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

## Have a Question or Feedback?

## Result in Radians per Second:

1 RPM = 0.10472 rad/s

Learn how we calculated this below

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

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

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.). Revolutions per Minute to Radians per Second Converter. Inch Calculator. Retrieved August 7, 2024, from https://www.inchcalculator.com/convert/revolution-per-minute-to-radian-per-second/

To convert a measurement in revolutions per minute to a measurement in radians per second, multiply the frequency by the following conversion ratio: 0.10472 radians per second/revolution per minute.

Since one revolution per minute is equal to 0.10472 radians per second, you can use this simple formula to convert:

radians per second = revolutions per minute × 0.10472

The frequency in radians per second is equal to the frequency in revolutions per minute multiplied by 0.10472.

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

radians per second = (5 RPM × 0.10472) = 0.523599 rad/s

### How Many Radians per Second Are in One Revolution per Minute?

There are **0.10472** radians per second in one revolution per minute, which is why we use this value in the formula above.

1 RPM = 0.10472 rad/s

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

rad/s = RPM / 60 × 2π

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

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

rad/s = 5 RPM / 60 × 2π

rad/s = 0.083333 × 2π

rad/s = 0.523599

Revolutions per minute and radians per second are both units used to measure frequency of rotation or revolution. Keep reading to learn more about each unit of measure.

## 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.

## 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.

## Revolution per Minute to Radian per Second Conversion Table

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

1 RPM | 0.10472 rad/s |

2 RPM | 0.20944 rad/s |

3 RPM | 0.314159 rad/s |

4 RPM | 0.418879 rad/s |

5 RPM | 0.523599 rad/s |

6 RPM | 0.628319 rad/s |

7 RPM | 0.733038 rad/s |

8 RPM | 0.837758 rad/s |

9 RPM | 0.942478 rad/s |

10 RPM | 1.0472 rad/s |

11 RPM | 1.1519 rad/s |

12 RPM | 1.2566 rad/s |

13 RPM | 1.3614 rad/s |

14 RPM | 1.4661 rad/s |

15 RPM | 1.5708 rad/s |

16 RPM | 1.6755 rad/s |

17 RPM | 1.7802 rad/s |

18 RPM | 1.885 rad/s |

19 RPM | 1.9897 rad/s |

20 RPM | 2.0944 rad/s |

21 RPM | 2.1991 rad/s |

22 RPM | 2.3038 rad/s |

23 RPM | 2.4086 rad/s |

24 RPM | 2.5133 rad/s |

25 RPM | 2.618 rad/s |

26 RPM | 2.7227 rad/s |

27 RPM | 2.8274 rad/s |

28 RPM | 2.9322 rad/s |

29 RPM | 3.0369 rad/s |

30 RPM | 3.1416 rad/s |

31 RPM | 3.2463 rad/s |

32 RPM | 3.351 rad/s |

33 RPM | 3.4558 rad/s |

34 RPM | 3.5605 rad/s |

35 RPM | 3.6652 rad/s |

36 RPM | 3.7699 rad/s |

37 RPM | 3.8746 rad/s |

38 RPM | 3.9794 rad/s |

39 RPM | 4.0841 rad/s |

40 RPM | 4.1888 rad/s |

## 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 Revolution per Minute & Radian per Second Conversions

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