How to convert degrees to radians is a standard math unit conversion used in trig, circles, and geometry. The core relationship is: rad = deg * pi / 180. The inverse is:deg = rad * 180 / pi.
Prefer instant calculations? Use Degrees ↔ radians.
Key takeaways
- Convert by multiplying degrees by
pi/180. - Convert back by multiplying radians by
180/pi. - 180 degrees equals pi radians.
- Round only after computing the full expression (especially if you plug into trig functions).
Degrees to radians (how to do it)
Take your angle in degrees (deg) and apply: rad = deg * pi / 180.
- Write down the degrees value.
- Multiply by pi.
- Divide by 180.
- Round at the end if needed.
Examples
Example 1: 90 degrees.
rad = 90 * pi / 180 = pi/2.
Example 2: 180 degrees.
rad = 180 * pi / 180 = pi.
Radians to degrees
If you already have radians and want degrees, use: deg = rad * 180 / pi.
- Write down the radians value.
- Multiply by 180.
- Divide by pi.
Where mistakes happen
- Confusing radians with degrees in calculators/software (for trig functions, most inputs require radians).
- Rounding pi too early instead of using a full-precision value.
Reference
The radians definition and the degrees ↔ radians conversion are explained by Wikipedia (Radian).
Next steps
Convert once, then reuse the result in your trig/geometry steps. If you need to check multiple values quickly, run Degrees ↔ radians and copy the output.