# Radians to Revolutions Converter

Enter the angle in radians below to get the value converted to revolutions. The calculator supports values containing decimals, fractions, and π: (π/2, 1/2π, etc)

## Result in Revolutions:

Do you want to convert revolutions to radians?

## How to Convert Radians to Revolutions

To convert a measurement in radians to a measurement in revolutions, multiply the angle by the following conversion ratio: 0.159155 revolutions/radian.

Since one radian is equal to 0.159155 revolutions, you can use this simple formula to convert:

revolutions = radians × 0.159155

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

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

### How Many Revolutions Are in a Radian?

There are **0.159155** revolutions in a radian, which is why we use this value in the formula above.

1 rad = 0.159155 r

Radians and revolutions 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 Revolution?

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.

Learn more about revolutions.

## 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/documents/20126/41483022/SI-Brochure-9-EN.pdf

## More Radian & Revolution Conversions

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