Convert radians to degrees
Convert radians to degrees instantly. 1 rad = 57.29578 °. Formula, worked examples and a quick reference table.
Last updated
One radian equals 57.29578 degrees. To convert any number of radians to degrees, multiply by 57.29577951.
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.
radians to degrees formula
To go the other way, use radian = degree ÷ 57.29577951.
About these units
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.
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.
Radian is also written radians and rads. Degree is also written degrees and deg.
Sources
radians to degrees conversion table
| Radian | Degree |
|---|---|
| 1 rad | 57.2958 ° |
| 2 rad | 114.5916 ° |
| 3 rad | 171.8873 ° |
| 5 rad | 286.4789 ° |
| 10 rad | 572.9578 ° |
| 20 rad | 1,145.9156 ° |
| 25 rad | 1,432.3945 ° |
| 50 rad | 2,864.789 ° |
| 100 rad | 5,729.578 ° |
| 250 rad | 14,323.9449 ° |
| 500 rad | 28,647.8898 ° |
| 1,000 rad | 57,295.7795 ° |
Frequently asked questions
How many degrees are in a radian? +
There are 57.29578 degrees in one radian.
What is 10 rad in °? +
10 rad equals 572.9578 °. Multiply 10 by 57.29577951.
How do I convert degree back to radian? +
Use radian = degree ÷ 57.29577951. The converter above handles both directions, or see our dedicated degrees to radians page.
How accurate is this radian to degree conversion? +
The factor used is 57.2957795131, 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 rad to ° in my head? +
Multiply by 115 and divide by 2. That approximates the true factor of 57.29578 to within 0.3564%, which is close enough for a mental estimate.