Wavelength Calculator
Enter any two of wavelength, frequency and wave speed — the calculator returns the third using the universal wave relation v = f·λ, with results converted into the SI prefixes that make sense at that scale.
Wavelength
2.9979 m
- In kilometres
- 0.0030 km
- In millimetres
- 2997.9246 mm
- In micrometres
- 2.9979e+6 µm
- In nanometres
- 2.9979e+9 nm
- Speed used
- 3e+8 m/s
- Frequency used
- 1e+8 Hz
From v = f·λ → λ = v / f. Wavelength is the distance between identical points on consecutive cycles of the wave.
How to use this calculator
Pick what you want to solve for from the dropdown — wavelength (λ), frequency (f), or wave speed (v). Then fill in the other two quantities; the unused field is ignored, so you can leave its default in place. Speed is entered in metres per second (m/s), frequency in hertz (Hz), and wavelength in metres (m). The defaults model a 100 MHz FM radio wave travelling at the speed of light in vacuum — switch the speed to 343.2 m/s for sound in 20 °C air, to roughly 1 500 m/s for sound in seawater, or to whatever phase velocity your medium has. The breakdown shows the result in the SI prefixes that make sense for the scale: kilometres down to nanometres for wavelength, kilohertz up to terahertz for frequency, and the answer as a fraction of the speed of light when you solve for speed.
How the calculation works
A periodic travelling wave repeats in both time and space. The temporal period is 1/f (where f is the frequency in hertz, the number of cycles per second). The spatial period is the wavelength λ — the distance between two identical points on consecutive cycles, such as crest to crest or zero-crossing to zero-crossing. In one period the wave moves forward by exactly one wavelength, so the phase velocity v in the medium equals f·λ. Rearranging gives the three working forms: λ = v / f, f = v / λ, and v = f·λ. The relation holds for every type of wave — electromagnetic, acoustic, water surface, transverse on a string — provided the medium is non-dispersive at the chosen frequency. For dispersive media (deep-water gravity waves, light in glass, plasma waves at low frequency) the phase velocity itself depends on frequency, and the formula still works at each frequency but v has to be read off a dispersion curve rather than treated as a constant. The speed of light in vacuum, c = 299 792 458 m/s, has been a defining constant of the SI metre since the 17th General Conference on Weights and Measures in 1983; the speed of sound in dry air at 20 °C is approximately 343.2 m/s and varies with temperature, humidity and pressure.
Worked example
A mid-FM-band radio station broadcasts at 100 MHz. Radio waves are electromagnetic, so in vacuum (and to a very good approximation in air) they travel at c = 299 792 458 m/s. Wavelength is λ = v / f = 299 792 458 / 100 000 000 = 2.997 924 58 m — about three metres, which is why FM antennas are roughly that length. Solving the inverse: middle A on a piano vibrates the air at 440 Hz. At 20 °C the speed of sound in dry air is 343.2 m/s, so the wavelength is 343.2 / 440 ≈ 0.780 m — three-quarters of a metre, which is why low-frequency sounds diffract easily around corners while high-frequency sounds (with sub-centimetre wavelengths) are highly directional. Finally, a wavelength of 550 nm (green light) corresponds to a frequency of 299 792 458 / 5.5 × 10⁻⁷ ≈ 5.45 × 10¹⁴ Hz, or 545 THz — squarely in the middle of the visible spectrum, where the human eye is most sensitive.
Frequently asked questions
What does v = f·λ mean?
It says that a wave’s propagation speed v equals its frequency f multiplied by its wavelength λ. Frequency counts how many full cycles the wave completes per second (in hertz); wavelength is the distance it travels in one such cycle. Multiply the two and you get the distance per second — that is, the speed at which the wave pattern moves through space. The relation is a definition, not an approximation, and applies to every kind of periodic wave: light, sound, water ripples, the standing waves on a guitar string. The three rearrangements — λ = v / f, f = v / λ, and v = f·λ — are all you need to switch between any pair of inputs.
Why does light travel at exactly 299 792 458 m/s?
Because of how the metre is defined. Since 1983, the 17th General Conference on Weights and Measures (CGPM) fixed the speed of light in vacuum at exactly c = 299 792 458 m/s and made the metre derive from it — one metre is the distance light travels in 1 / 299 792 458 of a second. This means c has no measurement uncertainty: it is a defining constant of the SI, alongside the second (defined by caesium atomic transitions), the kilogram (the Planck constant), and so on. Before 1983 the metre was defined by a wavelength of krypton-86 light, and before that by a platinum-iridium bar in Sèvres.
How fast does sound travel?
In dry air at 20 °C and standard pressure, sound travels at about 343.2 m/s — roughly one kilometre every three seconds, which is the rule of thumb for estimating distance to a lightning strike. The speed rises with temperature (about 0.6 m/s per °C) and falls with humidity (water vapour is lighter than the nitrogen and oxygen it displaces, so humid air actually conducts sound slightly faster, not slower — the common intuition is wrong). In water sound travels much faster, ~1 500 m/s, and in solids faster still — about 5 000 m/s in steel and 12 000 m/s in diamond. Sound cannot propagate through a vacuum because there is no medium for the pressure variations to travel through.
What is the wavelength of visible light?
Roughly 380 nm (violet end) to 750 nm (red end), with the eye most sensitive to green around 555 nm. In hertz that range corresponds to about 400 THz to 790 THz. Below 380 nm is ultraviolet, X-ray and gamma; above 750 nm is infrared, microwave and radio. The visible band is narrow precisely because human vision evolved around the peak of the Sun’s emission spectrum, which lies in that range — animals with different evolutionary pressures see different bands (bees see into the UV, snakes see into the IR).
What are radio wavelengths used for?
Different bands of the radio spectrum have very different wavelengths and properties. Long-wave AM at around 200 kHz has wavelengths near 1 500 m and follows the curvature of the Earth, reaching far beyond line of sight. Medium-wave AM at ~1 MHz has wavelengths near 300 m. FM at 88–108 MHz has wavelengths near 3 m and is mostly line-of-sight. Mobile-phone 4G/5G operates between roughly 600 MHz and 6 GHz — wavelengths of 5 cm to 50 cm — and millimetre-wave 5G uses 24–40 GHz, with wavelengths of 7–12 mm. Wavelength determines antenna size, diffraction around obstacles, atmospheric absorption and the size of objects the wave can detect (radar resolution).
When does v = f·λ fail?
In dispersive media, where the phase velocity itself depends on frequency. The formula still holds at each individual frequency, but v is no longer a single number for the medium. Examples: light travelling through glass (where the refractive index varies with colour — this is how a prism splits white light), deep-water gravity waves on the ocean (long-wavelength swells outrun short-wavelength ripples), and electromagnetic waves in a plasma below the plasma frequency (which is why the ionosphere reflects shortwave radio but is transparent to FM). For a single-frequency continuous wave the formula is always correct; for a pulse or wave packet you also need the group velocity, which can differ substantially from the phase velocity.