Decimal Degrees to DMS Converter
Geographic coordinates are written two main ways: as decimal degrees (for example 40.7128) used by GPS devices and mapping software, and as degrees, minutes, and seconds (40 degrees 42 minutes 46.08 seconds) used on nautical and topographic charts and in traditional surveying. This tool converts a decimal-degrees value into its degrees, minutes, and seconds parts. Enter a single coordinate value: a positive number for north latitude or east longitude, a negative number for south or west. The converter returns the whole degrees, whole minutes, and remaining seconds, along with the sign so you can read the hemisphere.
Decimal degrees to DMS formula
degrees = integer part of |decimal|
minutes = integer part of (fractional part * 60)
seconds = remaining fraction * 60
sign of decimal gives the hemisphere
Take the absolute value of the decimal coordinate. The whole-number part is the degrees. Multiply the leftover fraction by 60 to get minutes; the whole part of that is the minutes and the remainder, multiplied by 60 again, gives the seconds. The original sign is carried to the degrees so a negative input is read as south latitude or west longitude. There are 60 minutes in a degree and 60 seconds in a minute.
Worked example
Convert 40.7128 decimal degrees. The whole degrees are 40. The fraction 0.7128 times 60 is 42.768, so the minutes are 42. The leftover 0.768 times 60 is 46.08, so the seconds are 46.08. The result is 40 degrees, 42 minutes, 46.08 seconds. Because the input is positive, this is a north latitude (or east longitude); a value of -40.7128 would read the same magnitude but in the southern or western hemisphere.
Frequently asked questions
What are degrees, minutes, and seconds?
Degrees, minutes, and seconds (DMS) is a way of writing an angle, including a geographic coordinate, by dividing each degree into 60 minutes and each minute into 60 seconds, the same way an hour divides into minutes and seconds. It is the traditional format on charts and survey records, while decimal degrees is favoured by GPS and software.
How do I show the hemisphere?
The sign of the decimal value indicates the hemisphere: positive is north or east, negative is south or west. In DMS notation this is usually written as a letter (N, S, E, or W) after the value rather than a minus sign. This converter carries the sign onto the degrees so you can read which hemisphere applies.
Why convert between the two formats?
Different tools expect different formats. A GPS or web map typically uses decimal degrees, while a paper nautical chart, a topographic map, or a land-survey record often uses degrees, minutes, and seconds. Converting lets you transfer a position accurately between a device and a chart without misreading the coordinate.
How precise is one second of arc?
One second of latitude is about 30.9 metres on the ground, and one second of longitude is about 30.9 metres at the equator, shrinking toward the poles as meridians converge. So quoting seconds to two decimal places locates a point to well under a metre, which is finer than most handheld GPS accuracy.
Official sources
- NOAA National Geodetic Survey: coordinate systems and conversions.
- U.S. Geological Survey: how geographic coordinates are written.
Reviewed by the CalculatorHub team, edited by James Graham, 19 June 2026. See our methodology.