Wave Speed Calculator
The wave equation v = f x lambda relates the speed of any periodic wave to its frequency and wavelength. It applies universally, to sound travelling through air, ripples on water, and electromagnetic waves such as radio and light. Enter a frequency in hertz and a wavelength in metres and this calculator returns the wave speed in metres per second, along with the period (the time for one cycle). The relationship is a definition of how waves propagate and needs no empirical constant; just use consistent SI units.
Wave speed formula
Wave speed v = frequency f x wavelength lambda
Period T = 1 / frequency
Speed in km/h = v x 3.6
Angular frequency = 2 x pi x frequency
Speed is in metres per second when frequency is in hertz and wavelength is in metres. The period is the reciprocal of frequency, and angular frequency is 2 pi times frequency in radians per second.
Wave physics context
- The wave equation v = f x lambda holds for all periodic waves.
- Sound in dry air at 20 degrees Celsius travels at about 343 m/s.
- Electromagnetic waves travel at about 299,792,458 m/s in a vacuum.
- A musical note A4 at 440 Hz in air has a wavelength near 0.78 m.
- Always convert wavelength to metres before applying the equation.
Wave speed: frequently asked questions
What is the wave speed equation?
Wave speed equals frequency multiplied by wavelength: v = f x λ. Speed is in metres per second, frequency in hertz (cycles per second), and wavelength in metres. This single relationship holds for all periodic waves, including sound, water ripples, and electromagnetic waves such as light and radio.
How do I find frequency or wavelength from this?
Rearrange the same equation. Frequency equals speed divided by wavelength (f = v / λ), and wavelength equals speed divided by frequency (λ = v / f). This calculator returns wave speed from frequency and wavelength; use the rearranged forms to solve for the other quantities.
What is the period of a wave?
The period is the time for one complete cycle and is the reciprocal of frequency: T = 1 / f, measured in seconds. A wave at 50 hertz has a period of 0.02 seconds. This calculator reports the period alongside wave speed.
Does the wave equation work for light?
Yes. For electromagnetic waves in a vacuum the speed is the speed of light, about 299,792,458 metres per second, and v = f x λ relates its frequency and wavelength. In a medium the speed is lower by the refractive index, but the equation still holds with the speed in that medium.
What units should I use?
Use consistent SI units: frequency in hertz and wavelength in metres give speed in metres per second. If your wavelength is in centimetres or nanometres, convert to metres first. Mixing units is the most common source of error in wave calculations.
Official sources
- U.S. National Institute of Standards and Technology: The speed of light and SI constants.
- NASA: Anatomy of an Electromagnetic Wave.
Reviewed by the CalculatorHub team, edited by James Graham, 16 June 2026. See our methodology.