Convert between angle units
Angles come in several units, and switching between them trips people up. This calculator converts any value among degrees, radians, and gradians, and also shows the angle as turns and as a multiple of pi. Enter a value, pick its unit, and read all the equivalents.
The conversions
A full circle is 360 degrees, 2 pi radians, 400 gradians, or 1 turn. So radians = degrees times pi over 180, gradians = degrees times 10 over 9, and turns = degrees over 360. The tool first converts your input to degrees, then fans out to the rest.
When each unit is used
Degrees are everyday and navigational. Radians are the natural unit for calculus and the trig functions, since arc length equals radius times angle in radians. Gradians divide the right angle into 100 parts and appear in surveying.
Related tools
To evaluate trig functions at your angle, use the trig function calculator; for arc length from a radius and angle, the arc length calculator.
Worked example
180 degrees equals pi radians (about 3.14159), 200 gradians, and 0.5 of a turn — a straight angle, half a full circle.
FAQ
Why are radians a multiple of pi?
Because a full circle is 2 pi radians, common angles land on neat fractions of pi — 90 degrees is pi over 2, 60 degrees is pi over 3, and so on.
What is a gradian?
One hundredth of a right angle, so 100 gradians make 90 degrees. It is used mainly in surveying and some engineering.