# Radians to Revolutions Conversion

Enter the angle in radians below to get the value converted to revolutions.

**Results in Revolutions:**

## How to Convert Radians to Revolutions

To convert a radian measurement to a revolution measurement, multiply the angle by the conversion ratio. One radian is equal to 0.159155 revolutions, so use this simple formula to convert:

The angle in revolutions is equal to the radians multiplied by 0.159155.

**For example,**here's how to convert 5 radians to revolutions using the formula above.

Radians and revolutions are both units used to measure angle. Keep reading to learn more about each unit of measure.

## 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

*. 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 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.

## Revolutions

A revolution, or turn, is equal to 1 rotation around a circle, or 360°. Revolutions are commonly used to measure the speed of rotation, for example when measuring the revolutions per minute (RPM) of a vehicle's engine.

A revolution is sometimes also referred to as a turn, cycle, or complete rotation. Revolutions can be abbreviated as *r*, and are also sometimes abbreviated as *rev* or *cyc*. For example, 1 revolution can be written as 1 r, 1 rev, or 1 cyc.

## Radian to Revolution Conversion Table

Radians | Revolutions |
---|---|

1 rad | 0.159155 r |

2 rad | 0.31831 r |

3 rad | 0.477465 r |

4 rad | 0.63662 r |

5 rad | 0.795775 r |

6 rad | 0.95493 r |

7 rad | 1.1141 r |

8 rad | 1.2732 r |

9 rad | 1.4324 r |

10 rad | 1.5915 r |

11 rad | 1.7507 r |

12 rad | 1.9099 r |

13 rad | 2.069 r |

14 rad | 2.2282 r |

15 rad | 2.3873 r |

16 rad | 2.5465 r |

17 rad | 2.7056 r |

18 rad | 2.8648 r |

19 rad | 3.0239 r |

20 rad | 3.1831 r |

21 rad | 3.3423 r |

22 rad | 3.5014 r |

23 rad | 3.6606 r |

24 rad | 3.8197 r |

25 rad | 3.9789 r |

26 rad | 4.138 r |

27 rad | 4.2972 r |

28 rad | 4.4563 r |

29 rad | 4.6155 r |

30 rad | 4.7746 r |

31 rad | 4.9338 r |

32 rad | 5.093 r |

33 rad | 5.2521 r |

34 rad | 5.4113 r |

35 rad | 5.5704 r |

36 rad | 5.7296 r |

37 rad | 5.8887 r |

38 rad | 6.0479 r |

39 rad | 6.207 r |

40 rad | 6.3662 r |

## 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