Multiply degrees by π/180 to get radians. Calculators, programming languages and physics formulas almost always expect radians.
How to use the Degrees to Radians Converter
- Type the number of degrees into the Degrees field. Decimals such as 90 are fine.
- Read the answer in Radians – it updates as you type, with no button to press.
- To convert the other way, type into Radians and the degrees are recalculated.
- Press Copy results to copy both values with the page title, or Copy link to share this exact conversion.
This page converts only ° ⇄ rad. Need a different unit? Use the general angle converter, where you can choose any “from” and “to” unit.
How it works
Both units measure angle, so they are always in the same ratio: one degree equals 0.017453293 radians. The calculator multiplies the number of degrees you type by 0.017453293 to give radians, and when you type into the radians field it divides by the same factor to give degrees. Because the ratio never changes, doubling the degrees always doubles the radians. Results are calculated at full precision and rounded only for display (up to eight decimal places, with very large or small values shown in scientific notation).
How to convert degrees to radians
- Write down the value in degrees, for example 180 °.
- Multiply by the conversion factor 0.017453293 (because 1 degree = 0.017453293 rad).
- 180 × 0.017453293 = 3.1415927 rad.
- To go back from radians to degrees, divide by 0.017453293 – or multiply by 57.29578.
° to rad conversion table
| Degrees | Radians | Radians | Degrees |
|---|---|---|---|
| 1 ° | 0.017453293 rad | 1 rad | 57.29578 ° |
| 15 ° | 0.26179939 rad | 2 rad | 114.59156 ° |
| 30 ° | 0.52359878 rad | 5 rad | 286.4789 ° |
| 45 ° | 0.78539816 rad | 10 rad | 572.9578 ° |
| 57.2958 ° | 1.0000004 rad | 20 rad | 1,145.9156 ° |
| 60 ° | 1.0471976 rad | 50 rad | 2,864.789 ° |
| 90 ° | 1.5707963 rad | 100 rad | 5,729.578 ° |
| 120 ° | 2.0943951 rad | 1,000 rad | 57,295.78 ° |
| 180 ° | 3.1415927 rad | ||
| 270 ° | 4.712389 rad | ||
| 360 ° | 6.2831853 rad |
What is a degree?
A degree is 1/360 of a full turn. Navigation, construction and geometry use degrees.
What is a radian?
The radian is the SI unit of angle: the angle at which an arc equals the radius. A full circle is 2π radians, about 6.283.
Quick mental conversion
For a fast estimate, multiply degrees by about 0.017 to get radians; the error is about 2.6%. Use the calculator above when you need the exact figure.
Common mistakes to avoid
Feeding degrees into a calculator set to radians (or the reverse), and reading decimal degrees as degrees and minutes.
Formula
1 ° = 0.017453293 rad1 rad = 57.29578 °rad = ° × 0.017453293Worked example
Inputs — Degrees: 180 °.
Results — Radians = 3.14159265 rad.
Frequently asked questions
How many radians is 90°?
π/2, about 1.5708.
How many radians in a full circle?
2π, about 6.2832.
How many radians are in one degree?
1 ° = 0.017453293 rad.
How many degrees are in one radian?
1 rad = 57.29578 °.
How do I convert degrees to radians?
Multiply the number of degrees by 0.017453293. For example, 180 ° × 0.017453293 = 3.1415927 rad.
How do I convert radians back to degrees?
Divide by 0.017453293 (or multiply by 57.29578), or simply type the value into the radians field above.
What is 1 ° in radians?
1 ° = 0.017453293 rad.
What is 15 ° in radians?
15 ° = 0.26179939 rad.
Is this conversion exact?
Yes. The factor comes from the official definitions of both units (NIST and the SI), so the only difference you may see is rounding in the last displayed digit.
Can I convert to other units on this page?
This page converts only between degrees and radians. To pick any angle unit, use the general angle converter linked under Related calculators.
What formula does the Degrees to Radians Converter use?
1 ° = 0.017453293 rad.