How many radians are in a degree?

1 ° = 0.017453 rad. To convert any amount, multiply by 0.017453.

How do you convert degrees to radians?

Multiply the number of degrees by 0.017453 to get radians. The formula is shown in the "How it's calculated" section above.

Where does the conversion factor come from?

It's a published international standard. Most are defined exactly by international agreement (e.g. 1 inch = 25.4 mm exactly, 1 lb = 0.45359237 kg exactly). Source citations are listed under the formula above.

Unit converter — Angle

Degrees to radians converter

Convert degrees (°) to radians (rad). Source-cited conversion factor, exact to the displayed precision.

Results are mathematically exact for the displayed precision. How we calculate.

How it's calculated

Convert degrees to radians— the formula

Degrees convert to radians by multiplying by the published conversion factor. The factor below is exact to the precision shown, sourced from the citation under the formula.

rad = ° × 0.017453

° = rad × 57.2958

Radian: SI coherent derived unit for plane angle (BIPM). 1 full turn = 2π rad = 360° = 400 gon = 1 rev. 1° = 60 arcminutes = 3600 arcseconds (exact, by definition).

Questions

Frequently asked questions

How many radians are in a degree?
1 ° = 0.017453 rad. To convert any amount, multiply by 0.017453.
How do you convert degrees to radians?
Multiply the number of degrees by 0.017453 to get radians. The formula is shown in the "How it's calculated" section above.
Where does the conversion factor come from?
It's a published international standard. Most are defined exactly by international agreement (e.g. 1 inch = 25.4 mm exactly, 1 lb = 0.45359237 kg exactly). Source citations are listed under the formula above.