How this calculator works
Minutes and seconds are the sexagesimal parts of an angle: one degree is 60 minutes and one minute is 60 seconds. The calculator adds those parts as fractions of a degree. Every other readout comes from the same decimal degree value, so rounding one output never changes another. A negative angle carries its sign on the whole value.
Formula
decimal degrees = degrees + minutes / 60 + seconds / 3600. radians = degrees x pi / 180. gradians = degrees / 0.9. turns = degrees / 360. arcminutes = degrees x 60. arcseconds = degrees x 3600. milliradians = radians x 1000.
Worked example
51°30'26.64" is 51 + 30/60 + 26.64/3600 = 51.5074 degrees, or about 0.898974 radians. One radian is 57°17'44.81", which is about 57.2958 decimal degrees.
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Frequently asked questions
Why is a degree split into 60 rather than 100?
The sexagesimal system comes from Babylonian astronomy and remains standard for angles. Surveying, astronomy and navigation all use degrees, minutes and seconds.
How do I enter a negative angle?
Put the minus sign on the degrees field. Minutes and seconds always stay positive, and the minus sign applies to the combined angle, so -51 degrees 30 minutes means -51.5 degrees.
What is the difference between a gradian and a degree?
A right angle is 90 degrees but 100 gradians, so one gradian is exactly 0.9 degrees. Gradians are used in some European surveying work.