Revolutions per minute
Revolutions per minute (abbreviated rpm, RPM, rev/min, r/min, or with the notation min−1) is the number of turns in one minute. It is a unit of rotational speed or the frequency of rotation around a fixed axis.
|Revolution per minute|
|Unit of||Rotational speed|
|Symbol||rpm or r/min|
|1 rpm in ...||... is equal to ...|
|SI angular speed||2π/ rad/s ≈ 0.1047198 rad/s|
|SI frequency||1/ Hz ≈ 0.01666667 Hz|
|SI derived rotational frequency||1/ s−1, 1//s|
|SI derived rotational speed||1 min−1, 1/min|
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.
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 rpm = 1/ Hz. If it instead is considered a unit of angular velocity and the word "revolution" is considered to mean 2π radians, then 1 rpm = 2π/ rad/s.