rpm\text{rpm}

revolution per minute

FrequencyAngular speedexact by definition

A revolution per minute, treated here as a frequency, is exactly 1/60 hertz. It counts complete rotations per minute of a shaft, wheel, fan or rotor. The factor is exact by definition.

Watch out: The same abbreviation is used for angular speed, where 1 rpm is π/30≈0.10472\pi/30 \approx 0.10472 rad/s. As a frequency it is 0.01667 Hz. The two differ by 2π2\pi, so check which quantity a formula wants before substituting.

1 rpm\text{rpm} (Frequency)0.016666667 Hz\text{Hz}
1 rpm\text{rpm} (Angular speed)0.10471976 rad/s\text{rad/s}

About the revolution per minute

Rotational machinery is specified in rpm because a revolution is the thing that matters: a pump moves a fixed volume per revolution, a gear tooth engages once per revolution, and a bearing sees one load cycle per revolution. Typical values anchor the scale. A car engine idles near 700 rpm and redlines between 6,000 and 8,000, a desktop hard drive spins at 5,400 or 7,200 rpm, a laboratory centrifuge reaches 15,000 rpm, and a turbocharger can exceed 150,000 rpm.

Alternating-current motors tie rpm directly to supply frequency. The synchronous speed is N=120f/pN = 120f/p, with ff in hertz and pp the number of poles, so a two-pole motor on 60 Hz turns at 3,600 rpm and a four-pole at 1,800 rpm. On 50 Hz those become 3,000 and 1,500 rpm, which is why equipment moved between North America and Europe runs 20% slower or faster unless it is redesigned or driven by a variable frequency drive. Induction motors run slightly below synchronous speed, and that gap, called slip, is what produces their torque.

As a unit of angular speed

A revolution per minute as an angular speed is exactly 2π/60=π/302\pi/60 = \pi/30 radians per second, about 0.10472 rad/s. It is the standard nameplate unit for motors, pumps, fans and engines. The relation is exact by definition, though π/30\pi/30 is irrational and the decimal is rounded.

One revolution per minute in every frequency unit

16,666,700nanohertz (nHz)
525,960per year (1/yr)
16,666.7microhertz (μHz)
1,440per day (1/d)
60per hour (1/h)
16.6667millihertz (mHz)
1revolution per minute (rpm)this unit
1cycle per minute (cpm)
1beat per minute (bpm)
0.0166667hertz (Hz)
0.0166667cycle per second (cps)
0.0166667revolution per second (rev/s)
0.0000166667kilohertz (kHz)
1.66667e-08megahertz (MHz)
1.66667e-11gigahertz (GHz)
1.66667e-14terahertz (THz)
1.66667e-17petahertz (PHz)

One revolution per minute in every angular speed unit

21,600degree per hour (°/h)
1,440revolution per day (rev/d)
360degree per minute (°/min)
104.72milliradian per second (mrad/s)
60revolution per hour (rev/h)
6.28319radian per minute (rad/min)
6degree per second (°/s)
1revolution per minute (rpm)this unit
0.10472radian per second (rad/s)
0.0166667revolution per second (rev/s)
0.001thousand revolutions per minute (krpm)