cps Calculator

Created by Gabriela Diaz
Reviewed by Anna Szczepanek, PhD and Rijk de Wet
Last updated: Sep 30, 2022

The cps calculator will quickly help you convert any value in cycles per second (cps) to other units of frequency, including:

  • Ordinary frequency units: hertz (Hz), kilohertz (kHz), megahertz (MHz), cycles per minute (cpm); and
  • Angular frequency units: revolutions per minute (RPM), radians per second (rad/s), and degrees per second (°/s).

Scroll down and learn in no time how easy it is to convert between hertz and cycles per second!

How to use the cps calculator

With the cps calculator, you can instantly convert any value of frequency from cps (cycles per second) to other frequency units like hertz (Hz), radians per second (rad/s), revolutions per minute (RPM) and more. To use the cps calculator:

  1. In the first row, type in the frequency value in cps that you wish to convert to other frequency units.
  2. The calculator will show the results in the rows below!

Would you like to learn more about RPM and how to calculate them? Check our RPM calculator!

Frequency units

Frequency is a parameter that measures the repetitiveness of a given event. In sciences, it's often used as one of the main parameters to describe a wave's oscillatory nature (sound, vibration, light).

Since 1960, the SI unit to measure linear frequencies is hertz (Hz), named after the German physicist Heinrich Hertz, and it represents the number of times an event repeats in one second. Previously, frequencies were measured in cycles per second (cps), from where other units derive: cpm (cycles per minute) and cpy (cycles per year).

For rotatory motions, the angular frequency is used instead (you can learn more with our angular frequency calculator). This one is also known as a rotational or angular speed (ω). It's expressed in angular frequency units, e.g., as revolutions per minute (RPM) or as radians or degrees per second (rad/s or °/s, respectively).

In the table below, you can find the equivalence between some of the different ordinary frequency and angular frequency units:

cps

Hz

rad/s

°/s

0.5

0.5

π (3.1416)

180

1

1

2π (6.283)

360

1.5

1.5

3π (9.425)

540

2

2

4π (12.566)

720

2.5

2.5

5π (15.708)

900

3

3

6π (18.85)

1080

4

4

8π (25.133)

1440

5

5

10π (31.416)

1800

6

6

12π (37.7)

2160

7

7

14π (43.98)

2520

8

8

16π (50.27)

2880

9

9

18π (56.55)

3240

10

10

20π (62.83)

3600

🙋 Check the frequency calculator for an in-depth explanation of this subject.

How do I convert cycles per second to hertz?

To convert any frequency value from cps (cycles per second) to Hz (hertz), you just need to know that the number of hertz is precisely the same as that of cps. This means that if you'd like to know how many hertz is 4 cps, you'll find that it's exactly 4 Hz.

How do I convert cycles per second to radians per second?

To go from a frequency value in cps (cycles per second) to radians per second (rad/s):

  1. Use the conversion factor of:
    1 cps = 2π rad/s = 6.283 rad/s.
  2. Multiply your value in cps by the conversion factor.
  3. As an example, to convert four cycles per second to radians per second:
    4 cps × (2π rad/s/cps) = 8π rad/s = 25.133 rad/s

How do I convert cps to degrees per second?

In order to convert a frequency value from cps (cycles per second) to degrees per second (°/s):

  1. Use the equivalence between these frequency units:
    1 cps = 360 °/s.
  2. Multiply your value in cps by the conversion factor.
  3. For example, to convert four cycles per second to degrees per second:
    4 cps × (360 °/s/cps) = 1440 °/s

FAQ

How many hertz are in one cycle per second?

1 Hz. Every cycle per second (cps) is equivalent to 1 hertz (Hz). This means that every hertz represents a single cycle per second, 1 cps = 1 Hz.

How many cycles per second are in 1 kilohertz?

1,000 cycles per second (cps). There is one cycle per second (cps) in one hertz (Hz) (1 cps = 1 Hz). Therefore, 1,000 hertz (or 1 kHz) is 1,000 cps.

How many cycles per second are 60 Hz?

60 cycles per second (cps). Every cycle per second (cps) is equivalent to one hertz (Hz), 1 cps = 1 Hz. With this equivalence in mind, we get that 60 Hz = 60 cps.

Gabriela Diaz
Frequency in cps
cps
cpm
RPM
Hz
kHz
MHz
GHz
°/s
rad/s
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