Convert Degrees to Radians
Convert Degrees to Radians instantly. 1 Degree (°) equals 0.01745 Radians (rad).
Degrees to Radians conversion table
| Degrees (°) | Radians (rad) |
|---|---|
| 1 ° | 0.01745 rad |
| 2 ° | 0.03491 rad |
| 3 ° | 0.05236 rad |
| 5 ° | 0.08727 rad |
| 10 ° | 0.1745 rad |
| 20 ° | 0.3491 rad |
| 50 ° | 0.8727 rad |
| 100 ° | 1.7453 rad |
| 500 ° | 8.7266 rad |
| 1,000 ° | 17.4533 rad |
1 Degree = 0.01745 Radians · multiply Degrees by 0.01745
About converting Degrees to Radians
Degrees (°) and Radians (rad) are both units of angle, so converting between them is a single multiplication: multiply your Degrees figure by 0.01745. Ten Degrees comes to 0.1745 Radians, and a hundred works out at 1.7453 Radians.
Rule of thumb: going from Degrees to Radians divides, so the figure always shrinks — it takes about 57.2958 Degrees to make a single Radian. If your answer came out bigger, you have the conversion the wrong way round.
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.
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.
To put both in perspective: a right angle is 90 degrees, while a full circle is 2π radians.
The converter above updates as you type, and the table lists common values for quick reference. Need the opposite direction? Use the Radians to Degrees converter, or browse all Angle converters.
Frequently asked questions
How many Radians are in one Degree?
There are 0.01745 Radians in one Degree.
How do I convert Degrees to Radians?
Multiply the number of Degrees by 0.01745. For example, 10 Degrees = 0.1745 Radians.
What is 100 Degrees in Radians?
100 Degrees is equal to 1.7453 Radians.
How do I convert Radians to Degrees?
Multiply the Radians value by 57.2958 (or divide by 0.01745).
Is this Degrees to Radians conversion exact?
The definition is exact — Degrees and Radians 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 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.
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.