Convert Angle from Degrees to Radians

To convert an angle from degrees to radians, multiply the angle by the constant τ (tau) divided by 360°. For example, to convert 30° to radians multiply by τ (approximately 6.283) and then divide by 360° which gives us the angle of τ/12 radians.

Explanation

Observe that a full rotation in degrees is 360° and a full rotation in radians is τ radians. The constant τ is a naturally occuring number approximately equal to 6.2831853071. To convert an angle from degrees to radians, we multiply by τ over 360°. The degrees units cancel leaving us with the angle in radians.

Examples

To convert the angle of 30 degrees to radians multiply by the ratio of τ (6.283) radians divided by 360°.

To convert the angle of 60 degrees to radians multiply by the ratio of τ (6.283) radians divided by 360°.

Common Conversions

See the table below for common conversions.

0
30° τ/12
45° τ/8
60° τ/6
90° τ/4
120° τ/3
135° 3τ/8
150° 5τ/12
180° τ/2
210° 7τ/12
225° 5τ/8
240° 4τ/6
270° 3τ/4
300° 5τ/6
315° 7τ/8
330° 11τ/12
360° τ