Angle Converter

This angle converter switches between degrees and radians, and also covers gradians, arcminutes, arcseconds, and full turns. It is the quick way to check trigonometry or CAD values.

Updated
Runs in your browser. Your data is not uploaded.

Result
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How to use the Angle Converter

  1. Type the Value you want to convert.
  2. Pick the unit it is in under From, and the unit you want under To. The swap button flips them.
  3. The answer updates as you type. The table below it shows the same value in every other unit, each with its own copy button.

How it works

radians = degrees × π ÷ 180
degrees = radians × 180 ÷ π
1 gradian = 0.9°; 1 turn = 360°
1° = 60′ (arcminutes) = 3,600″ (arcseconds)

Examples

  • 90° = 1.570796 rad (π/2).
  • 1 rad = 57.29578°.
  • 45° = 50 gon.
  • 1° = 3,600″.

Degree to radian conversion table

Degree (°)Radian (rad)
1 °0.0174533 rad
15 °0.261799 rad
30 °0.523599 rad
45 °0.785398 rad
60 °1.047198 rad
90 °1.570796 rad
120 °2.094395 rad
180 °3.141593 rad
270 °4.712389 rad
360 °6.283185 rad

Why radians

Radians measure an angle by the length of the arc it cuts from a circle of radius 1. A full circle is 2π radians, so 180° is π radians. Programming languages and calculus use radians because the formulas stay simple; JavaScript's Math.sin, for example, expects radians. For coordinates split into degrees, minutes, and seconds, see Lat/Long to DMS.

Limitations

  • Angles are not wrapped to 0-360°; 720° stays 720°.
  • Mils (used in artillery) are not included.

Frequently asked questions

How do I convert degrees to radians?

Multiply by π and divide by 180. For example, 60° × π ÷ 180 = 1.0472 rad.

How many degrees is one radian?

About 57.2958°.

What is a gradian?

A unit that splits a right angle into 100 parts, so a full circle is 400 gradians (gon). Some surveying instruments use it.

Often used together with the Angle Converter.