Degrees Minutes Seconds Calculator

The conversion

A degree divides into 60 minutes, and a minute into 60 seconds — the same sexagesimal system as clock time:

decimal = degrees + minutes/60 + seconds/3600

So 51° 28′ 40.2″ is 51 + 28/60 + 40.2/3600 = 51.4778°.

Going back, take the whole degrees, multiply the remainder by 60 for the minutes, and repeat for the seconds.

Signs and hemispheres

Decimal coordinates carry the hemisphere in the sign: north and east are positive, south and west negative. DMS usually carries it as a letter instead. Note that only the degrees take the sign — minutes and seconds are always positive magnitudes, so −33° 52′ 05″ means −33.8681°, not −33 + 52/60.

How many decimal places you need

At the equator one degree of latitude is about 111 km, so four decimal places locates something to roughly 11 metres and six places to about 11 centimetres. Longitude lines converge towards the poles, so a degree of longitude shrinks from 111 km at the equator to nothing at the pole — which is why five or six places is the practical limit for anything but survey work.

One arcminute of latitude is, by original definition, one nautical mile. That is not a coincidence: the nautical mile was defined that way.