CPS Converter — Hz, RPM and Angular Rate

Background.

A motor nameplate says 1,800 rpm, a vibration analyser reports a peak at 30 Hz, and the control software wants radians per second. All three can describe the same shaft. Moving between them takes only two facts: a minute has 60 seconds, and one full turn is 360 degrees or 2π radians.

CPS, cycles per second, is the older name for what the SI now calls the hertz; old manuals and radio dials print it as c/s or cps. Your rate is converted to hertz first, then to the unit you ask for, and listed in every other unit alongside, with the time one cycle takes. The prefixes are decimal: 1 kHz is 1,000 Hz, 1 MHz a million, 1 GHz a billion.

One revolution counts as one cycle here. If you are counting something that happens several times per turn, such as gear teeth or fan blades, or once every two turns, like the spark in one cylinder of a four-stroke engine, apply that ratio yourself.

What is cps converter?

Cycles per second is a frequency: how many times a repeating event completes in one second. One cycle per second is one hertz, the SI unit, defined as a reciprocal second for periodic phenomena. Revolutions per minute and cycles per minute count the same repetitions over 60 seconds instead of one. Degrees per second and radians per second describe a rotation by the angle it sweeps, with one revolution equal to 360° or 2π rad; radians per second is the angular frequency physicists write as ω = 2πf.

How to use this calculator.

1. 01Type the rate into Rate. It must be zero or positive, since direction of rotation plays no part in the conversion.
2. 02Choose the unit it is in under From and the unit you want under To; the main result is that pair.
3. 03Use the other lines to see the rate in hertz, rpm, cycles per minute, degrees and radians per second at once, plus the period of one cycle.
4. 04If what you counted is not one event per revolution, scale it by events per turn before or after converting.

The formula.

Every unit has a fixed value in hertz: cycles or revolutions per minute are worth 1/60 Hz, degrees per second 1/360 Hz, radians per second 1/(2π) Hz, and the prefixed units 1,000, 10⁶ and 10⁹ Hz. The converter multiplies your number by the hertz value of the From unit, then divides by the hertz value of the To unit.

Worked through, rpm to Hz is ÷ 60; Hz to rad/s is × 2π, about 6.2832; rad/s to rpm is × 60 ÷ 2π, which simplifies to × 30/π, about 9.5493; and degrees per second to rpm is ÷ 6, because a minute holds 60 seconds and a turn 360 degrees. The period is 1 ÷ f seconds. A rate of zero has no period, since nothing repeats, and in that case the period line shows 0 rather than infinity.

A worked example.

Frequently asked questions.

References& sources.

1. [1]BIPM, The International System of Units (SI Brochure), 9th edition, defines hertz for periodic phenomena and the coherent radian unit.
2. [2]NIST Special Publication 811 lists frequency in hertz and angular velocity in radians per second.