Convert degrees to radians
Convert degrees to radians instantly. 1 ° = 0.017453 rad. Formula, worked examples and a quick reference table.
Last updated
One degree equals 0.017453 radians. To convert any number of degrees to radians, multiply by 0.01745329.
The converter above works in both directions and updates as you type. Below you will find the formula, a worked example and a reference table of common values.
Angle conversion is a small category with one important reason to exist. Degrees are how angles are described in everyday life and in navigation; radians are how they are handled in mathematics, because the radian is defined so that arc length equals radius times angle, which is what makes the derivatives of the trigonometric functions come out clean. Nearly every programming language expects radians, which is why a degree figure fed straight into a sine function is such a common bug.
degrees to radians formula
To go the other way, use degree = radian ÷ 0.01745329.
About these units
The 360-degree circle comes from Babylonian astronomy, and 360 survives because it divides evenly by so many numbers — a property no other round figure matches.
A radian is the angle at which the arc length equals the radius. A full circle is 2π radians, which is why radians are the natural unit in calculus.
Degree is also written degrees and deg. Radian is also written radians and rads.
Sources
degrees to radians conversion table
| Degree | Radian |
|---|---|
| 1 ° | 0.01745 rad |
| 2 ° | 0.03491 rad |
| 3 ° | 0.05236 rad |
| 5 ° | 0.08727 rad |
| 10 ° | 0.1745 rad |
| 20 ° | 0.3491 rad |
| 25 ° | 0.4363 rad |
| 50 ° | 0.8727 rad |
| 100 ° | 1.7453 rad |
| 250 ° | 4.3633 rad |
| 500 ° | 8.7266 rad |
| 1,000 ° | 17.4533 rad |
Frequently asked questions
How many radians are in a degree? +
There are 0.017453 radians in one degree.
What is 10 ° in rad? +
10 ° equals 0.1745 rad. Multiply 10 by 0.01745329.
How do I convert radian back to degree? +
Use degree = radian ÷ 0.01745329. The converter above handles both directions, or see our dedicated radians to degrees page.
How accurate is this degree to radian conversion? +
The factor used is 0.0174532925, carried at full double precision. Where a unit has an exact legal definition the factor is exact rather than approximate. Rounding is applied only to the displayed result, so the answer is never a calculation done on an already-rounded number.
Is there a quick way to estimate ° to rad in my head? +
Divide by 57.3. That reproduces the exact factor of 0.017453 to the precision you could read off a result anyway.