Free · Unit conversions

Degrees, Radians & Turns Angle Converter

Convert angles between degrees, radians, turns, gradians and arc components.

Formula & worked example
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How to use this calculator

Enter the known values in the units shown. Results update as you type.
Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
Use the worked example to check the method. Reset restores the starting fields.

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Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

A half-turn is 180 degrees or π radians, approximately 3.141592653589793. A full turn is 360 degrees or 2π radians.

Radians = degrees × π / 180; degrees = radians × 180 / π

Worked example

Enter these known values and leave the other values blank.

First angle: 180 deg

Equivalent angle: 3.1416 rad

Assumptions and limitations

An angle is converted without reducing it to the interval from zero to one turn. Negative and multi-turn values retain their sign and magnitude.
Arcminutes and arcseconds divide one degree into 60 and 3,600 parts. They are angular units, not elapsed minutes and seconds. Compound degrees/minutes/seconds use colon-separated components.
Radian results involving π are calculated numerically at the engine precision and rounded for display.

Common questions

How are turns and gradians related to degrees?

One turn is 360 degrees and 400 gradians. A right angle is 90 degrees, 100 gradians or one quarter-turn.

Can I enter degrees, minutes and seconds?

Select the compound angle unit and use colons, such as 12:30:0 for twelve degrees and thirty arcminutes. That equals 12.5 decimal degrees.

References

The calculation equations, inverse formulas, units, and input rules were imported from this source. Bookify provides the interface and equation solver.

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