Convert Angle from Radians to Degrees

To convert an angle from radians to degrees multiply by the common ratio of divided by (tau) radians. The figure on the left below shows an angle measured in radians. The figure on the right shows an angle measured in degrees.

Observe that one full rotation in degrees is and one full rotation in radians is radians. The constant is a naturally occurring number approximately equal to . To convert an angle from radians to degrees multiply by the common fraction:

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.

Steps
  1. Subsitute the angle of radians in for in the equation.

  2. Multiply by and subsitute the value of for the circle constant (tau).

  3. Divide by .

  4. The angle radians is equal to .

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.

Steps
  1. Subsitute the angle of radians in for in the equation.

  2. Multiply by and subsitute the value of for the circle constant (tau).

  3. Divide by .

  4. The angle radians is equal to .

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