Convert degrees to radians or radians to degrees, including familiar π fractions.
180° = π radians and 90° = π/2 radians. A full turn is 360° = 2π radians.
180° ≈ 3.141592654 radians.
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How to Use the Angle Converter
Enter an angle and select its current unit. When you start with degrees, the result is radians and an exact π fraction is shown when the degree input has at most six decimal places. When you start with radians, the result is degrees. The extra cards show both units and the number of complete turns.
Degrees and Radians Conversion Formulas
Half a turn measures 180 degrees or π radians. Multiply degrees by π/180 to get radians. Multiply radians by 180/π to get degrees. A full turn equals 360 degrees or 2π radians.
θ(°) = θ(rad) × 180/π
Worked Angle Conversions
45 degrees to radians
45 × π/180 = π/4 radians, approximately 0.785398 radians.
π/2 radians to degrees
(π/2) × 180/π = 90 degrees.
A negative angle
-90 degrees equals -π/2 radians. The negative sign indicates clockwise rotation in the standard coordinate convention.
Turns and Negative Angles
One turn is 360° or 2π radians. Divide degrees by 360 to find turns. Negative angles retain their sign; this converter does not automatically wrap results into a 0°–360° range because a rotation of -45° and one of 315° describe different signed turns even though they share a terminal direction.
Exact π Form Versus Decimal Approximation
A form such as π/6 is exact. A decimal such as 0.5235987756 is rounded. The tool uses π notation for degree inputs that can be represented by a finite decimal with up to six places; for other numeric inputs it still gives a decimal radian approximation.
Angle Converter FAQs
How many radians are 180 degrees?
π radians.
How many degrees are π/2 radians?
90 degrees.
Is π/4 equal to 45 degrees?
Yes. π/4 radians equals 45 degrees.
Method and references
The conversion formulas follow the educational references linked below. Check the method against your course requirements when a different angle convention applies.
Sources
Disclaimer
For educational use. Check your class or textbook convention when the problem defines a different range, sequence index, or notation.