Degrees and 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.
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.
Worked example
Convert 45 °: 45 × 0.01745329252 = 0.7853981634, so 45 degrees is 0.7853981634 radians. Likewise 180 ° = 3.141592654 rad.
Estimating in your head
Divide by 57.3, or remember the landmarks: 30° = π/6, 45° = π/4, 90° = π/2 and 180° = π.
Going the other way
To convert radians to degrees, divide by 0.01745329252 (or multiply by 57.2957795131). The swap button between the boxes opens that page.
How this works
rad = ° × 0.01745329252
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 radians are in a degree?
1 degree = 0.01745329252 radians. 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 degrees to radians?
Multiply by 0.01745329252. For example, 180 ° × 0.01745329252 = 3.141592654 rad.
What is 270 ° in radians?
270 ° = 4.71238898 rad. 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/degrees-to-radians/