Degrees to Radians
Convert an angle from degrees to radians.
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Example
180° = π rad
How it works
Degrees and radians are two different ways to measure the same angle. The formula converts degrees into radians by using the fact that a full turn is 360° and also 2\pi radians, so 1° must equal \pi/180 radians. Multiplying by \pi/180 rescales the angle into the radian system used in most advanced trigonometry and calculus.
When to use it
Use this when a problem gives an angle in degrees but your calculator, graph, or formula expects radians. It is especially common in trigonometry, physics, and any work with arc length, angular speed, or calculus.
Worked example, step by step
Convert 45° to radians rad = deg × π/180 rad = 45 × π/180 rad = 45π/180 rad = π/4 Final answer: 45° = π/4 rad
Common mistakes to avoid
- Multiplying by 180/π instead of π/180
- Forgetting to include the unit π in the answer
- Treating radians and degrees as different kinds of angles instead of equivalent measures
Did You Know?
Radians make calculus clean — a full circle is 2π radians, tied directly to its circumference.
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