What is frequency?
Frequency measures how many cycles of a repeating event occur per unit of time. It is measured in hertz (Hz), where 1 Hz equals one cycle per second. Frequency is fundamental in physics, electronics, music, and signal processing — describing everything from the pitch of a sound to the channel of a radio station.
How to use this calculator
Choose a method. If you know the period (the time for one complete cycle), enter it in seconds and the tool returns frequency as \(f = 1/T\). If you are working with a wave, switch to the wavelength & speed method and enter the wave speed (m/s) and wavelength (m); the calculator uses \(f = v/\lambda\). In both cases it also reports the period and the angular frequency \(\omega = 2\pi f\).
The formula explained
The core relationship is $$f = \frac{1}{T}$$ a shorter period means a higher frequency. For traveling waves, the wave speed links wavelength and frequency through \(v = f\lambda\), which rearranges to $$f = \frac{v}{\lambda}$$ Angular frequency, used widely in rotational and oscillatory systems, is \(\omega = 2\pi f\) and is expressed in radians per second.
Worked example
A sound wave travels at \(v = 343\ \text{m/s}\) with a wavelength of \(\lambda = 1.5\ \text{m}\). Then $$f = \frac{343}{1.5} \approx 228.67\ \text{Hz}$$ The period is \(T = 1/f \approx 0.004373\ \text{s}\), and the angular frequency is $$\omega = 2\pi \times 228.67 \approx 1436.8\ \text{rad/s}$$
FAQ
What units should I use? Period in seconds and wavelength/speed in metric units (m and m/s) give frequency in hertz.
Why is my result zero? The denominator (period or wavelength) cannot be zero — enter a positive value.
What is angular frequency for? It appears in sine-wave equations like \(x = A\cdot\sin(\omega t)\) and in AC circuit and rotational-motion analysis.
