The wavelength formula
Wavelength is wave speed divided by frequency: λ = v ÷ f, where v is speed in meters per second and f is frequency in hertz. A 340 m/s sound wave at 170 Hz has a wavelength of 2 m. Higher frequency means shorter wavelength. To work the other direction, use the frequency calculator.
The formula follows from the definitions: in one second the wave travels 340 m and completes 170 cycles, so each cycle must occupy 340 ÷ 170 = 2 m of space.
How to use this calculator
Enter the wave speed in meters per second and the frequency in hertz. The result is wavelength in meters. Frequency must be greater than zero. For sound in air use about 340 m/s; for light use about 3×10⁸ m/s. See also the frequency calculator.
The speed depends on the medium, not on the source, so a wave crossing from air into water keeps its frequency but changes speed — and therefore changes wavelength. Using the wrong speed for the medium is the most common error here.
Worked example
A sound wave travels at 340 m/s with a frequency of 170 Hz: 340 ÷ 170 = 2 m. Double the frequency to 340 Hz and the wavelength halves to 1 m, since wavelength is inversely proportional to frequency.
Wavelength sets the physical scale of a wave, which is why it matters in practice. Audible sound spans wavelengths from centimetres to many metres, visible light is measured in hundreds of nanometres, and radio antennas are cut to a fraction of the wavelength they transmit. Anything much smaller than the wavelength tends to be bent around rather than reflected, which is why bass carries through walls while treble does not. The wave speed in the formula is a velocity, and it changes with the medium the wave travels through.
Frequently asked questions
- How do I calculate wavelength?
- Divide the wave speed by the frequency: λ = v ÷ f.
- What are the units of wavelength?
- Meters (m) in SI units.
- Why must frequency not be zero?
- A frequency of zero would make wavelength undefined, since you cannot divide by zero.
- What is the speed of sound to use?
- About 340 m/s in air at room temperature; it varies with temperature and medium.
- What if my frequency is given in kHz or MHz?
- Convert it to hertz before entering: multiply kilohertz by 1,000 and megahertz by 1,000,000. A 100 MHz radio signal is 100,000,000 Hz, which with the speed of light gives a wavelength of about 3 m.