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Revolutions per minute (abbreviated rpm, RPM, rev/min, r/min) is a measure of the frequency of rotation, specifically the number of rotations around a fixed axis in one minute. It is used as a measure of rotational speed of a mechanical component. In the French language, tr/mn (tours par minute) is the common abbreviation. The German language uses the abbreviation U/min or u/min (Umdrehungen pro Minute).
According to the International System of Units (SI), rpm is not a unit. This is because the word revolution is a semantic annotation rather than a unit. The annotation is instead done as a subscript of the formula sign if needed. Because of the measured physical quantity, the formula sign has to be f for (rotational) frequency and ω or Ω for angular velocity. The corresponding basic SI derived unit is s^{−1} or Hz. When measuring angular speed, the unit radians per second is used.
Here the sign ↔ (correspondent) is used instead of = (equal). Formally, hertz (Hz) and radian per second (rad/s) are two different names for the same SI unit, s^{−1}. However, they are used for two different but proportional ISQ quantities: frequency and angular frequency (angular speed, magnitude of angular velocity). The conversion between a frequency f (measured in hertz) and an angular velocity ω (measured in radians per second) are:
Thus a disc rotating at 60 rpm is said to be rotating at either 2π rad/s or 1 Hz, where the former measures the angular velocity and the latter reflects the number of revolutions per second.
If the non-SI unit rpm is considered a unit of frequency, then 1~\text{rpm} = \frac{1}{60}~\text{Hz}. If it instead is considered a unit of angular velocity and the word "revolution" is considered to mean 2π radians, then 1~\text{rpm} = \frac{2\pi}{60}~\text{rad/s}.
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