What this calculator does
The wavelength formula relates three properties every travelling wave shares: speed, frequency and wavelength. Wave speed equals frequency times wavelength (v = fλ), so once any two of the three are known, the third follows directly. This calculator solves it for wavelength, given the wave's frequency and the speed it is travelling at.
The same formula covers sound, light, water waves and radio signals alike, because it describes wave behaviour generally rather than any one physical medium. What changes between them is the speed: sound travels at roughly 343 m/s in air at room temperature, while light and other electromagnetic waves travel at 299,792,458 m/s in a vacuum, which is why a sound wave and a radio wave at the same frequency have wildly different wavelengths.
The formula
Wavelength is wave speed divided by frequency: λ = v/f. Frequency is the number of complete wave cycles passing a point each second, measured in hertz, and speed is how fast the wave itself propagates through the medium. Period, the time for one full cycle, is simply the reciprocal of frequency.
| Term | Meaning |
|---|---|
| Wavelength (λ) | The distance between two equivalent points on consecutive wave cycles, such as crest to crest. |
| Frequency (f) | The number of complete wave cycles per second, in hertz (Hz). |
| Wave speed (v) | How fast the wave itself travels through its medium, in metres per second. |
The inputs explained
| Field | What to enter |
|---|---|
| Frequency (Hz) | The frequency of the wave, in hertz. For a musical note or radio signal this is the number usually quoted directly. |
| Wave speed (m/s) | The speed the wave travels at. Use roughly 343 m/s for sound in air at room temperature, or 299,792,458 m/s for light and radio waves in a vacuum. |
When to use it
Working out a musical note's wavelength
A concert-pitch A at 440 Hz, travelling through air at about 343 m/s, has a wavelength just under 0.78 m, which is why instrument sizes are roughly proportional to the wavelengths they are built to produce or resonate with.
Converting a radio frequency to an antenna length
Radio and Wi-Fi frequencies are usually quoted in hertz, but antenna design works in wavelength, so this calculator is the direct bridge between the two using the speed of light.
Checking the audible range against wavelength
Human hearing spans roughly 20 Hz to 20,000 Hz; converting both ends to wavelength in air shows just how much physical size that range corresponds to, from over 17 metres down to under 2 centimetres.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How does wavelength change with frequency, for a sound wave in air?
A range of audible frequencies, all travelling at the speed of sound in air.
| Frequency | Wavelength | Period |
|---|---|---|
| 20 Hz | 17.150 m | 0.050000 s |
| 100 Hz | 3.430 m | 0.010000 s |
| 440 Hz | 0.7795 m | 0.002273 s |
| 1,000 Hz | 0.3430 m | 0.001000 s |
| 5,000 Hz | 0.0686 m | 0.000200 s |
| 20,000 Hz | 0.0172 m | 0.00005000 s |
How does wavelength change with frequency, for light?
The same frequency range, but for an electromagnetic wave instead of sound.
| Frequency | Wavelength |
|---|---|
| 100,000,000 Hz | 2.998 m |
| 1,000,000,000 Hz | 0.2998 m |
| 100,000,000,000 Hz | 0.0030 m |
| 500,000,000,000,000 Hz | 0.000001 m |
| 600,000,000,000,000 Hz | 0.000000 m |
Questions
Why is wavelength different for the same frequency in sound versus light?
Wavelength depends on both frequency and speed, and sound and light travel at vastly different speeds: about 343 m/s for sound in air versus 299,792,458 m/s for light in a vacuum. At the same frequency, the much faster wave has a proportionally much longer wavelength.
Does the speed of sound change with temperature?
Yes, sound travels faster as air warms, roughly 343 m/s at 20°C and slightly slower in cold air. For a precise value at a specific temperature, use a dedicated speed-of-sound calculator rather than the fixed 343 m/s approximation.
What is the relationship between period and frequency?
Period is the time for one complete wave cycle, and frequency is the number of cycles per second, so the two are reciprocals of each other: period = 1 ÷ frequency.
Can this be used for water waves or other mechanical waves?
Yes. The formula v = fλ holds for any travelling wave, so entering the correct speed for that specific medium, whichever it is, gives the right wavelength.
For the speed of sound at a specific air temperature, see the speed of sound calculator. For how far light travels in a given time, see the speed of light calculator.