Radians to Circles Converter
Enter the angle in radians below to get the value converted to circles. The calculator supports values containing decimals, fractions, and π: (π/2, 1/2π, etc)
Result in Circles:
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How to Convert Radians to Circles
To convert a measurement in radians to a measurement in circles, multiply the angle by the following conversion ratio: 0.159155 circles/radian.
Since one radian is equal to 0.159155 circles, you can use this simple formula to convert:
circles = radians × 0.159155
The angle in circles is equal to the angle in radians multiplied by 0.159155.
For example, here's how to convert 5 radians to circles using the formula above.
circles = (5 rad × 0.159155) = 0.795775 cir
How Many Circles Are in a Radian?
There are 0.159155 circles in a radian, which is why we use this value in the formula above.
1 rad = 0.159155 cir
Radians and circles are both units used to measure angle. Keep reading to learn more about each unit of measure.
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.
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.
Radian to Circle Conversion Table
| Radians | Circles |
|---|---|
| 1 rad | 0.159155 cir |
| 2 rad | 0.31831 cir |
| 3 rad | 0.477465 cir |
| 4 rad | 0.63662 cir |
| 5 rad | 0.795775 cir |
| 6 rad | 0.95493 cir |
| 7 rad | 1.1141 cir |
| 8 rad | 1.2732 cir |
| 9 rad | 1.4324 cir |
| 10 rad | 1.5915 cir |
| 11 rad | 1.7507 cir |
| 12 rad | 1.9099 cir |
| 13 rad | 2.069 cir |
| 14 rad | 2.2282 cir |
| 15 rad | 2.3873 cir |
| 16 rad | 2.5465 cir |
| 17 rad | 2.7056 cir |
| 18 rad | 2.8648 cir |
| 19 rad | 3.0239 cir |
| 20 rad | 3.1831 cir |
| 21 rad | 3.3423 cir |
| 22 rad | 3.5014 cir |
| 23 rad | 3.6606 cir |
| 24 rad | 3.8197 cir |
| 25 rad | 3.9789 cir |
| 26 rad | 4.138 cir |
| 27 rad | 4.2972 cir |
| 28 rad | 4.4563 cir |
| 29 rad | 4.6155 cir |
| 30 rad | 4.7746 cir |
| 31 rad | 4.9338 cir |
| 32 rad | 5.093 cir |
| 33 rad | 5.2521 cir |
| 34 rad | 5.4113 cir |
| 35 rad | 5.5704 cir |
| 36 rad | 5.7296 cir |
| 37 rad | 5.8887 cir |
| 38 rad | 6.0479 cir |
| 39 rad | 6.207 cir |
| 40 rad | 6.3662 cir |
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