# 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

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

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

See the table below for common conversions.