---|---|
| Direction | Which direction to convert. The result lines change to match, so read the output for the direction you chose. |
| Decimal degrees | The decimal degrees value, used when converting to DMS. Negative for south or west. |
| Degrees | The degrees part, used when converting from DMS. This is where the sign goes for a southern or western coordinate. |
| Minutes | The minutes part, from 0 to 59. Always entered positive. |
| Seconds | The seconds part, from 0 to 59.99. Always entered positive. |
When to use it
Feeding a coordinate into mapping software
Most mapping APIs and GIS tools take decimal degrees, while coordinates printed on charts, deeds and older maps are in DMS. Converting is the routine first step.
Reading a coordinate off a chart
Nautical and aviation charts use degrees and minutes, often with decimal minutes rather than seconds, and getting them into a consistent form is necessary before doing anything with them.
Checking a coordinate for a sign error
A southern or western coordinate entered as positive lands in the wrong hemisphere entirely, which is the single most common coordinate mistake and one a conversion step tends to surface.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
What do decimal degrees look like in DMS?
Four decimal coordinates converted into degrees, minutes and seconds.
| Decimal degrees | DMS | Degrees | Minutes | Seconds |
|---|---|---|---|---|
| 40.7128 | 40° 42′ 46.08″ | 40 | 42 | 46.08 |
| 0.5 | 0° 30′ 0.00″ | 0 | 30 | 0.00 |
| -33.8688 | −33° 52′ 7.68″ | -33 | 52 | 7.68 |
| 90 | 90° 0′ 0.00″ | 90 | 0 | 0.00 |
What do DMS coordinates look like in decimal?
Three DMS coordinates converted into decimal degrees.
| Minutes entered | Decimal degrees | DMS entered | In radians |
|---|---|---|---|
| 0′ | 40.0128 | 40° 0′ 46.08″ | 0.698355 |
| 15′ | 40.2628 | 40° 15′ 46.08″ | 0.702718 |
| 30′ | 40.5128 | 40° 30′ 46.08″ | 0.707082 |
| 42′ | 40.7128 | 40° 42′ 46.08″ | 0.710572 |
| 59′ | 40.9961 | 40° 59′ 46.08″ | 0.715518 |
Questions
How do I convert DMS to decimal degrees?
Divide the minutes by 60, divide the seconds by 3,600, and add both to the degrees. For 40° 42′ 46.08″ that is 40 plus 0.7 plus 0.0128, giving 40.7128. Keep the sign on the degrees and apply it to the whole result.
Where does the minus sign go for southern or western coordinates?
On the whole value, which in practice means on the degrees. Minutes and seconds are always entered positive. A coordinate of 33° 52′ 7.68″ south is −33.8688 in decimal, not −33 plus positive minutes.
How precise is one arcsecond on the ground?
About 31 metres of latitude, since a degree of latitude is roughly 111 km and there are 3,600 arcseconds in a degree. Longitude arcseconds shrink towards the poles, being full size only at the equator.
How many decimal places should I keep?
Four decimal places gives about 11 metres of precision, which is enough for most mapping. Five gives about a metre, six about 10 centimetres. Carrying more than six is almost always false precision given the accuracy of the underlying position.
For angle units beyond coordinates, see the angle converter. For distances on the ground, see the length converter.