Cycles per Second to Radians per Second Converter

Enter the frequency in cycles per second below to convert it to radians per second.

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Result in Radians per Second:

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1 cps = 6.283185 rad/s

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

How to Convert Cycles per Second to Radians per Second

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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.
radians per second = (5 cps × 6.283185) = 31.415927 rad/s

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 = CyclesTimes

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

Table showing various cycle per second measurements converted to radians per second.
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

  1. 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

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