Circles to Radians Converter
Enter the angle in circles below to convert it to radians.
Result in Radians:
Do you want to convert radians to circles?
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How to Convert Circles to Radians
To convert a measurement in circles to a measurement in radians, multiply the angle by the following conversion ratio: 6.283185 radians/circle.
Since one circle is equal to 6.283185 radians, you can use this simple formula to convert:
radians = circles × 6.283185
The angle in radians is equal to the angle in circles multiplied by 6.283185.
For example, here's how to convert 5 circles to radians using the formula above.
radians = (5 cir × 6.283185) = 31.415927 rad
How Many Radians Are in a Circle?
There are 6.283185 radians in a circle, which is why we use this value in the formula above.
1 cir = 6.283185 rad
Circles and radians are both units used to measure angle. Keep reading to learn more about each unit of measure.
What Is a Circle?
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.
A circle is more commonly used to describe a round, symmetrical shape with no corners or edges than it is to describe plane angle. The shape is described by its radius and circumference.
Learn more about circles.
What Is a Radian?
A radian is the measurement of angle equal to the length of an arc divided by the radius of the circle or arc.[1] 1 radian is equal to 180/π degrees, 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 an angle in 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.
Radians are also considered to be a "unitless" unit. That is, when multiplying or dividing by radians, the result does not include radians as part of the final units.
For example, when determining the length of an arc for a given angle, we use the formula above, rearranged to be s = θr. If θ is in radians and r is in meters, then the units of s will be meters, not radian-meters. If θ were in degrees, however, then s would have units of degree-meters.
Learn more about radians.
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/documents/20126/41483022/SI-Brochure-9-EN.pdf