Radians and degrees
A radian is the angle that subtends an arc equal to the radius; a full turn is 2π radians. Mathematics, physics and programming languages measure angles in radians.
A degree is 1/360 of a full turn, exactly π/180 radians. Maps, compasses, construction, geometry classes and camera fields of view use degrees.
Worked example
Convert 1 rad: 1 × 57.29577951 = 57.29577951, so 1 radian is 57.29577951 degrees. Likewise 3 rad = 171.8873385 °.
Estimating in your head
One radian is about 57.3°, so multiply by 57.3. Landmarks: π/2 rad ≈ 1.571 rad is 90°, π rad is 180°.
Going the other way
To convert degrees to radians, divide by 57.29577951 (or multiply by 0.0174532925199). The swap button between the boxes opens that page.
How this works
° = rad × 57.29577951
A full turn is 360° or 2π radians, so 1° = π/180 rad and 1 rad = 180/π°. Results drop binary floating-point noise beyond 15 significant digits and display at the precision you choose (6 significant figures by default). Copy result copies the full value.
Frequently asked
How many degrees are in a radian?
1 radian = 57.29577951 degrees. The factor is exact by definition but has endless decimals, so it is shown rounded; the page uses the full value.
How do I convert radians to degrees?
Multiply by 57.29577951. For example, 3 rad × 57.29577951 = 171.8873385 °.
What is 3.14159265 rad in degrees?
3.14159265 rad = 179.9999998 °. The table next to the converter lists more common values.
Is the result rounded?
Only on screen. The page computes with the exact definitions and removes floating-point noise past 15 significant digits; pick 3 to 12 significant figures, or use Copy result for the full value.
Sources
- BIPM — The International System of Units (SI Brochure), 9th edition
- NIST SP 811 Appendix B.8 — Factors for units listed alphabetically
- Wikipedia — Radian
Reviewed Oct 17, 2026 · test vectors fixtures/units/angle/radians-to-degrees/