OneTaskBy Tim King · Updated
Frequency to Wavelength Calculator
Radio, Light and Sound, Both Ways
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How the Frequency to Wavelength Calculator works
This frequency to wavelength calculator converts either way for radio waves, light and sound. Enter a frequency in Hz, kHz, MHz, GHz or THz, or a wavelength from nanometres to kilometres, and get the other value with the working, the period and the quarter wavelength. For light it also names the radio band or colour and gives the photon energy.
Every wave obeys the same rule: the faster it travels, the longer each wave is for a given frequency. Radio engineers need wavelengths to cut aerials, physicists need them for light and spectra, and musicians and acousticians use them to place speakers and treat rooms. Because sound is almost a million times slower than light, the same frequency gives wildly different wavelengths.
How the frequency to wavelength calculator works
The formula is λ = v ÷ f, where λ is the wavelength, v the wave speed and f the frequency. Turned round, f = v ÷ λ. Light in a vacuum uses c = 299,792,458 m/s, sound in air at 20 °C uses 343 m/s and sound in water 1,481 m/s. The period is 1 ÷ f, and photon energy is Planck's constant times f, shown in electronvolts.
First example. FM radio at 100 MHz has λ = 299,792,458 ÷ 100,000,000 ≈ 3.00 m, a period of 10 ns and a quarter wave of about 75 cm, which is why car aerials are around that length.
Second example. A 532 nm green laser has f = 299,792,458 ÷ 0.000000532 ≈ 563.5 THz, and each photon carries about 2.33 eV.
How many metres long is a 440 Hz sound wave? In air, 343 ÷ 440 ≈ 0.78 m, or 779.5 mm.
Frequency, wavelength and band of common signals, light and sound
| Source | Frequency | Wavelength | Band or medium |
|---|---|---|---|
| UK mains hum | 50 Hz | 5,995.85 km | ELF/VLF radio |
| Middle C (in air) | 261.63 Hz | 1.31101 m | Sound in air |
| A4 tuning note (in air) | 440 Hz | 779.545 mm | Sound in air |
| Longwave BBC Radio 4 | 198 kHz | 1.5141 km | LF radio (longwave) |
| AM broadcast | 1 MHz | 299.792 m | MF radio (AM broadcast) |
| CB radio | 27 MHz | 11.1034 m | HF radio (shortwave) |
| FM broadcast | 100 MHz | 2.99792 m | VHF radio (FM, DAB) |
| DAB radio | 220 MHz | 1.36269 m | VHF radio (FM, DAB) |
| Digital TV | 600 MHz | 499.654 mm | UHF (TV, mobile, Wi-Fi 2.4 GHz) |
| 4G LTE | 1.8 GHz | 166.551 mm | UHF (TV, mobile, Wi-Fi 2.4 GHz) |
| Wi-Fi 2.4 GHz | 2.4 GHz | 124.914 mm | UHF (TV, mobile, Wi-Fi 2.4 GHz) |
| Microwave oven | 2.45 GHz | 122.364 mm | UHF (TV, mobile, Wi-Fi 2.4 GHz) |
| 5G (3.5 GHz) | 3.5 GHz | 85.655 mm | SHF microwave (Wi-Fi 5 GHz, satellite) |
| Wi-Fi 5 GHz | 5.5 GHz | 54.5077 mm | SHF microwave (Wi-Fi 5 GHz, satellite) |
| Wi-Fi 6E | 6 GHz | 49.9654 mm | SHF microwave (Wi-Fi 5 GHz, satellite) |
| Satellite TV (Ku band) | 12 GHz | 24.9827 mm | SHF microwave (Wi-Fi 5 GHz, satellite) |
| 5G mmWave | 28 GHz | 10.7069 mm | SHF microwave (Wi-Fi 5 GHz, satellite) |
| Car radar | 77 GHz | 3.89341 mm | EHF microwave (mmWave) |
| Thermal infrared | 30 THz | 9.99308 µm | Infrared |
| TV remote (940 nm) | 318.928 THz | 940 nm | Infrared |
| Red light (650 nm) | 461.219 THz | 650 nm | Visible light |
| Green light (530 nm) | 565.646 THz | 530 nm | Visible light |
| Blue light (450 nm) | 666.205 THz | 450 nm | Visible light |
| UV-A (365 nm) | 821.349 THz | 365 nm | Ultraviolet |
| Medical X-ray | 20 EHz | 14.9896 pm | X-rays |
Tips and pitfalls
- Pick the right wave speed. Sound and light at the same frequency differ in wavelength by about 870,000 times.
- Sound speed changes with temperature. Air at 0 °C carries sound at about 331 m/s, so wavelengths shrink in the cold.
- Light slows in glass and water. The wavelength shortens inside a material, but the frequency and colour stay the same.
- Aerials are cut a little short. Real dipoles are about 95% of the free-space half wavelength.
FAQ
How do you convert frequency to wavelength?
Divide the wave speed by the frequency. For radio and light that is 299,792,458 m/s, so a quick rule is 300 divided by the frequency in MHz gives the wavelength in metres. A 2.4 GHz Wi-Fi signal is therefore about 300 ÷ 2,400 = 0.125 m, or 12.5 cm.
How do you convert wavelength to frequency?
Divide the wave speed by the wavelength in metres. Red light at 650 nm is 299,792,458 ÷ 0.00000065, which is about 461 THz. Make sure the wavelength is in metres first, since nanometres and micrometres are easy to slip by a factor of a thousand.
What is the relationship between frequency and wavelength?
They are inversely proportional: double the frequency and the wavelength halves, as long as the wave speed stays the same. Their product always equals the wave speed, so a high-pitched note has short waves and a deep bass note has waves several metres long.
What is the wavelength of visible light?
Visible light runs from about 380 nm (violet) to 750 nm (red), which is roughly 400 to 790 THz. Shorter wavelengths are ultraviolet and longer ones infrared. The calculator names the colour for any wavelength in the visible range and the band for anything outside it.
How do you calculate photon energy from wavelength?
Photon energy is E = hc ÷ λ, which works out as about 1,240 divided by the wavelength in nanometres to give electronvolts. A 620 nm red photon has about 2 eV and a 310 nm ultraviolet photon about 4 eV, which is why UV can damage skin and visible light cannot.
See also: all Physics tools, Chemistry, Electronics.
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