Wavelength Calculator
Find a wave's length from its frequency. Enter the frequency (Hz, kHz, MHz, or GHz), pick the wave — light in vacuum, sound in air or water, or a custom speed in m/s — and get λ = v/f scaled sensibly from kilometers down to nanometers, plus the quarter-wave length used in antenna design.
Example: with Frequency 98.5 · Frequency unit MHz · Wave and medium Light / radio in vacuum (299,792,458 m/s) · Custom wave speed (m/s, if selected) 340 → Wavelength λ: 3.044 m.
- Quarter wavelength (λ/4)76.09 cm
- In feet / inches9.985 ft
Computed by the calculator below using its default values. Change any input to see your own numbers.
λ = v / f. Speed of light in vacuum is exactly 299,792,458 m/s (SI definition); sound in air at 20°C travels about 343 m/s.
One formula, every wave
Wavelength is how far a wave travels during one complete cycle, so it is simply speed divided by frequency: λ = v/f. The formula is identical for radio, light, and sound — what changes is the speed. Light in vacuum moves at exactly 299,792,458 m/s, so a 98.5 MHz FM station has a wavelength of about 3.04 m. Sound in room-temperature air crawls at 343 m/s, so concert-pitch A (440 Hz) is a 78 cm wave.
That speed difference is enormous: the same 1 kHz frequency is a 34 cm sound wave but a 300 km radio wave. Frequency belongs to the source; wavelength belongs to the medium the wave is passing through.
Why quarter-wave matters
Antennas, organ pipes, and speaker ports all resonate at fractions of a wavelength, and λ/4 is the workhorse. A monopole antenna over a ground plane is most efficient at a quarter of the signal's wavelength — about 76 cm for FM broadcast, which is why telescoping car antennas were around that length. Subwoofer transmission lines and closed pipes follow the same quarter-wave logic with the speed of sound instead of light. If you are sizing hardware, compute λ first and the geometry follows.
How it’s calculated
λ = v / f. Speeds used: light/radio in vacuum c = 299,792,458 m/s (exact, SI definition of the meter); sound in dry air at 20°C = 343 m/s; sound in seawater ≈ 1,481 m/s at 20°C; or your custom speed. Frequency scaled from Hz to GHz (×10³ per step). Output auto-scales km/m/cm/mm/µm/nm and converts to feet at 1 ft = 0.3048 m exactly.
Sound speeds are representative values — air speed shifts about 0.6 m/s per °C and water speed varies with temperature, salinity, and depth.
Wavelengths of familiar signals
| Signal | Frequency | Speed | Wavelength |
|---|---|---|---|
| AM radio station | 1,000 kHz | light | 299.8 m |
| FM radio station | 100 MHz | light | 3.00 m |
| Wi-Fi (2.4 GHz band) | 2.4 GHz | light | 12.49 cm |
| Wi-Fi (5 GHz band) | 5 GHz | light | 6.0 cm |
| Concert A (sound in air) | 440 Hz | 343 m/s | 78 cm |
| Middle C (sound in air) | 262 Hz | 343 m/s | 1.31 m |
Computed with λ = v/f using c = 299,792,458 m/s and 343 m/s for sound in 20°C air; rounded.
Common mistakes
- Using the speed of light for sound problems — a 440 Hz sound wave is 78 cm, not 681 km.
- Missing a prefix: MHz is 10⁶ Hz and GHz is 10⁹ Hz, so a slip of one prefix scales the answer 1,000×.
- Assuming wavelength stays fixed when a wave enters a new medium — frequency is what stays constant; wavelength stretches or shrinks with the speed.
- Quoting λ/4 antenna lengths from the full wavelength without dividing by four.
Frequently asked questions
What is the wavelength formula?
λ = v / f: wave speed divided by frequency. For light in vacuum v is c = 299,792,458 m/s; for sound in 20°C air it is about 343 m/s.
Does wavelength depend on the medium?
Yes. The source fixes the frequency, and the medium sets the speed, so λ = v/f changes when the wave crosses into a new material — light slows and shortens in glass, sound lengthens moving from air into water.
What is the wavelength of a 2.4 GHz Wi-Fi signal?
299,792,458 / 2.4×10⁹ ≈ 0.125 m, or 12.5 cm. That short wavelength is why small internal antennas work in phones and routers.
Why do radio masts get shorter as frequency rises?
Efficient antennas are sized to fractions of λ, usually λ/4 or λ/2. AM signals near 1 MHz are ~300 m long and need towers; 2.4 GHz waves are 12.5 cm, so a 3 cm quarter-wave element fits inside a router.
Can I use this for ocean or seismic waves?
Yes — pick Custom and enter the wave's speed in m/s. λ = v/f holds for any periodic wave as long as you know how fast it propagates.