Degrees to Radians
Type a value in either box to convert between degrees and radians. The factor is 0.0174533.
| Degrees | Radians |
|---|---|
| 1 ° | 0.017453 rad |
| 2 ° | 0.034907 rad |
| 3 ° | 0.05236 rad |
| 5 ° | 0.087266 rad |
| 10 ° | 0.174533 rad |
| 25 ° | 0.436332 rad |
| 50 ° | 0.872665 rad |
| 100 ° | 1.745329 rad |
How to use
- Enter a value in the Degrees field.
- The Radians figure appears immediately — no button to press.
- Typing in the Radians field converts back to Degrees the same way.
- Use the reference table for the values that come up most often.
Degrees to Radians formula
To convert degrees to radians, multiply by 0.0174532925.
rad = ° × 0.0174532925
Why this factor: the degree and the radian are both defined against the degree, so dividing one definition by the other gives 0.0174532925 directly. Both definitions are set out in full below.
To go the other way, divide by 0.0174532925 — or use the Radians to Degrees converter, which is the same calculation reversed.
Worked example
Take 90 ° and multiply by the factor 0.0174532925: the result is 1.570796 rad.
90 ° × 0.0174532925 = 1.570796 rad
The converter above does this for any value you type, in either direction.
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.
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.
Degrees vs Radians
The degree is a specialized unit while the radian is an SI 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 radians are in a degree?
One degree equals 0.0174532925 radians.
What is the formula to convert degrees to radians?
Multiply the number of degrees by 0.0174532925. To reverse it, divide by 0.0174532925 instead.
How do I convert radians back to degrees?
Divide by 0.0174532925, which is the same as multiplying by 57.2957795.
How many radians are in 10 degrees?
10 ° works out to 0.174533 rad.
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 degree defined?
Exactly 1/360 of a complete revolution. The choice of 360 comes from Babylonian base-60 arithmetic.