DMS to Decimal Degrees Converter

In short Decimal degrees = degrees + minutes ÷ 60 + seconds ÷ 3600, with the result made negative for south and west. So 51° 30′ 26.6″ N is 51 + 30÷60 + 26.6÷3600 = 51.507389, and 0° 7′ 40.1″ W is −0.127806. The conversion is exact in both directions and loses nothing, because DMS and decimal degrees are two spellings of the same quantity rather than two different grids. Two mistakes account for most bad data. The first is using both a minus sign and a hemisphere letter: −51.5074° N is a contradiction, since the minus IS the S. The second is over-precision. A decimal place of latitude is worth a fixed distance anywhere on earth — one place is 11.1 km, four places is 11.1 m, six places is 111 mm, and eight places is about a millimetre. Consumer GPS is accurate to a few metres at best, so any coordinate written with more than six decimal places is recording the rounding error of a floating-point number rather than a better position. Longitude behaves differently: a degree of longitude shrinks from 111 km at the equator to nothing at the poles, so the same number of decimal places buys less distance the further north or south you go.