# 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)

**Results in Circles:**

Do you want to convert circles to radians?

## 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.

### 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

*. For example, 1 radian can be written as 1 rad, 1*

^{R}^{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

## More Radian & Circle Conversions

- radians to milliradians
- radians to degrees
- radians to minutes of arc
- radians to seconds of arc
- radians to gradians
- radians to revolutions
- radians to mils
- milliradians to circles
- degrees to circles
- minutes of arc to circles
- seconds of arc to circles
- gradians to circles
- revolutions to circles
- mils to circles