Convert Radians to Degrees
Convert Radians to Degrees instantly. 1 Radian (rad) equals 57.2958 Degrees (°).
Radians to Degrees conversion table
| Radians (rad) | Degrees (°) |
|---|---|
| 1 rad | 57.2958 ° |
| 2 rad | 114.5916 ° |
| 3 rad | 171.8873 ° |
| 5 rad | 286.4789 ° |
| 10 rad | 572.9578 ° |
| 20 rad | 1,145.92 ° |
| 50 rad | 2,864.79 ° |
| 100 rad | 5,729.58 ° |
| 500 rad | 28,647.89 ° |
| 1,000 rad | 57,295.78 ° |
1 Radian = 57.2958 Degrees · multiply Radians by 57.2958
About converting Radians to Degrees
Radians (rad) and Degrees (°) are both units of angle, so converting between them is a single multiplication: multiply your Radians figure by 57.2958. Ten Radians comes to 572.9578 Degrees, and a hundred works out at 5,729.58 Degrees.
Rule of thumb: going from Radians to Degrees multiplies, so the figure always grows — one Radian is already 57.2958 Degrees. If your answer came out smaller, you have the conversion the wrong way round.
What is a Radian?
The radian is the SI unit of angle and the natural one for mathematics, because it is defined by the circle itself rather than by decree: it is the angle you have swept when the arc travelled around the rim is exactly as long as the radius. A full circle is exactly 2π radians, with no arbitrary count involved. That matters well beyond neatness — the calculus of sine and cosine only comes out clean in radians, and introducing degrees scatters stray constants through every derivative. It is why every programming language’s math library expects radians, and why feeding degrees to sin() is a classic bug in graphics and physics code.
What is a Degree?
The degree is the everyday unit of angle, and its division of the circle into 360 parts comes from Babylonian astronomy and the base-60 arithmetic that came with it. The number survived because it is unreasonably convenient: 360 divides evenly by 2, 3, 4, 5, 6, 8, 9, 10 and 12, so halves, thirds, quarters, fifths and sixths of a circle are all whole numbers of degrees. Nothing about it is natural or mathematically necessary — it is a human choice that stuck for thousands of years because the arithmetic is painless. Like the hectare, it is not an SI unit but is accepted for use with SI.
To put both in perspective: a full circle is 2π radians, while a right angle is 90 degrees.
The converter above updates as you type, and the table lists common values for quick reference. Need the opposite direction? Use the Degrees to Radians converter, or browse all Angle converters.
Frequently asked questions
How many Degrees are in one Radian?
There are 57.2958 Degrees in one Radian.
How do I convert Radians to Degrees?
Multiply the number of Radians by 57.2958. For example, 10 Radians = 572.9578 Degrees.
What is 100 Radians in Degrees?
100 Radians is equal to 5,729.58 Degrees.
How do I convert Degrees to Radians?
Multiply the Degrees value by 0.01745 (or divide by 57.2958).
Is this Radians to Degrees conversion exact?
The definition is exact — Radians and Degrees are both fixed against the same base by international agreement — but the decimal shown here is rounded for readability, because the true ratio does not terminate. For engineering or scientific work, carry more decimal places than this page displays.
What is a Radian?
The radian is the SI unit of angle and the natural one for mathematics, because it is defined by the circle itself rather than by decree: it is the angle you have swept when the arc travelled around the rim is exactly as long as the radius. A full circle is exactly 2π radians, with no arbitrary count involved. That matters well beyond neatness — the calculus of sine and cosine only comes out clean in radians, and introducing degrees scatters stray constants through every derivative. It is why every programming language’s math library expects radians, and why feeding degrees to sin() is a classic bug in graphics and physics code.
What is a Degree?
The degree is the everyday unit of angle, and its division of the circle into 360 parts comes from Babylonian astronomy and the base-60 arithmetic that came with it. The number survived because it is unreasonably convenient: 360 divides evenly by 2, 3, 4, 5, 6, 8, 9, 10 and 12, so halves, thirds, quarters, fifths and sixths of a circle are all whole numbers of degrees. Nothing about it is natural or mathematically necessary — it is a human choice that stuck for thousands of years because the arithmetic is painless. Like the hectare, it is not an SI unit but is accepted for use with SI.