Degrees to radians
Multiply degrees by 0.0174533 to get radians.
60 ° = 1.0472 rad
How to convert degrees to radians
The radian is the SI angle unit — the angle subtending an arc equal to the radius; a full turn is 2π rad. The degree is one 360th of a full turn — the everyday unit of angle.
Worked example — 60 °: 60 × 0.0174533 = 1.0472 rad.
Degrees to radians table
| Degrees | Radians |
|---|---|
| 1 ° | 0.0174533 rad |
| 15 ° | 0.261799 rad |
| 30 ° | 0.523599 rad |
| 45 ° | 0.785398 rad |
| 60 ° | 1.0472 rad |
| 90 ° | 1.5708 rad |
| 120 ° | 2.0944 rad |
| 180 ° | 3.1416 rad |
| 360 ° | 6.2832 rad |
Reverse and related
About degrees and radians
Degree (°)
1 ° = 0.0174533 radDefinition. One 360th of a full turn — the everyday unit of angle
History and origin
The degree, one 360th of a full turn, goes back to ancient Babylonian astronomers, whose base-60 counting made 360 a natural division of the circle. It has been the everyday angle measure ever since.
Current use
Degrees are used in geometry, navigation and construction, wherever angles are set out or read off.
Source: BIPM SI Brochure (2019); ISO 80000-3 (angle)
Radian (rad)
1 rad = 57.2958 °Definition. The SI angle unit — the angle subtending an arc equal to the radius; a full turn is 2π rad
History and origin
The radian is the natural mathematical measure of angle, the angle that cuts off an arc equal to the radius, so a full turn is 2π radians. The idea dates to the eighteenth century and the name was adopted in the 1870s.
Current use
Radians are used in trigonometry, physics and programming, where they make the mathematics of rotation simplest.
Source: BIPM SI Brochure (2019); ISO 80000-3 (angle)
Where people use this
Degrees: geometry, navigation, construction angles. Radians: trigonometry, physics, programming. 180° is exactly π radians.
Every value is carried to full double precision; the display is rounded.
Both units are defined in BIPM SI Brochure (2019); ISO 80000-3 (angle).
Questions people ask
How many radians is 180 degrees?
180° is exactly π radians (about 3.1416). To convert degrees to radians, multiply by π/180.
How do you convert degrees to radians?
Multiply the degrees by π/180, so 90° is π/2, about 1.571 radians, and 45° is π/4.
How many radians is 360 degrees?
A full turn, 360°, is 2π radians (about 6.283).
How many radians is 1 degree?
One degree is π/180 radians, about 0.01745 radians.