# Revolutions to Radians Conversion

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

**Results in Radians:**

## How to Convert Revolutions to Radians

To convert a revolution measurement to a radian measurement, multiply the angle by the conversion ratio. One revolution is equal to 6.283185 radians, so use this simple formula to convert:

The angle in radians is equal to the revolutions multiplied by 6.283185.

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

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

## 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.

## 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.

## Revolution to Radian Conversion Table

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

1 r | 6.2832 rad |

2 r | 12.57 rad |

3 r | 18.85 rad |

4 r | 25.13 rad |

5 r | 31.42 rad |

6 r | 37.7 rad |

7 r | 43.98 rad |

8 r | 50.27 rad |

9 r | 56.55 rad |

10 r | 62.83 rad |

11 r | 69.12 rad |

12 r | 75.4 rad |

13 r | 81.68 rad |

14 r | 87.96 rad |

15 r | 94.25 rad |

16 r | 100.53 rad |

17 r | 106.81 rad |

18 r | 113.1 rad |

19 r | 119.38 rad |

20 r | 125.66 rad |

21 r | 131.95 rad |

22 r | 138.23 rad |

23 r | 144.51 rad |

24 r | 150.8 rad |

25 r | 157.08 rad |

26 r | 163.36 rad |

27 r | 169.65 rad |

28 r | 175.93 rad |

29 r | 182.21 rad |

30 r | 188.5 rad |

31 r | 194.78 rad |

32 r | 201.06 rad |

33 r | 207.35 rad |

34 r | 213.63 rad |

35 r | 219.91 rad |

36 r | 226.19 rad |

37 r | 232.48 rad |

38 r | 238.76 rad |

39 r | 245.04 rad |

40 r | 251.33 rad |

## 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