Frequency to Wavelength Calculator (Vacuum, Air, Water, Glass)
Convert a frequency in Hz, kHz, MHz, GHz or THz to wavelength with λ = c ÷ (n × f). Choose the medium (vacuum, air, water, crown glass or silica fibre) and read the wavelength in m, cm, mm, µm or nm, with the wave speed in that medium and the period.
Last updated: October 2026
Wavelength
12.49 cm
Formula below · 3 sources (physics.nist.gov, hyperphysics.phy-astr.gsu.edu, physicsclassroom.com) · Updated Oct 2026
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About this calculator
An electromagnetic wave travels through vacuum at the speed of light, c = 299,792,458 m/s (an exact, defined value), and the wavelength λ, frequency f and speed are tied by c = f × λ. In a material the wave slows to v = c ÷ n, where n is the refractive index, while the frequency stays the same, so the wavelength shrinks:
λ = c ÷ (n × f)
With the defaults, 2.4 GHz in free space gives 299,792,458 ÷ 2,400,000,000 = 0.1249 m = 12.49 cm, the wavelength of the 2.4 GHz Wi-Fi band. In water (n = 1.333) the same signal has a wavelength of 9.37 cm.
Media
Air at sea level has n = 1.000293, so the vacuum figure is accurate to 0.03% in air, which is why radio and laser wavelengths are quoted for free space. Water (n = 1.333), crown glass (n = 1.52) and the silica core of an optical fibre (n = 1.444 at 1550 nm) shorten the wavelength noticeably: green light at 550 THz is 545 nm in vacuum, 409 nm in water and 359 nm in glass. The refractive index of a material varies slightly with frequency (dispersion); the values here are the usual visible-light figures.
Units
Pick the frequency unit and the wavelength unit that suit the wave: metres for broadcast radio, centimetres for Wi-Fi and microwaves, nanometres for light. The tiles under the result show the wavelength in metres, the wave speed in the chosen medium (c ÷ n) and the period T = 1 ÷ f in nanoseconds.
Limits
The formula is for electromagnetic waves. Sound travels at about 343 m/s in air and 1,480 m/s in water, so for sound divide that speed by the frequency instead (a 440 Hz tone in air: 343 ÷ 440 = 0.78 m). For the other direction, wavelength to frequency, use the companion calculator.
Refractive index of common media and the wavelength of a 550 THz (green) wave in each
Scroll sideways to see all columns →
| Medium | Refractive index n | Wave speed (m/s) | Wavelength at 550 THz |
|---|---|---|---|
| Vacuum | 1 | 299,792,458 | 545.08 nm |
| Air (sea level) | 1.000293 | 299,704,645 | 544.92 nm |
| Water | 1.333 | 224,900,569 | 408.91 nm |
| Silica optical fibre | 1.444 | 207,612,505 | 377.48 nm |
| Crown glass | 1.52 | 197,231,880 | 358.60 nm |
How to use
Enter the frequency, choose its unit, pick the medium and the wavelength unit. Example 1 (Wi-Fi): 2.4 GHz in vacuum, shown in cm. λ = 299,792,458 ÷ 2.4 × 10⁹ = 0.12491 m = 12.49 cm; period 0.4167 ns. Example 2 (FM radio): 100 MHz in air, shown in cm. λ = 299,792,458 ÷ (1.000293 × 10⁸) = 2.9970 m = 299.70 cm (299.79 cm in vacuum). Example 3 (green light): 550 THz, shown in nm. Vacuum: 299,792,458 ÷ 5.5 × 10¹⁴ = 545.08 nm; water: 545.08 ÷ 1.333 = 408.91 nm; crown glass: 545.08 ÷ 1.52 = 358.60 nm. The frequency, and the colour, are unchanged.
Frequently asked questions
What is the formula to convert frequency to wavelength?
Wavelength equals the wave speed divided by the frequency: λ = c ÷ f in vacuum, with c = 299,792,458 m/s. In a material divide once more by the refractive index n: λ = c ÷ (n × f). A 100 MHz signal has λ = 299,792,458 ÷ 100,000,000 = 2.998 m.
Why does the wavelength change in water or glass but the frequency does not?
Frequency is set by the source and cannot change as the wave crosses into a new material. The speed drops to c ÷ n, so to keep v = f × λ the wavelength drops by the same factor: 545 nm green light becomes 409 nm in water and is still green.
How do I convert GHz to wavelength in cm?
λ (cm) = 29.979 ÷ f (GHz). For 5 GHz: 29.979 ÷ 5 = 6.0 cm; for 2.4 GHz: 12.49 cm; for 24 GHz: 1.25 cm.
Does this work for sound?
No. Sound is not electromagnetic; it travels at about 343 m/s in air at 20 °C and about 1,480 m/s in water. Divide that speed by the frequency instead: a 440 Hz tone in air has λ = 343 ÷ 440 = 0.78 m, and the same tone in water 1,480 ÷ 440 = 3.36 m.
Which refractive index should I use for air?
n = 1.000293 at sea level for visible light; it is within 0.03% of vacuum, so most radio and optics work simply uses c. The index falls with altitude and rises slightly with humidity and pressure.
What is the period shown under the result?
The period T = 1 ÷ f is the time for one full cycle. 2.4 GHz has T = 1 ÷ 2.4 × 10⁹ s = 0.4167 ns; 50 Hz mains has T = 20 ms.
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Sources & references
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