How to use the Wavelength Calculator
- Choose whether you know the frequency or the wavelength.
- Enter the value — frequency in megahertz, wavelength in metres.
- Set the refractive index if the wave travels through glass, water or coaxial cable rather than vacuum.
- Read the converted quantity plus photon energy in electronvolts.
- Use the quarter-wave figure as a starting length for antenna design, then trim for the end effect.
How the calculation works
Wavelength and frequency are inversely related through the wave's propagation speed. For electromagnetic waves in a vacuum that speed is exactly 299,792,458 m/s by definition — the metre is defined from it rather than the other way around, so this is not a measured constant with uncertainty attached.
In any medium the wave slows by the refractive index, which shortens the wavelength while the frequency stays fixed. Frequency is set by the source and cannot change at a boundary; wavelength is what compresses. This is why coaxial cable has a velocity factor of roughly 0.66 to 0.85 and why cable lengths cut for a specific electrical length are always shorter than the free-space calculation suggests.
Photon energy follows the Planck relation E = hf, which means energy scales with frequency, not amplitude. That is the whole basis of the ionising/non-ionising distinction: a 2.4 GHz microwave photon carries about 10 microelectronvolts, while an ultraviolet photon at 400 nm carries 3.1 eV — enough to break chemical bonds. Increasing transmitter power adds more photons but never makes any one of them more energetic.
λ = v ÷ f, where v = c ÷ n and c = 299,792,458 m/s exactly; E = hf with h = 6.62607015 × 10⁻³⁴ J·s; quarter-wave = λ ÷ 4Source: BIPM SI Brochure, 9th edition, definition of the metre; CODATA 2018 value of the Planck constant.
Worked example
Designing a quarter-wave whip antenna for the 2.4 GHz Wi-Fi band.
- Enter 2400 MHz with a refractive index of 1 for air.
- λ = 299,792,458 ÷ 2.4 × 10⁹ = 0.1249 m.
- Quarter wave: 0.1249 ÷ 4 = 0.0312 m, or 31.2 mm.
- Trim by roughly 4% for the end effect: about 30 mm of radiating element.
A 2.4 GHz quarter-wave element is 31.2 mm in free space, trimmed to about 30 mm in practice.
Frequently asked questions
Does frequency or wavelength change in glass?+
Wavelength changes; frequency does not. Frequency is fixed by the source, so entering the medium compresses the wave rather than re-timing it.
How do I get wavelength in nanometres?+
The calculator shows it directly. Visible light spans roughly 380 nm (violet) to 750 nm (red).
Does this work for sound?+
The relationship λ = v ÷ f is identical, but you would substitute the speed of sound — about 343 m/s in air at 20 °C — rather than the speed of light.
Why trim an antenna below the calculated length?+
End capacitance makes a physical element behave electrically longer than it measures. A 3–5% trim is the usual starting correction.
Last reviewed September 1, 2026. We review this page whenever the underlying formula, tax year, published rate or standard changes.