Every wave, whether it is light, radio, sound or a ripple on a pond, obeys the same simple rule: its speed equals its wavelength times its frequency. This calculator uses that rule to turn a frequency into a wavelength or the reverse, with built-in speeds for light in a vacuum, air, water and glass and for sound in air, water and steel. For light and radio it also gives the photon energy and names the part of the electromagnetic spectrum, so it works for optics homework, antenna sizing and acoustics alike.
How to use the wavelength calculator
- Under Solve for, choose Wavelength, Frequency or Wave speed.
- Pick the Wave and medium: light or radio in a vacuum, light in air (n ≈ 1.000293), water (n ≈ 1.333) or glass (n ≈ 1.5), sound in air at 20 °C (343 m/s), in fresh water at 20 °C (1,481 m/s) or in steel (about 5,960 m/s). Choose Custom wave speed to enter your own value in m/s, km/h, mph, ft/s or fractions of c. This menu is hidden when you solve for the speed itself.
- Enter the Frequency (f) in Hz up to PHz, or the Wavelength (λ) in pm, Å, nm, µm, mm, cm, m, km, in or ft.
- Read the answer with readable conversions, the period T = 1/f and the wavenumber in cm⁻¹. Light and radio results add the photon energy and the part of the spectrum; sound results say whether the tone is audible, infrasound or ultrasound.
Wavelength formula
For electromagnetic waves the photon energy depends only on frequency, through the Planck constant h = 6.62607015 × 10⁻³⁴ J·s (exact in the SI):
Worked examples
Green light at 540 THz (the default)
λ = 299,792,458 m/s ÷ 5.4 × 10¹⁴ Hz = 555.2 nm
Photon energy: 6.62607015 × 10⁻³⁴ × 5.4 × 10¹⁴ J = 2.233 eV; the calculator places it in the green band. This frequency is no accident: the SI definition of the candela is based on light of exactly 540 × 10¹² Hz, near the peak of the eye's daylight sensitivity.
Concert A. Choose sound in air and enter 440 Hz: λ = 343 ÷ 440 = 0.780 m, a little over 30 inches.
Microwave oven and Wi-Fi. At 2.45 GHz in a vacuum, λ = 12.24 cm. In an oven without a turntable, the standing wave leaves hot spots roughly half a wavelength, about 6 cm, apart.
Entering a new medium
When a wave crosses into another material, its source keeps setting the pace, so the frequency stays the same. What changes is the speed, and the wavelength follows it. Select light in water with 540 THz and the wavelength drops to 416.5 nm, yet the photon energy remains 2.233 eV and the light still looks green. That is why the calculator labels the spectrum band from the vacuum wavelength, and why its note reminds you that only the wavelength shrinks.
Sound behaves the same way. A 1 kHz tone is 34.3 cm long in air, 1.48 m in water and 5.96 m in steel.
The electromagnetic spectrum
The calculator uses these boundaries, measured as vacuum wavelengths. Band edges are conventions and vary slightly between references.
| Band | Wavelength | Frequency | Photon energy |
|---|---|---|---|
| Radio | longer than 1 m | below 300 MHz | below 1.24 µeV |
| Microwave | 1 mm – 1 m | 300 MHz – 300 GHz | 1.24 µeV – 1.24 meV |
| Infrared | 750 nm – 1 mm | 300 GHz – 400 THz | 1.24 meV – 1.65 eV |
| Visible | 380 – 750 nm | 400 – 789 THz | 1.65 – 3.26 eV |
| Ultraviolet | 10 – 380 nm | 789 THz – 30 PHz | 3.26 – 124 eV |
| X-rays | 0.01 – 10 nm | 30 PHz – 30 EHz | 124 eV – 124 keV |
| Gamma rays | shorter than 0.01 nm | above 30 EHz | above 124 keV |
Within the visible range it splits further: violet 380–450 nm, blue 450–495 nm, green 495–570 nm, yellow 570–590 nm, orange 590–620 nm and red 620–750 nm.
For sound, people hear roughly 20 Hz to 20 kHz, which in air spans wavelengths from about 17 m down to 1.7 cm. Medical ultrasound runs far higher: 5 MHz in water is only about 0.30 mm, which is what lets it resolve fine detail. For soft tissue, enter a custom speed of about 1,540 m/s.
To link photon energies to mass, see the E = mc² calculator; for prefixes such as THz and nm, the metric prefix converter helps.
Frequently asked questions
How do I convert frequency to wavelength?
Divide the wave speed by the frequency: λ = v ÷ f. For light or radio in a vacuum, v = 299,792,458 m/s, so 100 MHz gives about 3.00 m. For sound in air at 20 °C, v ≈ 343 m/s, so 440 Hz gives about 0.780 m.
Does frequency change when light enters water or glass?
No. The frequency, and therefore the photon energy, stays the same. The wave slows down by the refractive index n, so the wavelength shrinks by the same factor: 540 THz light is 555.2 nm in a vacuum but about 416.5 nm in water.
How do I calculate photon energy from wavelength?
Use E = hc ÷ λ with the vacuum wavelength. In practical units, E in electronvolts ≈ 1,239.84 ÷ λ in nanometers, so a 650 nm red laser photon carries about 1.91 eV. The calculator shows this automatically for light and radio waves.
What is the wavelength of a microwave oven or 2.4 GHz Wi-Fi?
At 2.45 GHz the wavelength in air is about 12.2 cm. Each photon carries only about 10 millionths of an electronvolt, far too little to break chemical bonds, which is why microwaves heat food rather than ionize it.
Why does the calculator reject some wave speeds?
Nothing travels faster than light in a vacuum, so a custom wave speed, or a product of wavelength and frequency, above 299,792,458 m/s returns an error. Frequency, wavelength and speed must also be greater than zero.