Work out degrees minutes seconds converter instantly with clear inputs, formula shown and shareable results.
Degrees, minutes and seconds are a sexagesimal system: sixty seconds to the minute and sixty minutes to the degree. So 45 degrees 22 minutes 30 seconds is 45.375 degrees, or 0.79195 radians. The negative case applies the sign to the whole angle rather than to each component, which is the convention for latitude and longitude.
Decimal degrees
DD = degrees + minutes/60 + seconds/3600
Radians
rad = degrees x pi / 180
Enter the degrees as negative. The sign is applied to the total, so -33 degrees 52 minutes reads as -33.8667 rather than -33 plus 52 minutes.
It descends from Babylonian mathematics, which used base 60 because it divides evenly by 2, 3, 4, 5 and 6 - convenient before decimals existed.