Angle Unit Converter
Convert an angle between degrees, radians, gradians and full turns instantly, in either direction.
How it works
radians = degrees · π/180 · gradians = degrees ÷ 0.9 · turns = degrees ÷ 360
A full circle can be measured as 360 degrees, 2π radians, 400 gradians or 1 turn. Degrees are the everyday unit; radians are the natural unit for calculus and trigonometry because arc length equals radius times angle only in radians; gradians (or gon) divide the right angle into 100 parts and appear in surveying. This converter routes any input through degrees and outputs all four units.
Worked example
Starting from 90°: radians = 90·π/180 = 1.5708 rad, gradians = 90 ÷ 0.9 = 100 gon, and turns = 90 ÷ 360 = 0.25 of a full circle.
Sources: Angle — Wikipedia
Frequently asked questions
Why are radians used in mathematics?
In radians, the arc length of a circle is simply r·θ and the derivative of sin(x) is cos(x) without extra constants. Those clean relationships only hold when angles are measured in radians, which is why higher mathematics defaults to them.
What is a gradian?
A gradian, or gon, splits a right angle into 100 equal parts, so a full circle is 400 gradians. It is used mainly in surveying and some engineering because it fits the decimal system neatly.
How many degrees are in one radian?
One radian equals 180/π ≈ 57.2958 degrees. It is the angle at which the arc length equals the circle’s radius.
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This calculator is for educational purposes. Double-check important results before acting on them.