# Hertz to Radians Per Second Conversion

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

**Results in Radians Per Second:**

## How to Convert Hertz to Radians Per Second

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

The frequency in radians per second is equal to the hertz multiplied by 6.283185.

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

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

In other words, the angular frequency ω in radians per second is equal to 2 times pi times the frequency ƒ in hertz.

Hertz and radians per second are both units used to measure frequency. Keep reading to learn more about each unit of measure.

## Hertz

Hertz is formally defined as the frequency equalling one cycle per second.^{[1]}

The hertz is the SI derived unit for frequency in the metric system. Hertz can be abbreviated as *Hz*, for example 1 hertz can be written as 1 Hz.

Frequency in hertz can be expressed using the formula:
Hz = CyclesTime_{s}

## Radians Per Second

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

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

In formal expressions, the slash, or solidus (/), is used to separate units used to indicate division in an expression.^{[2]}

## Hertz to Radian Per Second Conversion Table

Hertz | Radians Per Second |
---|---|

1 Hz | 6.2832 rad/s |

2 Hz | 12.57 rad/s |

3 Hz | 18.85 rad/s |

4 Hz | 25.13 rad/s |

5 Hz | 31.42 rad/s |

6 Hz | 37.7 rad/s |

7 Hz | 43.98 rad/s |

8 Hz | 50.27 rad/s |

9 Hz | 56.55 rad/s |

10 Hz | 62.83 rad/s |

11 Hz | 69.12 rad/s |

12 Hz | 75.4 rad/s |

13 Hz | 81.68 rad/s |

14 Hz | 87.96 rad/s |

15 Hz | 94.25 rad/s |

16 Hz | 100.53 rad/s |

17 Hz | 106.81 rad/s |

18 Hz | 113.1 rad/s |

19 Hz | 119.38 rad/s |

20 Hz | 125.66 rad/s |

21 Hz | 131.95 rad/s |

22 Hz | 138.23 rad/s |

23 Hz | 144.51 rad/s |

24 Hz | 150.8 rad/s |

25 Hz | 157.08 rad/s |

26 Hz | 163.36 rad/s |

27 Hz | 169.65 rad/s |

28 Hz | 175.93 rad/s |

29 Hz | 182.21 rad/s |

30 Hz | 188.5 rad/s |

31 Hz | 194.78 rad/s |

32 Hz | 201.06 rad/s |

33 Hz | 207.35 rad/s |

34 Hz | 213.63 rad/s |

35 Hz | 219.91 rad/s |

36 Hz | 226.19 rad/s |

37 Hz | 232.48 rad/s |

38 Hz | 238.76 rad/s |

39 Hz | 245.04 rad/s |

40 Hz | 251.33 rad/s |

## References

- National Institute of Standards and Technology, SI Units - Time, https://www.nist.gov/pml/weights-and-measures/si-units-time
- 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