# Cycles per Second to Radians per Second Converter

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

**Results in Radians per Second:**

Do you want to convert radians per second to cycles per second?

## How to Convert Cycles per Second to Radians per Second

To convert a measurement in cycles per second to a measurement in radians per second, multiply the frequency by the following conversion ratio: 6.283185 radians per second/cycle per second.

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

radians per second = cycles per second × 6.283185

The frequency in radians per second is equal to the frequency in 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.

### How Many Radians per Second Are in One Cycle per Second?

There are **6.283185** radians per second in one cycle per second, which is why we use this value in the formula above.

1 cps = 6.283185 rad/s

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

## What Are 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 = Cycles / Time_{s}

Learn more about cycles per second.

## 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.

## 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

## More Cycle per Second & Radian per Second Conversions

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