Wavelength Calculator
Frequency to wavelength and back, for light, radio and sound. Get the photon energy, period and wavenumber, and see where your wave sits on the spectrum.
By Manzoor Ahmad, pharmacist · Updated How do you calculate wavelength?
Divide the wave’s speed by its frequency: λ = v ÷ f. A 100 MHz FM radio signal travelling at the speed of light (299,792,458 m/s) has a wavelength of 3.00 m. A 440 Hz note in air at 20 °C (343 m/s) has a wavelength of 0.78 m.
Electromagnetic spectrum
Wavelength, frequency and energy formulas
| Quantity | Formula | Notes |
|---|---|---|
| Wavelength | λ = v ÷ f | v = c ÷ n for light in a medium |
| Frequency | f = v ÷ λ = 1 ÷ T | unchanged when a wave enters a new medium |
| Photon energy | E = hf = hc ÷ λ | E (eV) ≈ 1239.84 ÷ λ (nm) |
| Wavenumber | ṽ = 1 ÷ λ | usually in cm⁻¹ |
| Speed of sound in air | v ≈ 331.3√(1 + T ÷ 273.15) | T in °C; 343 m/s at 20 °C |
Constants: c = 299,792,458 m/s (exact), h = 6.62607015 × 10⁻³⁴ J·s (exact), 1 eV = 1.602176634 × 10⁻¹⁹ J (exact).
Electromagnetic spectrum by wavelength
| Band | Wavelength | Frequency | Example |
|---|---|---|---|
| Gamma rays | < 10 pm | > 30 EHz | radioactive decay |
| X-rays | 10 pm – 10 nm | 30 PHz – 30 EHz | medical imaging |
| Ultraviolet | 10 – 380 nm | 790 THz – 30 PHz | sunburn, UV-C lamps |
| Visible | 380 – 750 nm | 400 – 790 THz | everything you see |
| Infrared | 750 nm – 1 mm | 300 GHz – 400 THz | TV remotes, heat |
| Microwaves | 1 mm – 1 m | 300 MHz – 300 GHz | Wi-Fi, ovens, 5G |
| Radio | > 1 m | < 300 MHz | FM, AM, shortwave |
Band edges are conventions, not sharp physical boundaries, and different agencies draw them slightly differently.
Wavelength FAQs
Wavelength equals wave speed divided by frequency: λ = v ÷ f. For light in a vacuum v = c = 299,792,458 m/s; for sound in air at 20 °C, v ≈ 343 m/s.
Divide the wave speed by the frequency. An FM station at 100 MHz has λ = 299,792,458 ÷ 100,000,000 = 3.00 m.
Use f = v ÷ λ. Green light at 532 nm has f = 299,792,458 ÷ 0.000000532 = 5.64 × 10¹⁴ Hz (564 THz).
Use E = hc ÷ λ. A handy shortcut is E (eV) = 1239.84 ÷ λ (nm), so a 500 nm photon carries 2.48 eV.
Visible light spans roughly 380 nm (violet) to 750 nm (red). Blue is around 450–495 nm, green 495–570 nm, yellow 570–590 nm and orange 590–620 nm.
In dry air, v ≈ 331.3 × √(1 + T ÷ 273.15) m/s, giving 343 m/s at 20 °C. Sound travels about 1,481 m/s in fresh water and about 5,960 m/s in steel.
Concert A (440 Hz) in air at 20 °C has a wavelength of 343.2 ÷ 440 = 0.78 m.
Yes. Frequency stays the same, but light slows to c ÷ n, so its wavelength shrinks by the refractive index n. 600 nm light becomes about 450 nm in water (n = 1.333).
They are inversely proportional: double the frequency and the wavelength halves, as long as the wave speed stays the same.
Period is the time for one complete cycle, T = 1 ÷ f. A 50 Hz mains supply has a period of 20 ms.
Wavenumber is the number of waves per unit length, 1 ÷ λ, usually quoted in cm⁻¹ in spectroscopy. A 10 µm infrared wave has a wavenumber of 1,000 cm⁻¹.
2.4 GHz has a wavelength of about 12.5 cm and 5 GHz about 6 cm. Microwave ovens use 2.45 GHz, roughly 12.2 cm.
Sources
Values use exact SI constants. Light in air is treated as vacuum (air’s index is 1.0003, a 0.03% difference). Sound speeds are typical and vary with temperature and material.