Radian ↔ Degree Converter
Instant Angle Conversion ⚡
Convert any angle between radians and degrees instantly. Enter either value and the other is calculated immediately.
Convert any angle between radians and degrees instantly. Enter either value and the other is calculated immediately.
Degrees to Radians: radians = degrees × π ÷ 180
Radians to Degrees: degrees = radians × 180 ÷ π
One full circle = 360° = 2π radians. A right angle = 90° = π/2 radians.
| Degrees | Radians (exact) | Decimal |
|---|---|---|
| 0° | 0 | 0 |
| 30° | π/6 | 0.5236 |
| 45° | π/4 | 0.7854 |
| 60° | π/3 | 1.0472 |
| 90° | π/2 | 1.5708 |
| 180° | π | 3.1416 |
| 270° | 3π/2 | 4.7124 |
| 360° | 2π | 6.2832 |
Why do we use radians?
Radians are the natural unit for angles in mathematics because they simplify calculus formulas. The derivative of sin(x) is cos(x) only when x is in radians. Degrees are more intuitive for everyday use, but radians are essential in higher maths.
What is π?
Pi (π) is approximately 3.14159265. It is the ratio of a circle's circumference to its diameter, and appears throughout mathematics. One radian is the angle subtended at the centre of a circle by an arc equal in length to the radius.
When do I need radians vs degrees?
Use degrees for everyday angles, bearings, and basic trigonometry. Use radians in calculus, physics, engineering, and when using most programming languages' built-in trig functions (which expect radians by default).