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

Convert 30 Degrees To Radians

30 Degree Angle

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

Convert 60 Degrees To Radians

60 Degree Angle

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.

degrees radians
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

Links

Angle | concept