Wavelength Calculator
Find the wavelength, frequency or speed of any wave from the other two with v = f × λ. Pick light, radio or sound, or type your own speed, and mix units freely. Advanced adds photon energy, wavenumber, where it sits in the spectrum, antenna lengths and the musical note.
λ = v ÷ f
The answer appears in the highlighted box; change its unit to see it another way. The speed comes from the wave type; pick "Other wave" to type your own.
Photon energy, wavenumber and period
Photon energy E = h × f applies to light, radio and other electromagnetic waves.
Where it sits in the spectrum
Judged by the wavelength in a vacuum, c ÷ f. Boundaries between regions are approximate and overlap in practice; the ITU radio bands are exact.
Radio antenna lengths
From the free-space wavelength c ÷ f times a velocity factor. Cut a little long and trim while you measure.
Musical note
The nearest note in 12-tone equal temperament. Change the tuning if your band tunes A4 to 442 or 432 Hz.
How your wavelength is worked out
Your numbers: the wave's speed divided by how many waves pass each second.
- 1
Speed of the wave
Light or radio in a vacuumv = 299,792,458 m/s
- 2
Frequency in Hz
100 MHz= 100,000,000 Hz
- 3
Divide v by f
299,792,458 ÷100,000,000= 2.99792458 m
- 4
Into your unit
2.99792458 malready metres
Read more: the formula, worked examples, the spectrum and antennas
A wave is a repeating ripple that carries energy: light, radio, Wi-Fi and X-rays are electromagnetic waves, while sound is a pressure wave in air, water or metal. The wavelength is the distance from one crest to the next, the frequency is how many crests pass each second, and the speed is how fast the crests move. Multiply the last two and you get the first: in one second, f waves of length λ go by, so the wave travels f × λ.
The formula
wave speed v = frequency f × wavelength λ
wavelength λ = v ÷ f
frequency f = v ÷ λ
period T = 1 ÷ f
wavenumber = 1 ÷ λ, angular wavenumber k = 2π ÷ λ
angular frequency ω = 2π × f
photon energy E = h × f = h × c ÷ λ
h = 6.62607015 × 10⁻³⁴ J·s, 1 eV = 1.602176634 × 10⁻¹⁹ J
light in a vacuum c = 299,792,458 m/s (all exact)
sound in dry air v ≈ 331.3 + 0.606 × T (°C)
antenna length = (c ÷ f) × fraction × velocity factor
note = A4 × 2^(semitones ÷ 12), A4 = 440 Hz
v in m/s, f in Hz, λ in m
Worked example
Wavelength (the default): an FM radio station on 100 MHz. Radio travels at c = 299,792,458 m/s. Frequency: 100 MHz = 100,000,000 Hz. Then λ = 299,792,458 ÷ 100,000,000 = 2.99792458 m, about 3 m or 9.836 ft. One wave takes T = 1 ÷ 100,000,000 = 0.00000001 s = 10 ns. It is in the radio part of the spectrum, in the VHF band (30 to 300 MHz).
Frequency: green light of 550 nm = 0.00000055 m. f = 299,792,458 ÷ 0.00000055 = 545,077,196,363,636 Hz = 545.08 THz.
Photon energy: for that green light, E = 6.62607015 × 10⁻³⁴ × 5.45077196 × 10¹⁴ = 3.6117 × 10⁻¹⁹ J. Divided by 1.602176634 × 10⁻¹⁹ J per eV, that is 2.2543 eV. Its wavenumber is 1 ÷ 0.000055 cm = 18,181.8 cm⁻¹. For the 100 MHz radio wave, E = 6.62607015 × 10⁻³⁴ × 100,000,000 = 6.62607015 × 10⁻²⁶ J = 4.1357 × 10⁻⁷ eV, millions of times too weak to break a chemical bond.
Sound: the note A4, 440 Hz, in air at 20 °C (about 343 m/s). λ = 343 ÷ 440 = 0.77955 m (77.95 cm, 2.558 ft). With the temperature formula, v ≈ 331.3 + 0.606 × 20 = 343.42 m/s, so λ = 343.42 ÷ 440 = 0.78050 m. In fresh water (about 1,480 m/s) the same note is 1,480 ÷ 440 = 3.3636 m long.
Speed: a 440 Hz note measured at 0.78 m long is moving at 440 × 0.78 = 343.2 m/s, the speed of sound in air at about 20 °C.
Antenna: a half-wave dipole for 100 MHz in thin wire (velocity factor 0.95): 2.99792458 ÷ 2 × 0.95 = 1.4240 m end to end (4.672 ft), so each leg is 0.7120 m. The old rule of thumb 468 ÷ 100 MHz = 4.68 ft agrees.
Musical note: 1,000 Hz is 12 × log₂(1,000 ÷ 440) = 14.213 semitones above A4. The nearest note is 14 semitones up, B5 at 440 × 2^(14 ÷ 12) = 987.77 Hz, so 1,000 Hz is 21.3 cents sharp of B5.
Everyday waves
| Wave | Frequency | Wavelength |
|---|---|---|
| Mains hum in air | 50 Hz | 6.86 m |
| A4 note in air | 440 Hz | 0.7795 m |
| AM radio | 1 MHz | 299.8 m |
| FM radio | 100 MHz | 2.998 m |
| Wi-Fi | 2.4 GHz | 12.49 cm |
| Wi-Fi | 5 GHz | 5.996 cm |
| Red light | 461.2 THz | 650 nm |
| Green light | 545.08 THz | 550 nm |
| Medical X-ray | 5.996 EHz | 0.05 nm |
The electromagnetic spectrum (approximate)
| Region | Wavelength in a vacuum |
|---|---|
| Radio | longer than about 1 m (below 300 MHz) |
| Microwave | about 1 mm to 1 m (300 MHz to 300 GHz) |
| Infrared | about 700 nm to 1 mm (300 GHz to 430 THz) |
| Visible light | about 380 to 700 nm (430 to 790 THz) |
| Ultraviolet | about 10 to 380 nm |
| X-ray | about 10 pm to 10 nm |
| Gamma ray | shorter than about 10 pm |
Visible colours (approximate)
| Colour | Wavelength | Photon energy |
|---|---|---|
| Violet | 380–450 nm | 2.76–3.26 eV |
| Blue | 450–485 nm | 2.56–2.76 eV |
| Cyan | 485–500 nm | 2.48–2.56 eV |
| Green | 500–565 nm | 2.19–2.48 eV |
| Yellow | 565–590 nm | 2.1–2.19 eV |
| Orange | 590–625 nm | 1.98–2.1 eV |
| Red | 625–700 nm | 1.77–1.98 eV |
Typical wave speeds
| Wave | Speed |
|---|---|
| Light or radio in a vacuum | 299,792,458 m/s (exact) |
| Sound in air, 20 °C | 343 m/s (approx.) |
| Sound in fresh water | 1,480 m/s (approx.) |
| Sound in seawater | 1,500 m/s (approx.) |
| Sound in steel | 5,960 m/s (approx.) |
| Light in glass (n ≈ 1.5) | 199,900,000 m/s (approx.) |
| Light in water (n ≈ 1.333) | 224,900,000 m/s (approx.) |
| Sound in air at 0 °C (formula) | 331.3 m/s (approx.) |
Notes
- c = 299,792,458 m/s, h = 6.62607015 × 10⁻³⁴ J·s and 1 eV = 1.602176634 × 10⁻¹⁹ J are exact by definition in the SI (since 2019).
- Sound speeds are typical values. Sound in air depends mostly on temperature (humidity adds a little); in water it changes with temperature, salt and depth; in solids with the material.
- When light enters glass or water it slows down and its wavelength gets shorter, but its frequency, colour and photon energy stay the same. That is why the spectrum and colour here use the vacuum wavelength.
- Region boundaries and colour names are approximate: different sources draw the lines a little differently, and X-rays and gamma rays overlap (they are really named by where they come from).
- Antenna lengths are starting points. Thickness, nearby objects and height above ground change the best length, so trim while measuring with an SWR meter or analyser.
Common questions
What is the wavelength formula?
Wavelength λ = wave speed v ÷ frequency f. With v in metres per second and f in hertz, λ comes out in metres. A 100 MHz radio wave travels at the speed of light, 299,792,458 m/s, so λ = 299,792,458 ÷ 100,000,000 = 2.998 m.
How do I find frequency from wavelength?
Turn the formula round: f = v ÷ λ. Green light of 550 nm (0.00000055 m) has f = 299,792,458 ÷ 0.00000055 = 545.08 THz, that is 545 million million waves a second.
What speed should I use?
Light, radio, Wi-Fi, X-rays and every other electromagnetic wave travel at c = 299,792,458 m/s in a vacuum (exactly) and only about 0.03% slower in air. Sound is far slower: about 343 m/s in air at 20 °C, about 1,480 m/s in fresh water and about 5,960 m/s in steel. Those sound speeds are approximate and change with temperature.
How does temperature change the speed of sound?
Sound is faster in warm air. A common approximation for dry air is v ≈ 331.3 + 0.606 × T, with T in °C. At 0 °C that gives 331.3 m/s, at 20 °C 343.4 m/s and at 35 °C 352.5 m/s, so a 440 Hz note is about 0.78 m long in a warm room.
How do I work out the energy of a photon?
E = h × f, with Planck's constant h = 6.62607015 × 10⁻³⁴ J·s (exact). Divide by 1.602176634 × 10⁻¹⁹ to get electronvolts. A shortcut: E in eV ≈ 1,239.84 ÷ wavelength in nm, so 550 nm green light carries about 2.254 eV.
How long should a half-wave dipole antenna be?
Half the free-space wavelength times a velocity factor of about 0.95 for a thin wire: at 100 MHz that is 2.998 ÷ 2 × 0.95 = 1.424 m in total, or two legs of about 0.712 m. The old rule 468 ÷ f in MHz gives the same in feet. Always cut a little long and trim while measuring.
What is the difference between frequency and period?
Frequency is how many waves pass each second (hertz); period is how long one wave takes (seconds). They are the reverse of each other: T = 1 ÷ f. A 50 Hz mains supply has a period of 20 ms.
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