Convert Radians to Degrees (rad to °)
1 radian (rad) = 57.29577951 degrees (°). 1 ° = 0.01745329252 rad. Example: 1 rad = 1 × 57.29577951 = 57.29577951 °.
Also searched as radians to degrees, rad to deg, rad to °, convert radians into degrees, radian to degree and how many degrees in a radian.
1 rad = 57.29577951 °
Type in either box. Scientific notation works: 1.5e-3.
Converting a list? Use the bulk radian to degree converter to paste a column from Excel.
How to Convert Radian to Degree
- 1 rad = 57.29577951 °
- 1 ° = 0.01745329252 rad
- Example: convert 1 rad to °: 1 rad = 1 × 57.29577951 ° = 57.29577951 °
Formula
° = rad × 57.29577951308
Derivation from SI units:
- The SI unit of plane angle: the angle subtended at the centre of a circle by an arc equal in length to the radius (1 rad = 1 m/m).
- 1° = π/180 rad exactly; a full turn is 360°.
Both units are defined exactly, so the factor is exact. Radian definition: radian; Degree definition: degree.
Worked examples
- 1 rad is 57.29577951 °.
1 rad × 57.29577951 = 57.29577951 ° - An angle of 3.14159 rad (π) is 179.999848 °.
3.14159 rad × 57.29577951 = 179.999848 °
Radian to Degree conversion table
| Radians (rad) | Degrees (°) |
|---|---|
| 0.5 rad | 28.64788976 ° |
| 1 rad | 57.29577951 ° |
| 1.5 rad | 85.94366927 ° |
| 2 rad | 114.591559 ° |
| 3 rad | 171.8873385 ° |
| 3.14159 rad | 179.999848 ° |
| 4 rad | 229.1831181 ° |
| 5 rad | 286.4788976 ° |
| 6 rad | 343.7746771 ° |
| 6.28318 rad | 359.9996959 ° |
Where it's used
Angles in radians from calculus, physics formulas and calculator results are converted to degrees for geometry, drawings and navigation. Multiply by 180/π, about 57.2958.
Radian to other angle units
| Conversion | 1 rad equals |
|---|---|
| radian to degree | 57.29577951 ° |
| radian to gradian | 63.66197724 gon |
| radian to revolution | 0.1591549431 rev |
| radian to minute of arc | 3437.746771 ′ |
| radian to second of arc | 206264.8062 ″ |
Frequently asked questions
How do I convert radians to degrees?
Multiply by 180/π: 1 rad = 57.29577951 ° and π/3 rad = 60°.
Why is π radians equal to 180°?
A full circle is 2π radians (its circumference divided by its radius) and also 360°, so π radians is half a turn, 180°.
How many degrees are in 1 radian?
1 rad = 57.29577951 °.
Is the rad to ° conversion exact?
Yes. Both units are defined exactly, so the ratio is exact; its decimal form does not terminate and is shown here to 10 significant figures (more with the precision selector).
Sources
- The International System of Units (SI), 9th edition (SI Brochure), Bureau International des Poids et Mesures , Table 4 (radian) and Table 8 (non-SI units accepted for use with the SI).
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
Cite this page
APA
Scientific Converters. (2026, October 15). Convert Radians to Degrees (rad to °). Retrieved October 25, 2026, from https://scientificconverters.com/angle/radians-to-degrees/
IEEE
Scientific Converters, "Convert Radians to Degrees (rad to °)," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/angle/radians-to-degrees/