Degrees to radians (° to rad)

The formula

rad = ° × 0.01745329252

Where the factor comes from — each unit by its definition, then its size in SI:

• 1° = π / 180 × rad = 0.0174532925199 rad
• 1 rad is the SI unit of angle.

Dividing the two SI sizes gives the factor: 0.0174532925199 (rounded for display; the underlying ratio is fixed by the definitions). The reverse factor is 57.2957795131.

Calculators on this site take angles in degrees, but the maths underneath runs in radians: a full turn is 360° or 2π rad.

Worked examples

• A projectile launched for maximum range: 45° = 0.785398 rad — 45 × 0.01745329252 = 0.785398
• A right angle: 90° = 1.5708 rad — 90 × 0.01745329252 = 1.5708
• One radian: 57.2958° = 1 rad — 57.2958 × 0.01745329252 = 1

Frequently asked questions