Two gears with twenty and twelve teeth are in mesh and turn against each other, the small one exactly five thirds as fast as the large one, as the gear ratio demands. On the right a tachometer needle wavers by the red zone, below it the slotted disc of an encoder turns slowly with a blinking sensor, and at the bottom a marker travels along the scale to three thousand.
Quantity data sheet
Non-SI · rotational mechanics sheet 1/1 · rev. 2026-09Revolution per minute
Non-SI unit · quantity: rotational frequency n · 1 min⁻¹ = 1/60 s⁻¹
The unit you read off a motor nameplate and check with a flashing lamp
On the nameplate of any electric motor, next to the kilowatts and volts, a number like 1450 is stamped: that is how many times the shaft turns in a minute under rated load. This quantity is the easiest to imagine and the hardest to see, because already at a few hundred revolutions per minute the eye stops telling the spokes apart and the wheel blurs into a disc.
So measuring it took cunning. A mechanical tachometer spun weights out by centrifugal force, an electric one used a generator, and the stroboscope did the simplest thing of all: it lights the shaft with short flashes, and when their frequency matches the rotation, the mark on the shaft freezes as if the shaft were standing still. But it also freezes when the flashes are half as frequent, and many a fitter has stumbled into that trap.
The International System of Units has no revolution per minute, only the reciprocal second and the radian per second, but machine tools, motors and turntables keep talking in minutes, because round numbers fit neatly into them: 1500 for a four-pole motor on a fifty-hertz grid, 3000 for a two-pole one, thirty-three and a third for a long-playing record.
Standards write min⁻¹ or r/min, while rpm lives in lowercase on nameplates and in catalogues; uppercase RPM is common, but the standards do not like it. The number of revolutions is denoted by the letter n, and angular velocity by the letter ω, in radians per second.
Rotational frequency in revolutions per second and angular velocity in radians per second are separated by a factor of 2π: a shaft at 3000 rpm makes fifty revolutions per second, but its angular velocity is about 314 rad/s. Writing it as “50 Hz” for ω means being off by more than six times.
01 · Definition
shaft · gearing · flash · trapThe revolution per minute is the rotational frequency at which a body makes one full turn in sixty seconds. It equals one sixtieth of a reciprocal second, and the angular velocity of such rotation is 2π/60 radians per second, that is, about one tenth.
Rotational frequency is convenient because it can be counted rather than measured: all you need is the number of turns made in a known time. That is why it passes so easily through gear trains — a pair of wheels divides or multiplies it by the ratio of their tooth counts — and why it is so loved in industry, where every machine tool is described by a set of spindle speed steps.
A stroboscope measures rotational frequency by coincidence: when the flash rate equals the rotation rate, a marked point on the shaft is in the same place at every flash and seems motionless. But the same happens if the flashes are fewer by a whole-number factor: the shaft manages two, three or four turns between them, and the eye does not notice. This is checked by doubling the flash rate — with a true coincidence two marks then appear, while with a multiple one the stillness remains.
An induction motor always runs slightly below synchronous speed, and a stroboscope fed from the same mains shows this difference as a slow backward drift of the mark. By counting how many times the mark goes round in a minute, the fitter gets the slip directly in revolutions, without any tachometer.
The orange wheel sits on the motor shaft, the turquoise one on the output shaft, with a single mark glowing on it. The wheels are always in mesh: the small one turns as many times faster than the large one as it has fewer teeth, and in the opposite direction. In ordinary light they are shown slowed down; switch on the stroboscope, and both wheels appear the way the flashes show them: motionless, slowly creeping forward or backward, and sometimes with two or three marks at once.
Along the axis is the flash rate. The tall orange stroke is the only honest coincidence, where a flash falls on every turn; the turquoise strokes to its left are flashes every two, three and four turns, where the mark also stands still; the red dashes to the right are flashes more frequent than a turn, where the mark doubles and triples. The white line is your lamp.
02 · Conversion
units · peripheral speed · power and torqueFrom the motor nameplate to the cutter edge
The first tab converts revolutions into frequency per second, radians and degrees. The second turns them into peripheral speed at the edge of tools of various diameters, and the third shows what torque is needed to transmit a given power at these revolutions.
A rule to remember: to get radians per second, divide revolutions per minute by 9.55, and to get torque in newton-metres, multiply kilowatts by 9550 and divide by the revolutions.
The revolutions on an induction motor’s nameplate are rated, under full load; at no load the shaft turns at almost synchronous speed, and under overload it lags further behind. For gear calculations the rated figure is used; for a stroboscope check, whatever is actually there.
| Quantity | Value | Note |
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Almost nine orders of magnitude separate the Earth’s rotation from a dental turbine, and all of them are written in one and the same unit, although days per revolution suit the lower end better and kilohertz the upper. Note that nature’s record-holder, the fastest known pulsar, spins almost like the spindle of a high-speed milling machine, except that it weighs one and a half to two solar masses and is a couple of dozen kilometres across.
04 · Measuring instruments
centrifugal · stroboscope · optical · encoderFour ways to count what cannot be seen
Two hinged weights spread further apart the faster the axle turns, pulling a sleeve with them, and the sleeve turns the needle. The same scheme served for a hundred years as the governor of steam engines: the rising sleeve closed the steam valve.
The lamp flashes at an adjustable rate, and the fitter tunes it until the mark on the shaft freezes; the dial of the instrument is marked directly in flashes per minute. It never touches the shaft, but needs the doubling check, or you may read half the true speed.
A strip of reflective tape is stuck on the shaft, and the instrument counts how many times per second the reflected beam returns to the photodiode. There is no half trap here, but there is another one: a second shiny spot on the shaft will double the reading.
A disc with hundreds or thousands of slots sits right on the shaft, and the rotational frequency is obtained by dividing the number of pulses by the time and by the number of slots. This is how it is measured in every servo drive and CNC machine, hundreds of times per second.
05 · Writing rules
min⁻¹ · r/min · rpm · no dotsRevolutions are neither hertz nor radians
Rotational frequency is written with the letter n and the unit min⁻¹ or r/min, angular velocity with the letter ω in radians per second, and the abbreviation rpm is written in lowercase, without dots.
The first error confuses the minute with the second and overstates the frequency sixty times. The second writes angular velocity in hertz and loses the factor 2π. The third puts dots into an abbreviation that has none. The fourth adds an inverse power to a unit that already contains “per minute”, the fifth forgets time altogether, and the sixth turns a frequency into a duration.
06 · Neighbouring units
s⁻¹ · rad/s · hpThe revolution per minute rests on three neighbours: frequency per second, into which it converts by dividing by sixty, angular velocity with its factor 2π, and power, which the shaft transmits together with torque.
The SI unit for rotational frequency; the hertz is formally a reciprocal second too, but it is customarily kept for periodic oscillations rather than rotation.
All the mechanics of rotation is written in it: power is torque multiplied by angular velocity, and peripheral speed is angular velocity multiplied by radius.
Watt measured it by a horse turning a capstan, that is, through revolutions and effort; on a dynamometer bench engine power is still obtained from torque and revolutions.
Next to it in the catalogue stand horsepower, which Watt derived from the turning of a capstan, and kilowatt-hour, where the disc of the old meter also counted revolutions — not of a shaft, but of energy.
07 · Historical section
archive · how people learned to see rotationFrom Watt’s weights to Edgerton’s flashes
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The revolution per minute has no standard of its own, and does not need one: the second is enough, and a revolution is counted by definition. For a long time, though, the role of a reference revolution count was played by the electrical grid. A synchronous motor turns strictly in step with its frequency, and so turntable platters carried stroboscopic dots: under a lamp flickering a hundred times a second, a row of one hundred and eighty dots stood still exactly at thirty-three and a third revolutions.
The accuracy of such a check was the accuracy of the grid, and power systems keep the daily count of cycles so strictly that mains clocks do not drift from astronomical time by more than seconds for years. So the most widespread standard of rotational speed stood not in a laboratory but at the power station, and every music lover checked a turntable against it without knowing it.