Convert Angle from Degrees to Radians Examples

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 occurring 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°.

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

  2. Simplify the fraction .

  3. The angle is (tau) twelfths radians

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°.

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

  2. Simplify the fraction .

  3. The angle is (tau) sixths radians

Common Conversions

Common Measured Angles

See the table below for common conversions.

Degrees Radians

Examples