Wavelength & Frequency Calculator
Convert between wavelength, frequency and photon energy for light, sound and any other wave.
How to use this calculator
- 1Choose whether you have the frequency or the wavelength.
- 2Pick the wave type — light in vacuum, sound in air or water, or enter a custom speed.
- 3For light, enter frequency in terahertz and wavelength in nanometres; other wave types use hertz and metres.
How the calculation works
v = λf λ = v ÷ f f = v ÷ λ E = hf- v
- Wave speed in the medium — 299,792,458 m/s for light in vacuum
- λ
- Wavelength
- f
- Frequency in hertz
- h
- Planck constant, exactly 6.62607015 × 10⁻³⁴ J·s
v = λf is the defining wave relationship and holds for every wave — light, sound, water, seismic. Only the speed changes with the medium.
The speed of light is exact by definition: since 1983 the metre has been defined as the distance light travels in 1/299,792,458 of a second, so the constant carries no uncertainty.
The Planck constant became exact in the 2019 SI revision, when it was fixed at 6.62607015 × 10⁻³⁴ J·s to define the kilogram. Photon energy E = hf therefore also carries no constant-related uncertainty.
When a wave enters a new medium its frequency stays the same and its wavelength changes — frequency is set by the source, speed by the medium, and wavelength follows.
Worked example
Light at 500 THz
- 1.Frequency: 500 THz = 5 × 10¹⁴ Hz.
- 2.λ = c ÷ f = 299,792,458 ÷ 5 × 10¹⁴ = 5.996 × 10⁻⁷ m.
- 3.In nanometres: 599.6 nm — orange light, near the boundary with yellow.
- 4.Photon energy: E = hf = 6.62607015 × 10⁻³⁴ × 5 × 10¹⁴ = 3.313 × 10⁻¹⁹ J, or 2.068 eV.
Result: 599.58 nm — visible orange, 2.07 eV per photon
One relationship, every wave
v = λf applies to every wave there is. A wave travels one wavelength in one period, so speed is wavelength divided by period, which is wavelength times frequency. Nothing about the medium or the wave type changes that — only the value of v differs, from 343 m/s for sound in air to 299,792,458 m/s for light in vacuum.
The inverse relationship between wavelength and frequency at fixed speed is what gives the electromagnetic spectrum its structure: radio waves are long and low-frequency, gamma rays are short and high-frequency, and the same equation describes both.
What changes when a wave enters a new medium
This is where intuition often fails. When light passes from air into glass it slows down, but its frequency does not change — the frequency is fixed by whatever produced the wave. Since v = λf and v has dropped while f is constant, the wavelength must shorten.
That is exactly why refraction happens: the change in wavelength at the boundary bends the wavefront. And because the slowdown differs slightly by wavelength, different colours bend by different amounts, which is dispersion — the mechanism behind a prism and a rainbow.
Photon energy and why ultraviolet is different
For electromagnetic waves there is a second relationship: E = hf, so each photon carries energy proportional to frequency. This is what separates types of radiation by effect rather than merely by intensity. Infrared photons carry roughly 1 eV or less and mostly deposit heat. Visible light runs about 1.6–3.3 eV. Ultraviolet begins above that, and around 3–4 eV photons start to carry enough energy to break chemical bonds.
That threshold is why UV causes sunburn and DNA damage while a far more intense infrared source merely warms you. It is not about total energy delivered — it is about whether any individual photon carries enough to do the damage. A very bright red lamp will never cause sunburn no matter how long you sit under it.
What this assumes, and where it stops
Assumptions
- Light travels in vacuum unless a custom speed is entered. In air the difference is under 0.03%, but glass and water slow it substantially.
- The speed of sound in air is taken at 20 °C; it rises roughly 0.6 m/s per degree Celsius.
- The wave is monochromatic — a single frequency rather than a band.
Limitations
- Photon energy is physically meaningful for electromagnetic waves. It is shown for other wave types for completeness but does not describe sound, which is a pressure wave in matter rather than a photon stream.
- Does not model dispersion, where speed varies with wavelength in a real medium.
- Spectral band labels are approximate — the boundaries between colours, and between visible and ultraviolet, are conventions rather than sharp physical lines.
Common questions
Does the frequency or the wavelength change when light enters glass?
The wavelength changes; the frequency does not. Frequency is set by the source and is preserved across a boundary, while speed is set by the medium. Since v = λf, a drop in speed with constant frequency forces the wavelength to shorten — and that shortening at an angled boundary is what bends the light.
Why is ultraviolet harmful when infrared is not?
Because of energy per photon, not total energy. E = hf, so UV photons carry several electronvolts — enough to break chemical bonds and damage DNA. Infrared photons carry far less and mostly just deposit heat. An extremely intense infrared source will burn you thermally but will never cause the photochemical damage that comparatively weak UV does.
Formula and content last reviewed on .
Results are estimates for information only, not professional advice.
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