How to Convert Degrees to Radians (2026)

Degrees and radians are two ways to measure the same thing — an angle. Degrees are familiar from everyday life (a right angle is 90°, a full rotation is 360°). Radians are the natural unit in mathematics and physics: one radian is the angle subtended at the centre of a circle by an arc equal in length to the radius. The conversion between them is exact: 360° = 2π radians.

The Conversion Formula

To convert degrees to radians, multiply by π/180. To convert radians to degrees, multiply by 180/π.

• Degrees → Radians: radians = degrees × (π / 180)
• Radians → Degrees: degrees = radians × (180 / π)

For example, 45° × (π / 180) = π/4 ≈ 0.7854 rad. And π/3 × (180 / π) = 60°.

Common Angle Reference Table

When Radians Matter

Most programming languages and scientific calculators use radians by default. The trigonometric functions sin(), cos(), and tan() in JavaScript, Python, C, and most other languages all expect radian input. Passing degrees directly produces wrong results — Math.sin(90) in JavaScript does not return 1; Math.sin(Math.PI / 2) does. Radians also simplify calculus: the derivative of sin(x) is cos(x) only when x is in radians. In physics, angular velocity (rad/s) and arc length formulas (s = rθ) require radians throughout.

Use the Angle Converter to convert between degrees, radians, gradians, and turns instantly.