Angular frequency

Prof. Dr. Thorsten Jungmann (last updated 2026-05-04)

The angular frequency (German: Kreisfrequenz) is a measure of the rate of change of a periodic function.

1 Quantity symbol and unit

The quantity symbol of the angular frequency is the lower-case Greek letter $\omega$ (omega).
In principle, its unit is the same as the unit of the frequency, the hertz (Hz).

$$[f]=\mathrm{Hz}=1/s=s^{-1}=[\omega ]$$

However, to distinguish the two quantities from each other, electrical engineering gives $\omega$ the unit $1/s=s^{-1}$ (‘(one) per second’).

$$[\omega ]=1/s=s^{-1}$$ $$[f]=\mathrm{Hz}$$

The relationship between the frequency $f$ and the angular frequency $\omega$ is:

$$\omega =2\cdot \pi \cdot f$$

where:

• $\pi$ is the number pi, $\pi \approx 3.14159$ ($2\pi$ for a full circle of 360°)
• $f$ is the frequency

2 Example and typical order of magnitude

In the European power grid, $\omega =2\pi f=2\pi \cdot 50\mathrm{Hz}\approx 314{\mathrm{s}}^{-1}$ with $f=50\mathrm{Hz}$.

3 Example phrasings

• ‘The angular frequency of the mains voltage is approximately equal to 314 per second.’

4 Related quantities

• As shown above, the angular frequency is related via the number pi, $\pi$, to the frequency $f$.
• The angular frequency is relevant for understanding AC circuits and the Apparent impedance of components such as inductors and capacitors.