The formula
° = rad × 57.29577951
Where the factor comes from — each unit by its definition, then its size in SI:
1 rad is the SI unit of angle.1° = π / 180 × rad = 0.0174532925199 rad
Dividing the two SI sizes gives the factor: 57.2957795131 (rounded for display; the underlying ratio is fixed by the definitions). The reverse factor is 0.0174532925199.
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: 0.785398 rad = 45° — 0.785398 × 57.29577951 = 45
- A right angle: 1.5708 rad = 90° — 1.5708 × 57.29577951 = 90
- One radian: 1 rad = 57.2958° — 1 × 57.29577951 = 57.2958
Frequently asked questions
How many degrees is 1 rad?
1 rad = 57.2957795131 °.
How do I convert degrees back to radians?
Divide by 57.2957795131 — or multiply by 0.0174532925199: 1 ° = 0.0174532925199 rad.