Radians to Degrees Converter
Convert either direction between degrees, radians, and turns, with clean π multiples like π/2 shown automatically.
- as a multiple of π
Runs entirely on your device - nothing is ever uploaded.
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How to use the radians converter
- Type a value in degrees, radians, or turns - any box works as input.
- The other two units convert instantly in both directions.
- Read the exact π-multiple form for common angles like 90° = π/2.
The conversion factors
A full turn is 360° = 2π rad: degrees × π/180 = radians, radians × 180/π = degrees, turns × 360 = degrees.
Why radians exist
Degrees are arbitrary - 360 comes from ancient calendars. Radians are natural: one radian wraps exactly one radius along the circle, so a full turn is 2π by definition. Calculus only works in radians, because the derivative of sin(x) is cos(x) solely in radian measure, and physics formulas for arc length and angular speed assume them. Use degrees for everyday angles and radians the moment math is involved.