# Revolutions per minute

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/min (tours par minute) is the common abbreviation. The German language uses the abbreviation U/min or u/min (Umdrehungen pro Minute).

## International System of Units

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.

{\displaystyle {\begin{aligned}1~{\text{rad/s}}&\leftrightarrow {\frac {1}{2\pi }}~{\text{Hz}}\\&\leftrightarrow {\frac {60}{2\pi }}~{\text{rpm}}\end{aligned}}}
{\displaystyle {\begin{aligned}1~{\text{rpm}}&\leftrightarrow {\frac {1}{60}}~{\text{Hz}}\\&\leftrightarrow {\frac {2\pi }{60}}~{\text{rad/s}}\end{aligned}}}
{\displaystyle {\begin{aligned}1~{\text{Hz}}&\leftrightarrow 2\pi ~{\text{rad/s}}\\&\leftrightarrow 60~{\text{rpm}}\end{aligned}}}

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:

${\displaystyle \omega =2\pi f\,\,\!{\text{, }}\,\,f={\frac {\omega }{2\pi }}{\text{.}}\,\!}$

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 ${\displaystyle 1~{\text{rpm}}={\frac {1}{60}}~{\text{Hz}}}$. If it instead is considered a unit of angular velocity and the word "revolution" is considered to mean 2π radians, then ${\displaystyle 1~{\text{rpm}}={\frac {2\pi }{60}}~{\text{rad/s}}}$.

Other Languages
беларуская (тарашкевіца)‎: АНХ
български: Оборот в минута
Deutsch: Rpm (Einheit)
Esperanto: Rivolua nombro
français: Tour par minute
한국어: 분당 회전수
hrvatski: Broj okretaja
Bahasa Indonesia: Rotasi per menit
italiano: Giri al minuto
македонски: Вртеж во минута

Nordfriisk: Rpm
norsk nynorsk: Omdreiingar per minutt
Simple English: Revolutions per minute
srpskohrvatski / српскохрватски: Broj okretaja
українська: Оберт за хвилину
Tiếng Việt: Số vòng quay