CPS Converter — Hz, RPM and Angular Rate

Background.

Cycles per second, hertz, revolutions per minute and angular speed can describe the same repeating motion at different scales. One hertz is one cycle each second. Multiplying by sixty gives sixty cycles per minute, and a rotating object completing one revolution per cycle is therefore turning at 60 rpm. One complete turn is also 360 degrees or 2π radians, so 1 Hz corresponds to 360 degrees per second and 2π radians per second.

This converter routes every selection through hertz, the SI special name for reciprocal seconds when describing periodic phenomena. It then reports the same rate in the most common frequency and rotation units, plus the time for one cycle. SI prefixes are decimal: a kilohertz is 1,000 Hz, a megahertz is one million Hz and a gigahertz is one billion Hz.

The relationship does not supply missing machine physics. RPM equals cycles per minute only when one revolution is the cycle of interest. A multi-pole motor, geared shaft, four-stroke engine event or encoder can produce several or a fraction of an event per revolution; include that separate ratio before using the converter. At a zero rate there is no finite repeating period, so the page displays zero as an explicit sentinel rather than attempting to return infinity.

What is cps converter?

CPS means cycles per second, numerically identical to hertz for a periodic phenomenon. Angular rate describes that same cycle as an angle: one revolution is 360 degrees or 2π radians. RPM and cycles per minute divide by 60 to reach hertz. The converter preserves the quantity and changes only its unit.

How to use this calculator.

1. 01Enter the non-negative rate and choose the unit it currently uses.
2. 02Choose the target unit; the main result shows that pair.
3. 03Use the simultaneous Hz, rpm, degree and radian outputs to cross-check the cycle definition.
4. 04If an event occurs more or less than once per revolution, apply that event-per-revolution ratio separately.

The formula.

First multiply the input by its hertz-per-unit factor. RPM and cycles per minute use 1/60, degrees per second uses 1/360, and radians per second uses 1/(2π). SI-prefixed hertz uses powers of one thousand. Divide the resulting hertz value by the target unit's factor. The period is the reciprocal of hertz for a positive rate. Decimal.js carries the calculation and results cross the output boundary only after rounding to ten decimal places.

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.