# Revolutions to Radians Converter

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

**Results in Radians:**

Do you want to convert radians to revolutions?

## How to Convert Revolutions to Radians

To convert a measurement in revolutions to a measurement in radians, multiply the angle by the following conversion ratio: 6.283185 radians/revolution.

Since one revolution is equal to 6.283185 radians, you can use this simple formula to convert:

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

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

### How Many Radians Are in a Revolution?

There are **6.283185** radians in a revolution, which is why we use this value in the formula above.

1 r = 6.283185 rad

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

## 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.

## 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.

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

## More Revolution & Radian Conversions

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