What is the formula for DMS to decimal degrees?

Decimal = degrees + minutes / 60 + seconds / 3600. The result is then made negative if the hemisphere is south (S) or west (W).

How do the hemisphere letters affect the sign?

North (N) and east (E) give positive decimal values. South (S) and west (W) give negative values. The minus sign in decimal coordinates encodes exactly this.

Can minutes or seconds be 60 or more?

No. Minutes and seconds must each be in the range 0 to under 60, just like a clock. Sixty minutes equal one degree and sixty seconds equal one minute, so any value of 60 or more should be carried into the next unit.

How precise is the decimal output?

Decimal degrees are exact arithmetic from the inputs. About six decimal places gives roughly 0.1 metre resolution at the equator, which is more than enough for any consumer mapping use.

DMS to Decimal Lat/Lng Converter

This tool converts DMS coordinates — degrees, minutes and seconds with a hemisphere letter — into signed decimal latitude and longitude, the format expected by Google Maps, Leaflet, PostGIS and almost every mapping API. Enter 51°30'26.5" N, 0°7'39.9" W and get back 51.507361, -0.127750.

How it works

Each coordinate is rebuilt from its three sexagesimal parts:

decimal = degrees + (minutes / 60) + (seconds / 3600)

There are 60 minutes in a degree and 3600 seconds in a degree, so dividing by 60 and 3600 brings the smaller units back to fractions of a degree. The hemisphere letter then sets the sign: N and E stay positive, while S and W flip the value negative.

Tips and notes

Keep minutes and seconds below 60 — they behave like a clock. If a source gives you 90 seconds, that is one minute and 30 seconds, so carry the extra minute first. The conversion is pure arithmetic and runs entirely in your browser; nothing is sent anywhere. To reverse the process, use the Lat/Lng to DMS converter.