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 \(\pi/30 \approx 0.10472\) rad/s. As a frequency it is 0.01667 Hz. The two differ by \(2\pi\), so check which quantity a formula wants before substituting.
| 1 rpm (Frequency) | 0.016666667 Hz |
| 1 rpm (Angular speed) | 0.10471976 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 \(N = 120f/p\), with \(f\) in hertz and \(p\) 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.
A revolution per minute as an angular speed is exactly \(2\pi/60 = \pi/30\) 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 \(\pi/30\) is irrational and the decimal is rounded.