Radians to Degrees
An instant radians-to-degrees converter, with the formula and a reference table below.
| Radians | Degrees |
|---|---|
| 1 rad | 57.29578 ° |
| 2 rad | 114.591559 ° |
| 3 rad | 171.887339 ° |
| 5 rad | 286.478898 ° |
| 10 rad | 572.957795 ° |
| 25 rad | 1432.394488 ° |
| 50 rad | 2864.788976 ° |
| 100 rad | 5729.577951 ° |
How to use
- Enter a value in the Radians field.
- The Degrees figure appears immediately — no button to press.
- Typing in the Degrees field converts back to Radians the same way.
- Use the reference table for the values that come up most often.
Radians to Degrees formula
The factor from radians to degrees is 57.2957795.
° = rad × 57.2957795
Why this factor: the radian and the degree are both defined against the degree, so dividing one definition by the other gives 57.2957795 directly. Both definitions are set out in full below.
To go the other way, divide by 57.2957795 — or use the Degrees to Radians converter, which is the same calculation reversed.
Worked example
Given 45 rad, multiplying by 57.2957795 yields 2578.310078 °.
45 rad × 57.2957795 = 2578.310078 °
The converter above does this for any value you type, in either direction.
What is a radian?
A radian is the angle that subtends an arc equal in length to the circle's radius — the natural unit of angle.
Definition: A full turn is exactly 2π radians, so one radian is 180/π degrees, about 57.29578°.
Where it is used: Calculus and trigonometry, physics, and every standard programming library's sin, cos and tan.
Worth knowing: Programming maths functions almost always expect radians. Passing degrees to Math.sin() is one of the most common numerical bugs.
What is a degree?
A degree is one 360th of a full turn, the everyday unit of angle.
Definition: Exactly 1/360 of a complete revolution. The choice of 360 comes from Babylonian base-60 arithmetic.
Where it is used: Geometry, navigation bearings, latitude and longitude, and CSS rotations.
Radians vs Degrees
The radian is an SI unit while the degree is a specialized unit. That is why the factor between them is not a round number: the two systems were defined independently and only later tied together by exact agreement.
Frequently asked questions
How many degrees are in a radian?
One radian equals 57.2957795 degrees.
What is the formula to convert radians to degrees?
Multiply the number of radians by 57.2957795. To reverse it, divide by 57.2957795 instead.
How do I convert degrees back to radians?
Divide by 57.2957795, which is the same as multiplying by 0.0174532925.
How many degrees are in 10 radians?
10 rad works out to 572.957795 °.
Is there anything to watch out for with radians?
Programming maths functions almost always expect radians. Passing degrees to Math.sin() is one of the most common numerical bugs.
How is the radian defined?
A full turn is exactly 2π radians, so one radian is 180/π degrees, about 57.29578°.