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
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)
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 . If it instead is considered a unit of angular velocity and the word "revolution" is considered to mean
2π radians, then .