Enter the frequency in radians per second below to get the value converted to revolutions per minute.

## Have a Question or Feedback?

## Result in Revolutions per Minute:

1 rad/s = 9.549297 RPM

Learn how we calculated this below

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Do you want to convert revolutions per minute to radians per second?

## How to Convert Radians per Second to Revolutions per Minute

By

Joe Sexton

Joe is the creator of Inch Calculator and has over 20 years of experience in engineering and construction. He holds several degrees and certifications.

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Reviewed by

Ethan Dederick, PhD

Ethan has a PhD in astrophysics and is currently a satellite imaging scientist. He specializes in math, science, and astrophysics.

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## Cite As:

Sexton, J. (n.d.). Radians per Second to Revolutions per Minute Converter. Inch Calculator. Retrieved July 31, 2024, from https://www.inchcalculator.com/convert/radian-per-second-to-revolution-per-minute/

To convert a measurement in radians per second to a measurement in revolutions per minute, multiply the frequency by the following conversion ratio: 9.549297 revolutions per minute/radian per second.

Since one radian per second is equal to 9.549297 revolutions per minute, you can use this simple formula to convert:

revolutions per minute = radians per second × 9.549297

The frequency in revolutions per minute is equal to the frequency in radians per second multiplied by 9.549297.

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

revolutions per minute = (5 rad/s × 9.549297) = 47.746483 RPM

### How Many Revolutions per Minute Are in One Radian per Second?

There are **9.549297** revolutions per minute in one radian per second, which is why we use this value in the formula above.

1 rad/s = 9.549297 RPM

The following formula can also be used to convert the angular frequency in radians per second to the frequency in revolutions per minute:

RPM = 60 × rad/s / 2π

Thus, the frequency in revolutions per minutes is equal to the angular frequency in radians per second divided by 2π times 60.

**For example,** here's how to convert 5 rad/s to RPM using this formula.

RPM = 60 × 5 rad/s / 2π

RPM = 300 / 2π

RPM = 47.746483

Radians per second and revolutions per minute are both units used to measure frequency. Keep reading to learn more about each unit of measure.

## What Are Radians per Second?

Radians per second are a measure of angular frequency, or rotational speed, equal to the change in the angular orientation of an object over one second.

Radians per second can be abbreviated as *rad/s*; for example, 1 radian per second can be written as 1 rad/s.

In the expressions of units, the slash, or solidus (/), is used to express a change in one or more units relative to a change in one or more other units.^{[1]} For example, rad/s is expressing a change in angle relative to a change in time.

Learn more about radians per second.

## What Are Revolutions per Minute?

Revolutions per minute are a measure of the number of rotations, turns, or revolutions, that an object makes each minute.

Revolutions per minute can be abbreviated as *RPM*, and are also sometimes abbreviated as *rev/min* or *r/min*. For example, 1 revolution per minute can be written as 1 RPM, 1 rev/min, or 1 r/min.

Revolutions per minute can be expressed using the formula:

RPM = Revolutions / Time in Minutes

Learn more about revolutions per minute.

## Radian per Second to Revolution per Minute Conversion Table

Radians Per Second | Revolutions Per Minute |
---|---|

1 rad/s | 9.5493 RPM |

2 rad/s | 19.1 RPM |

3 rad/s | 28.65 RPM |

4 rad/s | 38.2 RPM |

5 rad/s | 47.75 RPM |

6 rad/s | 57.3 RPM |

7 rad/s | 66.85 RPM |

8 rad/s | 76.39 RPM |

9 rad/s | 85.94 RPM |

10 rad/s | 95.49 RPM |

11 rad/s | 105.04 RPM |

12 rad/s | 114.59 RPM |

13 rad/s | 124.14 RPM |

14 rad/s | 133.69 RPM |

15 rad/s | 143.24 RPM |

16 rad/s | 152.79 RPM |

17 rad/s | 162.34 RPM |

18 rad/s | 171.89 RPM |

19 rad/s | 181.44 RPM |

20 rad/s | 190.99 RPM |

21 rad/s | 200.54 RPM |

22 rad/s | 210.08 RPM |

23 rad/s | 219.63 RPM |

24 rad/s | 229.18 RPM |

25 rad/s | 238.73 RPM |

26 rad/s | 248.28 RPM |

27 rad/s | 257.83 RPM |

28 rad/s | 267.38 RPM |

29 rad/s | 276.93 RPM |

30 rad/s | 286.48 RPM |

31 rad/s | 296.03 RPM |

32 rad/s | 305.58 RPM |

33 rad/s | 315.13 RPM |

34 rad/s | 324.68 RPM |

35 rad/s | 334.23 RPM |

36 rad/s | 343.77 RPM |

37 rad/s | 353.32 RPM |

38 rad/s | 362.87 RPM |

39 rad/s | 372.42 RPM |

40 rad/s | 381.97 RPM |

## References

- National Institute of Standards and Technology, NIST Guide to the SI, Chapter 6: Rules and Style Conventions for Printing and Using Units, https://www.nist.gov/pml/special-publication-811/nist-guide-si-chapter-6-rules-and-style-conventions-printing-and-using

## More Radian per Second & Revolution per Minute Conversions

- radians per second to hertz
- radians per second to kilohertz
- radians per second to megahertz
- radians per second to gigahertz
- radians per second to terahertz
- radians per second to cycles per second
- radians per second to degrees per second
- hertz to revolutions per minute
- kilohertz to revolutions per minute
- megahertz to revolutions per minute
- gigahertz to revolutions per minute
- terahertz to revolutions per minute
- cycles per second to revolutions per minute
- degrees per second to revolutions per minute