Degrees to Radians Converter

Multiply by π and divide by 180.

A full turn is 360° and also 2π radians, so the two units are locked together by that single ratio. Because π is irrational, no decimal factor is ever exact — which is why radian answers are usually left as fractions of π.

Convert 45°:

The cleanest way to do it by hand is to cancel first: 45/180 = 1/4, so the answer is π/4 exactly. Reach for the decimal only at the end.

Trigonometry runs on a handful of angles, and knowing them as π fractions saves constant conversion:

• 30° = π/6 ≈ 0.5236 rad
• 45° = π/4 ≈ 0.7854 rad
• 60° = π/3 ≈ 1.0472 rad
• 90° = π/2 ≈ 1.5708 rad
• 120° = 2π/3 ≈ 2.0944 rad
• 180° = π ≈ 3.1416 rad
• 270° = 3π/2 ≈ 4.7124 rad
• 360° = 2π ≈ 6.2832 rad

A radian is the angle that sweeps an arc as long as the circle's radius. That definition makes the radian dimensionless, and it is what lets the clean formulas work: arc length is simply $s = r\theta$, and the derivative of $\sin x$ is $\cos x$ only when $x$ is in radians. In degrees that derivative picks up a stray factor of π/180.

This is also why every programming language's trigonometric functions take radians. Math.sin(90) in JavaScript does not give 1 — it gives the sine of 90 radians, about 0.894. You need Math.sin(90 * Math.PI / 180).

How many radians is 1 degree? 0.01745329 rad, which is π/180.

How many degrees is 1 radian? 57.29578°, which is 180/π.

How many radians in a circle? 2π, about 6.283185.

Why does my code give the wrong sine? Almost certainly because you passed degrees. Standard library trigonometric functions expect radians; multiply your angle by π/180 first.

Is a radian an SI unit? It is the SI unit of plane angle, but it is dimensionless — a ratio of two lengths — so it can appear and vanish from formulas without breaking the units.