Radians to degrees formula
Use a single relationship between the two angle units: degrees = radians × 180/π.
Radians to degrees
degrees = radians × 180 / π
Because a half turn is π radians and 180°, multiplying by 180/π changes the unit without changing the angle.
Deriving the conversion
A complete rotation measures 2π radians and 360 degrees. Dividing both by two gives π radians = 180 degrees. Dividing by π gives the factor 180/π for each radian.
For example, π/4 × 180/π simplifies to 45. The π terms cancel before any rounding is introduced.
Examples
Common angle conversions
π/6→30°
π/4→45°
π/2→90°
π→180°
2π→360°
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