Angle converters
Convert angles between radians and degrees.
About angle conversion
Angles are measured in degrees in everyday life — a right angle is 90°, a full turn 360° — and in radians in mathematics, physics and programming, where a full turn is 2π radians. The degree is arbitrary (360 comes from Babylonian astronomy); the radian is natural: it is the angle whose arc length equals the radius, which is why calculus and trigonometric functions work cleanly in radians.
Conversion factors at a glance
| Degrees | Radians |
|---|---|
| 1° | 0.01745 rad (π/180) |
| 30° | π/6 ≈ 0.5236 rad |
| 45° | π/4 ≈ 0.7854 rad |
| 90° | π/2 ≈ 1.5708 rad |
| 180° | π ≈ 3.1416 rad |
| 360° | 2π ≈ 6.2832 rad |
| 57.2958° | 1 rad |
Which converter do I need?
Degrees to radians when a formula, a programming language (JavaScript's Math.sin, Python's math.cos) or a physics problem expects radians and you are thinking in degrees. Radians to degrees when a calculation returns radians and you need a number you can picture or set on a protractor, a CNC machine or a CSS rotation.
A common slip
Calculators have a DEG/RAD mode. If sin(30) returns −0.988 instead of 0.5, the calculator is in radians and the 30 was read as 30 radians — about 1 719 degrees. Convert first, or switch the mode.
Common questions
How many degrees is 1 radian? 57.3°. How many radians is 180°? π, about 3.14. How many radians in a full circle? 2π, about 6.28. Why do calculators have a RAD mode? Because trigonometric formulas in calculus assume radians; degrees are for measuring, radians are for computing.