Degrees to Radians
Convert an angle from degrees to radians.
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Example
180° = π rad
How it works
A full turn around a circle is split into 360 degrees, but the radian system measures angles using the radius of the circle, so the two units need a fixed conversion factor. Since 180 degrees corresponds exactly to half a turn, that angle is equal to π radians, which is why multiplying degrees by π/180 converts any degree measure into radians. This is especially useful because many formulas in trigonometry and calculus are written in radians, not degrees.
When to use it
Use this when an angle is given in degrees but a math formula expects radians, such as in trigonometry, physics, or calculus. It is also helpful when working with circles, rotation, or arc-length problems.
Worked example, step by step
Convert 45° to radians Step 1: Write the conversion formula: rad = deg × π/180 Step 2: Substitute 45 for deg: rad = 45 × π/180 Step 3: Simplify the fraction: rad = π/4 Final answer: 45° = π/4 rad
Common mistakes to avoid
- Using 180/π instead of π/180 when converting degrees to radians
- Forgetting to include π in the answer, leaving a decimal too early
- Mixing up degrees and radians in a formula that requires one specific unit
Did You Know?
Radians make calculus clean — a full circle is 2π radians, tied directly to its circumference.
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