The frequency never changes. The wavelength changes in everything — which is why λ = c/f is the answer to a question about empty space.
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Refractive index 1. The reference case, and what λ = c/f alone gives you.
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Frequency2.4 GHz
In vacuum124914000 nm · 124.914 mm
In vacuum124914000 nm · 124.914 mm
Microwave. The frequency is the same in every medium — it is fixed by the source — so it is the wavelength that moves.
The same wave, in the other units
Photon energy9.9256e-6 eV · 1.5903e-24 J
Wavenumber0.0800554 cm⁻¹
Speed here299792000 m/s
Quarter wavelength31.228 mm
Wavenumber is quoted on the vacuum wavelength by convention whatever the medium, which is why it does not move when you change the selector above. Photon energy follows the frequency, so it does not move either.
What this converter covers
Frequency, vacuum wavelength, wavelength in the medium, photon energy, wavenumber and the quarter-wave length — with eleven media including the coax velocity factors an antenna or stub is actually cut to.
Frequency ↔ wavelength either way, in vacuum and in a chosen medium
Coax velocity factors for RG-58, RG-8X, LMR-400 and open-wire line
Optical fibre, water, glass and acrylic refractive indices
Photon energy in eV and joules, and spectroscopic wavenumber
The quarter-wave length, which is what a stub gets cut to
Coax velocity factors Medium, not just vacuum Photon energy Exact SI constants
Free, no signup — exact by definition, not an estimate.
Updated 7 September 2026
At a glance
Formula shown
λ_vacuum = c / f · λ_medium = λ_vacuum / n · E = hf · ν̃ = 1 / λ_vacuum
Scenario support
1 GHz = 29.98 cm · 1550 nm → 1056 nm in fibre · 100 MHz λ/4 = 495 mm in RG-58
Educational estimate
Planning support from the values you enter — not professional advice.
λ = c/f is the vacuum answer
A wave has a frequency and a wavelength, and the two are joined by the speed it travels at. In empty space that speed is c, and the relationship is the one everybody learns: wavelength is the speed divided by the frequency.
What that formula quietly assumes is empty space. Put the wave into glass, water or a coaxial cable and it slows down — by a quarter in water, by a third in coax with a solid polyethylene dielectric. The frequency does not change: it is set by whatever is driving the wave, and the far end of a cable receives exactly as many cycles per second as the near end sends. So if the speed drops and the frequency is fixed, the only thing that can absorb the difference is the wavelength, which shortens by exactly the same factor.
That factor is the refractive index, n — or in cable work, its reciprocal, the velocity factor. The wavelength in a medium is the vacuum wavelength divided by n, and this is not a small correction in most materials. It is 32% in optical fibre and 34% in ordinary coax.
Which means “the wavelength” is an incomplete phrase, and reaching for λ = c/f alone gives the right answer only when the wave really is in vacuum, or near enough — which is why the tool above asks what the wave is travelling through before it answers.
The stub that comes out too long
This is where the mistake actually gets made, because the numbers involved are lengths you cut with a knife.
Take a quarter-wave stub for 100 MHz. In free space the wavelength is 2.998 m, so a quarter of it is 749 mm. Cut 749 mm of RG-58, fit it, and it does not work — because RG-58 has a velocity factor of 0.66, so the wavelength inside the cable is only 1.979 m and the quarter wave is 495 mm. The free-space figure is 51.5% too long: more than half as long again as it should be.
A quarter wavelength at 100 MHz in four common feedlines
Line
Velocity factor
Quarter wave at 100 MHz
Free space
1.00
749 mm
450 Ω window line
0.91
682 mm
LMR-400
0.85
637 mm
RG-8X
0.82
615 mm
RG-58
0.66
495 mm
Two things follow. The correction is specific to the cable, so a length that was right in RG-58 is wrong in LMR-400 by 29% — swapping cable type on an existing design means re-cutting, not just re-terminating. And the velocity factor depends on the dielectric: solid polyethylene is slow, foamed dielectric is faster because part of the field travels through the gas in the foam, and open-wire line is fastest of all because it is mostly air.
Note that this correction applies to anything cut to a wavelength inside the line — stubs, matching sections, delay lines, phasing harnesses. An antenna radiating into air is a different case: it works in free space, so its length starts from the free-space wavelength, with its own separate correction for the conductor’s thickness.
Inside an optical fibre
Telecoms runs on 1550 nm, and that number is a vacuum wavelength. Inside standard single-mode fibre, whose index is about 1.468 at that wavelength, the actual wavelength is 1056 nm — a third shorter than the number printed on the laser.
For most purposes the vacuum figure is the right one to quote, because it identifies the source and it is what every component is specified against. But anything that depends on the physical length of a wave needs the in-fibre figure: the spacing of a fibre Bragg grating, the length of a resonant cavity, the path difference in an interferometer, the phase accumulated over a run of fibre.
The same division also explains the propagation delay people meet more often. Light covers 300 mm in a nanosecond in vacuum; in fibre it covers about 204 mm, so a kilometre of fibre adds roughly 4.9 µs of latency rather than 3.3 µs. That is the same refractive index doing the same thing, showing up as time instead of distance.
Photon energy and wavenumber
Two more quantities describe the same wave, and both are worth knowing which side of the vacuum question they sit on.
Photon energy is Planck’s constant times the frequency. Since frequency is invariant, so is photon energy — a photon does not lose energy by entering glass. In practice it is quoted in electronvolts, and the useful shortcut is that energy in eV is about 1240 divided by the vacuum wavelength in nanometres. That 1240 is hc/e, and since the 2019 SI it is exactly 1239.8419 nm·eV rather than a measured approximation. Green light at 550 nm is 2.25 eV; the visible band runs from roughly 1.65 eV at the red end to 3.26 eV at the violet.
Wavenumber, written ν̃ and quoted in reciprocal centimetres, is spectroscopy’s preferred unit: simply one divided by the wavelength in centimetres. It is proportional to energy, which makes spectra additive in a way wavelength is not — two vibrational modes at 1000 and 1600 cm⁻¹ combine at 2600 cm⁻¹, which is not true of their wavelengths. By convention it is always defined on the vacuum wavelength, whatever medium the measurement was made in, which is why the figure in the tool above does not move when the medium changes.
Air, vacuum and why line tables say which
Air has a refractive index of about 1.000293 — three parts in ten thousand from vacuum. For every practical purpose on this page that is nothing: an antenna cut for air and one cut for vacuum are the same antenna.
It stops being nothing in spectroscopy. The sodium D line is at 589.00 nm in vacuum and 588.83 nm in air, and that 0.17 nm gap is far larger than the precision of the measurement. So spectral line tables must state which they quote, and the convention is genuinely split: many astronomical and laboratory tables give air wavelengths above 200 nm, where air is transparent, and vacuum wavelengths below it, where it is not — which means a single table can switch conventions partway down.
The practical consequence is that comparing a measured line against a published one requires knowing both conventions, and a 0.03% discrepancy between two sources for the same line is usually this and not an error. Air’s index also varies with temperature, pressure and humidity, which is why precision work uses a proper equation for it rather than a single number.
Related calculators
Other conversions with a constant behind them:
Scientific NotationScientific, engineering and decimal forms with significant figures counted — and ambiguous inputs flagged rather than silently resolved.
EnergyJoules, kilojoules, calories, food Calories, kWh, BTU and therms — with the two calories listed apart, since one is a thousand of the other.
PowerWatts, kilowatts, horsepower and BTU per hour — with mechanical and metric horsepower listed apart, since they differ by 1.4% under one word.
LengthMillimetres to miles on the exact 1959 factors, with the mil kept clearly apart from the millimetre — they differ 25-fold.
Speedmph, km/h, m/s, ft/s and knots on exact factors, with the nautical mile behind the knot explained rather than assumed.
PPMppm to percent, mg/L and µg/m³ — asking which liquid or which gas, because without that the conversion has no answer.
Since the 2019 revision of the SI, the speed of light, the Planck constant and the elementary charge are all exact by definition — the metre is defined from the first of them rather than the other way round. So every conversion on this page is exact arithmetic and not a measured value with an uncertainty. The refractive indices are the exception and are genuinely measured, which is why each one is attributed and why the cable figures are given as the published velocity factors rather than as indices.
The International System of Units (SI Brochure, 9th edition) — the defining constantsBureau International des Poids et Mesures (BIPM) · verified 2026-09-07 · That the speed of light, the Planck constant and the elementary charge are exact by definition since the 2019 revision, so every conversion here is exact arithmetic rather than a measured approximation
The ARRL Handbook — transmission lines and velocity factorAmerican Radio Relay League · verified 2026-09-07 · The published velocity factors for RG-58, RG-8X, LMR-400 and open-wire line, and the practice of cutting stubs and matching sections to the electrical rather than the free-space wavelength
Edlén’s equation and the refractive index of airNational Institute of Standards and Technology, US · verified 2026-09-07 · The refractive index of air near 1.000293 at standard conditions, and that the air-versus-vacuum distinction is significant enough for spectral line tables to state which they use
Conversion note
Three limits worth naming. First, refractive index is not a constant of a material — it varies with wavelength, which is what dispersion is, and with temperature, pressure and humidity for gases. The indices here are typical values at the conditions stated, good for design and estimation, and not a substitute for the figure in a component's own datasheet where a fraction of a percent matters. Second, cable velocity factors are nominal. Real cable varies between manufacturers and batches, and a length cut from a table is a starting point; anything that has to resonate should be trimmed against a measurement rather than trusted from arithmetic. The FR-4 microstrip figure in particular is a rough effective index — the real value depends on trace width, board thickness and how much of the field travels in air, and needs a proper transmission-line calculation. Third, this converts a single frequency. Real signals occupy a bandwidth, real sources have a linewidth, and in a dispersive medium the group velocity that carries information differs from the phase velocity used here.
Published the Frequency to Wavelength Converter: frequency, vacuum wavelength, wavelength in a chosen medium, photon energy, wavenumber and the quarter-wave length.
Asks what the wave is travelling through, because lambda = c/f is the vacuum answer. Frequency is fixed by the source and does not change in a material, so the wavelength shortens by exactly the refractive index.
Covers the case where this is got wrong in practice: a quarter-wave stub for 100 MHz is 749 mm in free space and 495 mm in RG-58 coax, so cutting to the free-space length makes it 51.5 percent too long. Includes published velocity factors for RG-58, RG-8X, LMR-400 and open-wire line.
Shows that a 1550 nm telecom laser has a 1056 nm wavelength inside standard single-mode fibre, and that the same index is what makes fibre latency about 4.9 microseconds per kilometre rather than 3.3.
Distinguishes a wavelength read as a spec-sheet vacuum figure from one measured in the medium, since those give different frequencies -- the same conflation the page is about.
Keeps wavenumber and photon energy on the vacuum wavelength and the frequency respectively, so neither moves when the medium changes, which is the convention and is asserted in the suite.
Every constant is exact by the 2019 SI definitions, so the conversions are exact arithmetic. Verified by 92 automated cases including round-trips through both the medium and vacuum wavelengths for six media at four frequencies.
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