Wavelength Calculator
Solve the wave equation either way. Enter speed and frequency to get the wavelength, or switch to reverse mode to find frequency from a known wavelength. For light, the calculator also reports the photon energy, the wavenumber, the electromagnetic spectrum band, and the visible colour.
Formula
Worked example
A 50 Hz wave at the speed of light: λ = 299,792,458 ÷ 50 = 5,995,849.16 m (about 5,996 km). A 500 nm green light photon has frequency f = 299,792,458 ÷ 0.0000005 = 5.996×10¹⁴ Hz and energy E = 6.626×10⁻³⁴ × 5.996×10¹⁴ ≈ 3.97×10⁻¹⁹ J (about 2.48 eV).
How wavelength is calculated
A wave repeats its shape over a fixed distance called the wavelength, written with the Greek letter lambda (λ). The calculator uses the wave equation λ = v / f, dividing the wave speed in metres per second by the frequency in hertz. Because the speed of a wave is set by the medium it travels through, and the frequency is set by the source, dividing one by the other gives the spatial length of a single oscillation. Switch the "Solve for" mode to reverse the calculation and find frequency from a known wavelength with f = v / λ. The result is reported in metres, nanometres and millimetres so you can read it at any scale.
Choosing the right wave speed
Electromagnetic waves, radio, light, microwaves and X-rays, travel at 299,792,458 m/s in a vacuum, the default preset here. Inside a medium they slow down by the refractive index, so light moves at about 225,000,000 m/s in water and 197,000,000 m/s in glass while its frequency stays the same, which means its wavelength shortens. Sound waves move far more slowly, about 343 m/s in dry air at 20 °C, 1,481 m/s in fresh water and 5,960 m/s in steel. Picking the wrong speed is the most common mistake when computing wavelength, so the calculator offers presets for the common media plus a custom field.
Photon energy, wavenumber and the spectrum
For light, the calculator also reports the energy of a single photon using Planck’s relation E = h · f, equivalent to E = h · c / λ, where h is Planck’s constant (6.62607015×10⁻³⁴ J·s). The energy is shown in joules, electronvolts (eV) and kilojoules per mole, the units used in spectroscopy and photochemistry. The wavenumber, the number of wave cycles per centimetre (1 / λ in cm⁻¹), is a common axis in infrared spectroscopy. Finally the calculator labels the electromagnetic spectrum band the wave falls into (radio, microwave, infrared, visible, ultraviolet, X-ray or gamma) and, for visible light, names the approximate colour your eye would see.
Why frequency and wavelength trade off
For any fixed wave speed, frequency and wavelength are inversely proportional: as one rises, the other falls. A 100 MHz FM radio station has a wavelength of roughly 3 metres, while a 2.4 GHz Wi-Fi signal has a wavelength of about 12.5 centimetres, even though both are electromagnetic waves moving at the same speed. This trade-off explains why high-frequency signals can carry more detail but are more easily blocked, and why low-frequency sound carries further around obstacles. The same relationship sets photon energy: shorter wavelengths mean higher frequencies and more energetic photons.
Electromagnetic spectrum by wavelength
| Band | Wavelength (vacuum) | Typical use |
|---|---|---|
| Radio | > 1 m | Broadcast, Wi-Fi, mobile |
| Microwave | 1 mm to 1 m | Radar, ovens, satellite |
| Infrared | 750 nm to 1 mm | Heat, night vision, fibre optics |
| Visible | 380 to 750 nm | Human sight, lasers |
| Ultraviolet | 10 to 380 nm | Sterilisation, sunburn |
| X-ray | 0.01 to 10 nm | Medical imaging |
| Gamma | < 0.01 nm | Nuclear, radiotherapy |
Approximate vacuum wavelength ranges; boundaries are conventional and overlap slightly.
Frequently asked questions
What units does this calculator use?
Speed is in metres per second (m/s). You can enter frequency in Hz, kHz, MHz, GHz or THz, and a known wavelength in nm, µm, mm, cm or m. The wavelength result is shown in metres, nanometres and millimetres at once, and photon energy in joules, electronvolts and kilojoules per mole, so you rarely need to convert by hand.
How do I find frequency from wavelength?
Switch the "Solve for" dropdown to Frequency, then enter the wave speed and the known wavelength. The calculator applies f = v / λ. For example, 500 nm light in vacuum gives f = 299,792,458 ÷ 0.0000005 ≈ 5.996×10¹⁴ Hz. To find the speed instead, use v = f × λ.
How is photon energy related to wavelength?
A photon’s energy is E = h · f = h · c / λ, where h is Planck’s constant. Shorter wavelengths carry more energy: a 400 nm violet photon holds about 3.1 eV, while a 700 nm red photon holds about 1.8 eV. Photon energy is only meaningful for light, so the calculator reports it for the light presets and the custom speed.
Why does light change wavelength in water or glass?
When light enters a denser medium it slows down by the refractive index (about 1.33 for water, 1.52 for glass), but its frequency stays fixed because that is set by the source. Since λ = v / f, a smaller speed at the same frequency gives a shorter wavelength. This is why a 500 nm beam becomes roughly 375 nm inside glass even though its colour and frequency are unchanged.