Degrees to Radians Converter

Convert any angle in degrees to radians. radians = degrees × π/180.

Inputs

Result

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How to use this calculator

  • Enter angle in degrees.
  • Read the equivalent in radians (and as a multiple of π).

About this calculator

Degrees and radians are two ways to measure angles. 180° = π radians. To convert degrees to radians, multiply by π/180. Common values: 30° = π/6, 45° = π/4, 60° = π/3, 90° = π/2, 180° = π, 360° = 2π.

Frequently asked

Why use radians?+
In calculus, derivatives of trig functions are simpler in radians: d/dx sin(x) = cos(x) only when x is in radians. Engineering frequently uses radians too.
How is 180° = π?+
A radian is the angle that subtends an arc equal to the radius. The full circle has circumference 2πr, so 360° corresponds to 2π radians, and 180° to π.
Are degrees just an arbitrary unit?+
Historically, yes — Babylonians used 360 because of their base-60 number system and the rough length of a year. Radians are more "natural" mathematically.
Common conversions?+
30°→π/6, 45°→π/4, 60°→π/3, 90°→π/2, 120°→2π/3, 135°→3π/4, 150°→5π/6, 180°→π.
Can I do partial-degree input?+
Yes — the calculator handles any decimal degree value.

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