Rotational frequency

Prof. Dr. Thorsten Jungmann (last updated 2025-09-03)

The rotational frequency (German: Drehzahl, also Umdrehungen or Rotationsgeschwindigkeit), also called rotational speed, describes the number of revolutions per unit of time of a rotating body.

1 Quantity symbol and unit

The quantity symbol is $n$. The unit is revolutions per minute:

$$[n]=\mathrm{mi}{\mathrm{n}}^{-1}$$

or rpm (revolutions per minute).

Alternatively, revolutions per second (${\mathrm{s}}^{-1}$) are also used. The relationship:

$$n[{\mathrm{s}}^{-1}]=\frac{n[\mathrm{mi}{\mathrm{n}}^{-1}]}{60}$$

2 Practical and worked examples

• A car engine runs at about $800\mathrm{mi}{\mathrm{n}}^{-1}$ in idle operation and at up to $6000\mathrm{mi}{\mathrm{n}}^{-1}$ under full load.
• A hard disk rotates at $5400\mathrm{mi}{\mathrm{n}}^{-1}$ or $7200\mathrm{mi}{\mathrm{n}}^{-1}$.
• Case fans typically operate at $1000\text{-}3000\mathrm{mi}{\mathrm{n}}^{-1}$.

3 Typical orders of magnitude

Second hand of a clock ($1\mathrm{mi}{\mathrm{n}}^{-1}$), household appliances ($10\text{-}100\mathrm{mi}{\mathrm{n}}^{-1}$), electric motors ($500\text{-}6000\mathrm{mi}{\mathrm{n}}^{-1}$), high-speed spindles ($>100000\mathrm{mi}{\mathrm{n}}^{-1}$).

4 Example phrasings

‘The electric motor runs at a rotational frequency of $1500\mathrm{mi}{\mathrm{n}}^{-1}$.’
‘The centrifuge reaches $15000\mathrm{rpm}$.’

5 Related quantities

• Angular velocity ($\omega$): $\omega =2\pi \cdot n$ (with $n$ in ${\mathrm{s}}^{-1}$).
• Frequency ($f$): For AC generators, $f=n\cdot p$ applies (p = number of pole pairs).

6 Relevant components

• Electric motor
• Generator
• Case fan