DMS to Decimal Degrees Converter
Charts, surveys and aviation often quote coordinates in degrees, minutes and seconds (DMS), while GPS devices and web maps use decimal degrees. This converter takes the degrees, minutes and seconds and a hemisphere sign, then returns the decimal degrees value. The conversion is exact: there are 60 arc-minutes per degree and 3,600 arc-seconds per degree. Enter 1 in the sign field for North or East, and -1 for South or West, so the result carries the right sign for mapping software.
DMS to decimal degrees formula
Decimal degrees = sign * (degrees + minutes / 60 + seconds / 3,600)
Total arc-seconds = degrees * 3,600 + minutes * 60 + seconds
sign = 1 for North or East, -1 for South or West
The conversion is exact because the relationship between degrees, minutes and seconds is defined, not measured. The total arc-seconds figure is a handy cross-check.
DMS context
- One degree contains 60 arc-minutes; one arc-minute contains 60 arc-seconds.
- North and east are positive; south and west are negative decimal degrees.
- Latitude degrees run 0 to 90; longitude degrees run 0 to 180.
- One arc-second of latitude is roughly 31 meters on the ground.
- GPS and web maps expect decimal degrees, making DMS conversion a frequent need.
DMS conversion: frequently asked questions
How do you convert DMS to decimal degrees?
Decimal degrees equal the degrees plus the minutes divided by 60 plus the seconds divided by 3,600. For example 40 degrees 26 minutes 46 seconds equals 40 + 26/60 + 46/3600, about 40.4461 degrees. South and west values are then made negative.
Why divide minutes by 60 and seconds by 3,600?
There are 60 arc-minutes in one degree and 60 arc-seconds in one arc-minute, so 3,600 arc-seconds in one degree. Dividing each unit by its size relative to a degree converts the sexagesimal parts into a single decimal degree value.
How do hemispheres affect the sign?
North latitude and east longitude are positive; south latitude and west longitude are negative. This converter has a hemisphere selector input (enter 1 for North or East, and -1 for South or West) that sets the sign of the final decimal value.
What range should each part fall in?
Degrees range from 0 to 90 for latitude or 0 to 180 for longitude. Minutes and seconds each range from 0 up to (but not including) 60. Values outside these ranges usually indicate a typo, though the math still computes.
Where is DMS still used?
Degrees, minutes and seconds remain common in navigation charts, surveying, aviation, and many printed maps. GPS devices and web mapping use decimal degrees, so converting between the two is a frequent task.
Official sources
- U.S. Geological Survey: U.S. Geological Survey.
- NOAA National Geodetic Survey: National Geodetic Survey.
Reviewed by the CalculatorHub team, edited by James Graham, 17 June 2026. See our methodology.