Convert Angle from Radians to Degrees

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

Explanation

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

Examples

Convert 1 Radian to Degrees

1 Radian

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

Convert 2 Radians to Degrees

2 Radians

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

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
Degrees | concept
Radians | concept
Circle | concept