Convert Cycles Per Second to Radians Per Second

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

Results in Radians Per Second:

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

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:

radians per second = cycles per second × 6.283185

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.

5 cps = (5 × 6.283185) = 31.415927 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.

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.

Cycle Per Second Measurements and Equivalent Radian Per Second Conversions

Common cycle per second values converted to the equivalent radian per second value
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