Circles to Radians Conversion
Enter the angle in circles below to get the value converted to radians.
How to Convert Circles to Radians
To convert a circle measurement to a radian measurement, multiply the angle by the conversion ratio. One circle is equal to 6.283185 radians, so use this simple formula to convert:
The angle in radians is equal to the circles multiplied by 6.283185.
Circles and radians are both units used to measure angle. Keep reading to learn more about each unit of measure.
Circles
A circle is the equivalent of 1 revolution around a circle, or 360°.
A circle is sometimes also referred to as a revolution. Circles can be abbreviated as cir; for example, 1 circle can be written as 1 cir.
Radians
A radian is the measurement of angle equal to the start to the end of an arc divided by the radius of the circle or arc.[1] 1 radian is equal to 180/π, or about 57.29578°. There are about 6.28318 radians in a circle.
The radian is the SI derived unit for angle in the metric system. Radians can be abbreviated as rad, and are also sometimes abbreviated as c, r, or R. For example, 1 radian can be written as 1 rad, 1 c, 1 r, or 1 R.
Radians are often expressed using their definition. The formula to find radians is θ = s/r, where the angle in radians θ is equal to the arc length s divided by the radius r. Thus, radians may also be expressed as the formula of arc length over the radius.
Circle to Radian Conversion Table
| Circles | Radians |
|---|---|
| 1 cir | 6.2832 rad |
| 2 cir | 12.57 rad |
| 3 cir | 18.85 rad |
| 4 cir | 25.13 rad |
| 5 cir | 31.42 rad |
| 6 cir | 37.7 rad |
| 7 cir | 43.98 rad |
| 8 cir | 50.27 rad |
| 9 cir | 56.55 rad |
| 10 cir | 62.83 rad |
| 11 cir | 69.12 rad |
| 12 cir | 75.4 rad |
| 13 cir | 81.68 rad |
| 14 cir | 87.96 rad |
| 15 cir | 94.25 rad |
| 16 cir | 100.53 rad |
| 17 cir | 106.81 rad |
| 18 cir | 113.1 rad |
| 19 cir | 119.38 rad |
| 20 cir | 125.66 rad |
| 21 cir | 131.95 rad |
| 22 cir | 138.23 rad |
| 23 cir | 144.51 rad |
| 24 cir | 150.8 rad |
| 25 cir | 157.08 rad |
| 26 cir | 163.36 rad |
| 27 cir | 169.65 rad |
| 28 cir | 175.93 rad |
| 29 cir | 182.21 rad |
| 30 cir | 188.5 rad |
| 31 cir | 194.78 rad |
| 32 cir | 201.06 rad |
| 33 cir | 207.35 rad |
| 34 cir | 213.63 rad |
| 35 cir | 219.91 rad |
| 36 cir | 226.19 rad |
| 37 cir | 232.48 rad |
| 38 cir | 238.76 rad |
| 39 cir | 245.04 rad |
| 40 cir | 251.33 rad |
References
- International Bureau of Weights and Measures, The International System of Units, 9th Edition, 2019, https://www.bipm.org/utils/common/pdf/si-brochure/SI-Brochure-9.pdf
