# Cycles Per Second to Radians Per Second Conversion

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

**Results in Radians Per Second:**

## How to Convert Cycles Per Second to Radians Per Second

To convert a cycle per second measurement to a radian per second measurement, multiply the frequency by the conversion ratio. One cycle per second 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 cycles per second multiplied by 6.283185.

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

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

## Cycles Per Second

Cycles per second are a measure of the number of oscillations, or cycles, that occur per second.

Cycles per second can be abbreviated as *cps*, and are also sometimes abbreviated as *c/s* or *cycles/second*. For example, 1 cycle per second can be written as 1 cps, 1 c/s, or 1 cycles/second.

Cycles per second can be expressed using the formula:
cps = 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.^{[1]}

## Cycle Per Second to Radian Per Second Conversion Table

Cycles Per Second | Radians Per Second |
---|---|

1 cps | 6.2832 rad/s |

2 cps | 12.57 rad/s |

3 cps | 18.85 rad/s |

4 cps | 25.13 rad/s |

5 cps | 31.42 rad/s |

6 cps | 37.7 rad/s |

7 cps | 43.98 rad/s |

8 cps | 50.27 rad/s |

9 cps | 56.55 rad/s |

10 cps | 62.83 rad/s |

11 cps | 69.12 rad/s |

12 cps | 75.4 rad/s |

13 cps | 81.68 rad/s |

14 cps | 87.96 rad/s |

15 cps | 94.25 rad/s |

16 cps | 100.53 rad/s |

17 cps | 106.81 rad/s |

18 cps | 113.1 rad/s |

19 cps | 119.38 rad/s |

20 cps | 125.66 rad/s |

21 cps | 131.95 rad/s |

22 cps | 138.23 rad/s |

23 cps | 144.51 rad/s |

24 cps | 150.8 rad/s |

25 cps | 157.08 rad/s |

26 cps | 163.36 rad/s |

27 cps | 169.65 rad/s |

28 cps | 175.93 rad/s |

29 cps | 182.21 rad/s |

30 cps | 188.5 rad/s |

31 cps | 194.78 rad/s |

32 cps | 201.06 rad/s |

33 cps | 207.35 rad/s |

34 cps | 213.63 rad/s |

35 cps | 219.91 rad/s |

36 cps | 226.19 rad/s |

37 cps | 232.48 rad/s |

38 cps | 238.76 rad/s |

39 cps | 245.04 rad/s |

40 cps | 251.33 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