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Convert between degrees, radians, gradians, turns, and arc units for math and science.
Angle conversion is the process of changing an angle measurement from one unit to another, such as degrees to radians or gradians, while preserving the same angular position.
| Description | Degrees | Radians | Gradians |
|---|---|---|---|
| 30° | 30 | π/6 ≈ 0.524 | 33.33 |
| 45° | 45 | π/4 ≈ 0.785 | 50 |
| 60° | 60 | π/3 ≈ 1.047 | 66.67 |
| Right angle | 90 | π/2 ≈ 1.571 | 100 |
| Straight angle | 180 | π ≈ 3.142 | 200 |
| Full rotation | 360 | 2π ≈ 6.283 | 400 |
Multiply degrees by π/180 (≈ 0.01745) to convert to radians.
rad = deg × (π ÷ 180)
Multiply radians by 180/π (≈ 57.296) to convert to degrees.
deg = rad × (180 ÷ π)
Multiply degrees by 10/9 (≈ 1.111) to convert to gradians.
grad = deg × (10 ÷ 9)
Formula
rad = deg × π ÷ 180 | grad = deg × 10 ÷ 9 | 1 turn = 360° = 2π rad = 400 gradrad = Radian — SI unit; angle subtended by an arc equal to the radius
deg (°) = Degree — 1/360 of a full rotation; the most common everyday unit
grad = Gradian (gon) — 1/400 of a full rotation; used in surveying
turn = Full rotation = 360° = 2π radians = 400 gradians
Worked Example
Convert 90° to radians
Did you know? The radian is defined so that the arc length equals the radius when the angle is 1 rad. This makes it the 'natural' unit for angles in mathematics and physics — derivatives of trigonometric functions only simplify nicely when angles are in radians.
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