Angle conversion
How to convert angles
Angle units describe the same amount of rotation in different ways. Start from one full turn, choose the matching ratio, and keep π in the calculation until the final step.
Open the angle converterUse one full rotation as the reference
360° = 2π radians = 400 gradians = 1 turn
To convert an angle, multiply by a ratio equal to one. Put the unit you want to remove in the denominator and the unit you want in the numerator.
Degrees and radians
For degrees to radians, multiply by π/180. For example, 135° × π/180 = 3π/4 radians, or about 2.35619 radians.
For radians to degrees, multiply by 180/π. An angle of 2.5 radians is about 143.239°. Keep π unrounded until the end to reduce rounding error.
Gradians and turns
Multiply degrees by 10/9 to get gradians, so 90° is 100 gradians. Divide degrees by 360 to get turns, so 810° is 2.25 turns. Values above 360° and negative values are valid; only wrap them when the problem specifically asks for an equivalent angle within one rotation.
Common mistakes
- Do not treat radians as a unitless decimal before applying π.
- Check whether a calculator is in degree or radian mode.
- Do not discard complete rotations when motion or accumulated rotation matters.
Convert with ToolPixels
The free Angle Converter converts the supported units in your browser. Enter a value, choose the source and target units, select the needed precision, and review the displayed formula before using the result.