Radians to degrees
Multiply radians by 57.2958 to get degrees.
3 rad = 171.8873 °
How to convert radians to degrees
The degree is one 360th of a full turn — the everyday unit of angle. The radian is the SI angle unit — the angle subtending an arc equal to the radius; a full turn is 2π rad.
Worked example — 3 rad: 3 × 57.2958 = 171.8873 °.
Radians to degrees table
| Radians | Degrees |
|---|---|
| 0.5 rad | 28.6479 ° |
| 1 rad | 57.2958 ° |
| 1.5708 rad | 90.0002 ° |
| 2 rad | 114.5916 ° |
| 3 rad | 171.8873 ° |
| 3.1416 rad | 180.0004 ° |
| 4 rad | 229.1831 ° |
| 5 rad | 286.4789 ° |
| 6.2832 rad | 360.0008 ° |
Reverse and related
About radians and degrees
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)
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)
Where people use this
Radians: trigonometry, physics, programming. Degrees: geometry, navigation, construction angles. π radians is exactly 180°.
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 degrees is π radians?
π radians is exactly 180°. To convert radians to degrees, multiply by 180/π.
How do you convert radians to degrees?
Multiply the radians by 180/π, so 1 radian is about 57.3° and π/2 is 90°.
How many degrees is 2π radians?
2π radians is a full turn, 360°.
How many degrees is 1 radian?
One radian is about 57.296°.