Convert Degrees to Radians (° to rad)
1 degree (°) = 0.01745329252 radians (rad). 1 rad = 57.29577951 °. Example: 180 ° = 180 × 0.01745329252 = 3.141592654 rad.
Also searched as degrees to radians, deg to rad, ° to rad, convert degrees into radians, degree to radian and 180 degrees in radians.
1 ° = 0.01745329252 rad
Type in either box. Scientific notation works: 1.5e-3.
Converting a list? Use the bulk degree to radian converter to paste a column from Excel.
How to Convert Degree to Radian
- 1 ° = 0.01745329252 rad
- 1 rad = 57.29577951 °
- Example: convert 180 ° to rad: 180 ° = 180 × 0.01745329252 rad = 3.141592654 rad
Formula
rad = ° × 0.01745329251994
or rad = ° ÷ 57.29577951308
Derivation from SI units:
- 1° = π/180 rad exactly; a full turn is 360°.
- 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).
Both units are defined exactly, so the factor is exact. Degree definition: degree; Radian definition: radian.
Worked examples
- An angle of 180 ° is 3.141592654 rad (π).
180 ° × 0.01745329252 = 3.141592654 rad - An angle of 45 ° is 0.7853981634 rad (π/4).
45 ° × 0.01745329252 = 0.7853981634 rad
Degree to Radian conversion table
| Degrees (°) | Radians (rad) |
|---|---|
| 1 ° | 0.01745329252 rad |
| 15 ° | 0.2617993878 rad |
| 30 ° | 0.5235987756 rad |
| 45 ° | 0.7853981634 rad |
| 60 ° | 1.047197551 rad |
| 90 ° | 1.570796327 rad |
| 120 ° | 2.094395102 rad |
| 180 ° | 3.141592654 rad |
| 270 ° | 4.71238898 rad |
| 360 ° | 6.283185307 rad |
Where it's used
Angles in degrees are converted to radians for trigonometry, arc length s = rθ, angular speed and calculus, where formulas assume radians. Multiply by π/180.
Degree to other angle units
| Conversion | 1 ° equals |
|---|---|
| degree to radian | 0.01745329252 rad |
| degree to gradian | 1.111111111 gon |
| degree to revolution | 0.002777777778 rev |
| degree to minute of arc | 60 ′ |
| degree to second of arc | 3600 ″ |
Frequently asked questions
How do I convert degrees to radians?
Multiply by π/180: 90° = π/2 ≈ 1.570796327 rad and 60° = π/3.
What are common angles in radians?
30° = π/6, 45° = π/4, 60° = π/3, 90° = π/2, 180° = π and 360° = 2π.
How many radians are in 1 degree?
1 ° = 0.01745329252 rad.
Is the ° to rad 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 Degrees to Radians (° to rad). Retrieved October 25, 2026, from https://scientificconverters.com/angle/degrees-to-radians/
IEEE
Scientific Converters, "Convert Degrees to Radians (° to rad)," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/angle/degrees-to-radians/