Editing Revolutions per minute (section)

== Standards ==
[[ISO 80000-3]]:2019 defines a [[physical quantity]] called [[rotation (quantity)|''rotation'']] (or ''number of revolutions''), [[dimensionless]], whose [[instantaneous rate of change]] is called ''[[rotational frequency]]'' (or ''rate of rotation''), with units of [[reciprocal second]]s (s<sup>−1</sup>).<ref>[https://www.iso.org/obp/ui/#iso:std:iso:80000:-3:ed-2:v1:en ISO 80000-3:2019].</ref>

A related but distinct quantity for describing rotation is ''[[angular frequency]]'' (or ''angular speed'', the magnitude of [[angular velocity]]), for which the SI unit is the [[radian per second]] (rad/s).

Although they have the same [[dimension (physics)|dimensions]] (reciprocal time) and base unit (s<sup>−1</sup>), the hertz (Hz) and radians per second (rad/s) are special names used to express two different but proportional [[International System of Quantities|ISQ]] quantities: frequency and angular frequency, respectively. The conversions between a frequency {{mvar|f}} and an angular frequency {{mvar|ω}} are
: <math>\omega = 2 \pi f, \quad f = \frac{\omega}{2 \pi}.</math>

Thus a disc rotating at 60&nbsp;rpm is said to have an angular speed of 2''π''&nbsp;rad/s and a rotation frequency of 1&nbsp;Hz.

The [[International System of Units]] (SI) does not recognize rpm as a unit. It defines units of [[angular frequency]] and [[angular velocity]] as rad&nbsp;s<sup>−1</sup>, and units of [[frequency]] as [[Hertz|Hz]], equal to s<sup>−1</sup>.

: <math>\begin{array}{rcrcr}
 1~\dfrac{\text{rad}}{\text{s}}                &=& \dfrac{1}{2\pi}~\text{Hz} &=& \dfrac{60}{2\pi}~\text{rpm} \\
 2\pi~\dfrac{\text{rad}}{\text{s}}             &=& 1~\text{Hz}               &=& 60~\text{rpm} \\
 \dfrac{2\pi}{60}~\dfrac{\text{rad}}{\text{s}} &=& \dfrac{1}{60}~\text{Hz}   &=& 1~\text{rpm}
\end{array}</math>