Wavelength calculator
Divide the wave speed by the frequency and get the wavelength in metres: sound at 340 m/s with a 440 Hz pitch spans a little over three quarters of a metre per cycle. Handy for acoustics homework, antenna checks and lab reports. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Speed
- 340
- Frequency in hertz
- 440
- Wavelength
- 0.7727272727
Wavelength is the spatial period of a progressive wave: the distance between successive crests, troughs or equivalent phase points along the direction of travel. When you know how fast the wave propagates and how many cycles occur each second, the relationship is simply lambda equals speed divided by frequency. This calculator applies that textbook formula with clear validation, so a zero frequency fails loudly instead of producing infinity or a silent NaN. Use it for acoustics homework, radio and antenna design checks, lab reports that mix air sound speed with measured pitch, or pipelines that need a deterministic physics step without calling an external model.
What wavelength means and why λ equals v over f
A progressive wave carries energy through a medium or through free space by repeating a pattern in both space and time. Frequency counts how many full cycles pass a fixed point each second and is measured in hertz. Wave speed is how far a given phase front advances per second and is measured in metres per second for SI work.
Because one cycle occupies one wavelength in space and one period in time, and period is the reciprocal of frequency, rearranging the definitions yields the compact relation lambda equals v divided by f. The same algebra recovers speed as wavelength times frequency or frequency as speed divided by wavelength, which is why laboratory exercises often give two of the three quantities and ask for the third. This capability solves for wavelength only: you supply speed and frequency, and it returns the length of one spatial cycle.
The derivation assumes a constant-speed progressive wave in a uniform medium; it does not invent dispersion curves, refractive-index tables or Doppler shifts. Treat the output as the fundamental geometric link between the three quantities, then layer medium-specific corrections when your problem statement requires them. Identical inputs always produce identical floating-point results because the implementation is pure arithmetic with no network calls, randomness or wall-clock dependence.
How to choose speed and frequency inputs correctly
Speed is the full propagation magnitude in metres per second for the medium and wave type you care about. Typical classroom values include about three hundred forty metres per second for sound in dry air near room temperature, about fifteen hundred metres per second for sound in water, and the speed of light in vacuum for electromagnetic problems when you work in SI.
Frequency must be a finite non-zero number in hertz; musical pitch, radio carrier frequency, or a lab oscillator reading all map cleanly once you convert kilohertz or megahertz into hertz if your problem uses those prefixes. Zero frequency is rejected with an invalid-input error because division by zero is undefined and would not represent a meaningful wavelength.
Keep units consistent throughout: mixing kilometres per hour for speed with a frequency still expressed in kilohertz without conversion will yield a number that is mathematically well-formed but wrong for the physical situation you intended. Positive speeds are the usual case; the calculator still performs the division for any finite non-zero frequency so advanced exercises that use signed conventions are not blocked, but you remain responsible for interpreting the sign of the result.
Reading the result and using it in study or automation
For a concert A at four hundred forty hertz travelling at three hundred forty metres per second in air, the wavelength is three hundred forty divided by four hundred forty, a little under one metre, which matches the scale students expect for audible sound in a room. For radio waves, the same formula with the speed of light and a megahertz-scale frequency produces wavelengths on the order of metres to centimetres, which is why antenna design talks about quarter-wave and half-wave elements. Failed validation never charges balance.
Use the tool to grade wave-equation worksheets, prefill parameters for a simulation before adding dispersion, or assert fixed values in continuous integration that must not depend on external services. When your application needs period, wave number or angular frequency as well, compute those from frequency and wavelength in a following step rather than expecting this capability to expand beyond its single well-defined contract.
What you can do with it
Physics and acoustics homework
Check student work that asks for the wavelength of a tone at a given air speed and pitch, or of a string wave with a known propagation speed.
RF and antenna rough sizing
Convert carrier frequency and the speed of light into a free-space wavelength before choosing quarter-wave or half-wave element lengths.
FAQ
What formula does the wavelength calculator use?
It uses the standard progressive-wave relation λ = v / f, where v is wave speed in metres per second and f is frequency in hertz. The wavelength is returned in metres.
What units should I use for speed and frequency?
Use metres per second for speed and hertz for frequency so the wavelength is in metres. Convert kHz, MHz or km/h yourself before calling the tool.
Does this account for Doppler shift or medium dispersion?
No. It applies only the geometric relation λ = v / f for the speed and frequency you supply. Apply Doppler or dispersion corrections outside this step if needed.
Is the wavelength calculator free?
The browser tool is free and runs entirely on your device.
Why is a frequency of zero refused?
Because wavelength is speed divided by frequency, and dividing by zero has no answer. Instead of showing infinity, the calculator stops and asks for a non-zero frequency in hertz.
Related tools
For developers — API access
Everything on this page is available programmatically. This section is for teams who want to wire it into their own systems; everyone else can just use the tool above.
API endpoint
Prefer to automate it? One authenticated POST creates the task; the result comes back by webhook or a signed link. The same capability also runs here on the web, by email and from Telegram — and soon from our app too.
Call it from your stack
curl -X POST https://api.kit.forhosting.com/phys/wavelength \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"speed":340,"frequency":440}'const res = await fetch("https://api.kit.forhosting.com/phys/wavelength", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"speed": 340,
"frequency": 440
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/phys/wavelength",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"speed": 340,
"frequency": 440
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/phys/wavelength", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"speed":340,"frequency":440}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"speed":340,"frequency":440}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/phys/wavelength", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"speed": 340,
"frequency": 440
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "phys.wavelength",
"status": "queued",
"_links": {
"result": "/tasks/tsk_…/result"
}
}The API is asynchronous: the call returns a task_id immediately and the result arrives by webhook. Polling is capped at 1 req/s per task.
Pricing
Published price — no tokens, no invented credits. A failed task is never charged.
Errors
| HTTP | Code | Meaning |
|---|---|---|
401 | unauthorized | Missing or invalid API key. |
402 | insufficient_balance | Your balance doesn't cover the task price. |
404 | unknown_type | That task type doesn't exist. |
429 | rate_limited | Too many requests. Use the webhook instead of polling. |
Technical notes
The browser tool is free and runs locally; the same pure arithmetic is available over the API at the published base price of $0.002 per successful request.
How to choose speed and frequency inputs correctly
Missing fields, non-numeric strings and non-finite values are likewise rejected with messages that name the field so API clients and students can fix the request.
Reading the result and using it in study or automation
The response returns wavelength, the echoed speed and frequency, and a units object that labels wavelength in metres, speed in metres per second and frequency in hertz. The published API base price is $0.002 per successful item; the on-page calculator remains free for interactive use.
Integration use cases
Lab reports and CI golden values
Produce deterministic wavelength figures from measured frequency and tabulated medium speed for reports or automated physics self-checks.
Technical questions
Why is zero frequency rejected?
Wavelength is speed divided by frequency. A zero frequency would make the division undefined, so the capability returns invalid_input instead of infinity or NaN.