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The radian (symbol rad) is the unit for measuring angles, and is the standard unit of angular measure used in many areas of mathematics.
The length of an arc of a unit circle is numerically equal to the measurement in radians of the angle that it subtends; one radian is just under 57.3 degrees.
An arc of a circle with the same length as the radius of that circle subtends an angle of 1 radian. The circumference subtends an angle of 2π radians.
A complete revolution is 2π radians (shown here with a circle of radius one and thus circumference 2π).
Conversions
| Radians | Degrees |
|---|---|
| 0 | 0° |
| π/12 | 15° |
| π/6 | 30° |
| π/4 | 45° |
| 1 | 57.3° |
| π/3 | 60° |
| π/2 | 90° |
| π | 180° |
| 2π | 360° |