Cycles per second (cps) is the older name for hertz; it survives in vibration analysis, audio and rotating machinery. One cps is one full cycle each second, 60 cycles per minute and 2π radians per second.
How to use the CPS Calculator
- Pick the unit you are starting from in the From menu and type your value.
- Pick the unit you want in the To menu. The heading changes to match, for example “Cycles per Second to Hertz Converter”.
- The most common frequency units are shown below at the same time, so you can compare them at a glance.
- Type into any result to convert backwards, then use Copy results. The copied text starts with the heading for your chosen units.
Results update as you type. Everything is calculated in your browser.
How it works
Each of the 9 frequency units on this page is defined by an exact factor relative to the hertz, the base unit: 1 cps = 1 Hz and 1 cpm = 0.016666667 Hz, for example. The calculator first turns the value you type into hertz, then turns that into the unit you picked in the “To” menu and into cycles per minute, revolutions per minute and kilohertz. Typing into any result works backwards the same way, so the cycles per second and hertz values always describe the same amount.
How to convert frequency units
- Choose the unit you have in the From menu and type the value, for example 60 cps.
- Choose the unit you want in the To menu, for example hertz. The page heading changes to “Cycles per Second to Hertz Converter”.
- The calculator multiplies by the hertz factor of the “from” unit and divides by the factor of the “to” unit: 60 cps × 1 ÷ 1 = 60 Hz.
1 cycle per second in common units
| Unit | Value |
|---|---|
| Hertz (Hz) | 1 |
| Cycles per minute (cpm) | 60 |
| Revolutions per minute (rpm) | 60 |
| Kilohertz (kHz) | 0.001 |
| Radians per second (rad/s) | 6.2831853 |
| Degrees per second (°/s) | 360 |
Cycles per second conversion table
| Cycles per second | Hz | cpm | rpm | kHz |
|---|---|---|---|---|
| 1 | 1 | 60 | 60 | 0.001 |
| 10 | 10 | 600 | 600 | 0.01 |
| 50 | 50 | 3,000 | 3,000 | 0.05 |
| 60 | 60 | 3,600 | 3,600 | 0.06 |
| 100 | 100 | 6,000 | 6,000 | 0.1 |
| 1,000 | 1,000 | 60,000 | 60,000 | 1 |
Frequency units explained
- Cycle per second (cps)
- Cycles per second is the older name for hertz; 1 cps = 1 Hz.
- Hertz (Hz)
- The hertz is the SI unit of frequency: one cycle per second, named after Heinrich Hertz. Mains electricity is 50 or 60 Hz.
- Revolution per minute (rpm)
- Revolutions per minute measure rotational speed of engines, motors and drives; 60 rpm is 1 Hz.
Formula
1 cps = 1 Hz
1 cps = 60 cpm
1 cps = 60 rpm
1 cps = 0.001 kHz
1 cps = 6.2831853 rad/s
Worked example
Inputs: From: 60 cps.
Results: To = 60 Hz; Cycles per minute = 3,600 cpm; Revolutions per minute = 3,600 rpm; Kilohertz = 0.06 kHz; Radians per second = 376.99111843 rad/s; Degrees per second = 21,600 °/s.
Frequently asked questions
Is cps the same as Hz?
Yes, 1 cps = 1 Hz.
How many cpm is 1 cps?
60 cpm.
How do I get rad/s?
Multiply cps by 2π (about 6.2832).
How many hertz are in one cycle per second?
1 cps = 1 Hz.
How many cycles per minute are in one cycle per second?
1 cps = 60 cpm.
How many revolutions per minute are in one cycle per second?
1 cps = 60 rpm.
Are these frequency conversions exact?
Yes. Every factor is an exact definition (for example 1 cps = 1 Hz), so any difference you see is rounding in the last displayed digit.