Compton wavelength calculator
The electron's rest mass of 9.1093837015 × 10⁻³¹ kg gives a Compton wavelength of about 2.426 pm, matching the tabulated value. Enter any rest mass in kilograms to get λ in metres and the reduced length. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Mass
- 0
- Wavelength
- 0 m
- Wavelength m
- 0
- Reduced wavelength
- 0
- H
- 0
This Compton wavelength calculator returns the characteristic quantum length of a particle from its rest mass using the closed-form relation λ equals Planck's constant h divided by the product of rest mass m and the speed of light c. The constants are the exact SI 2019 values: h equals 6.62607015 times ten to the minus thirty-four joule-seconds and c equals 299792458 metres per second. With mass in kilograms the Compton wavelength is in metres, the SI length used in particle-physics tables, quantum-field-theory notes, and laboratory cross-checks. A well-known check is the electron rest mass 9.1093837015 times ten to the minus thirty-one kilograms, which yields about 2.426 picometres and matches the tabulated Compton wavelength of the electron. The engine uses only finite arithmetic with no network calls, no sampling, and no date-dependent shortcuts.
Where Compton wavelength fits in study, research, and software
Students meet the Compton wavelength when a textbook moves from classical waves to quantum scattering, when a contest problem asks for λ of an electron, proton, or muon from rest mass, or when they compare particle scales without a full quantum-field-theory course. Teachers can pre-generate answer keys for modest rest-mass values without trusting opaque calculator apps that silently switch from metres to picometres or drop scientific notation.
Developers call the same contract from scripts to seed deterministic test vectors for particle-physics modules, to normalize user-entered rest mass before Compton-scattering demos, or to satisfy programming-challenge statements that demand λ rather than a hand-waved electron constant. Contest practice often needs a fast, offline source of Compton lengths so solutions can be checked without graphing calculators under time pressure.
Product and education tools use the formula when a learner types a rest mass in kilograms and the UI must show the Compton wavelength in metres next to the reduced length ħ over m c.
What you can do with it
Homework and particle-physics table checks
Compute λ from textbook rest-mass values for the electron, proton, or muon and verify the Compton length before scattering or QFT problems.
Education tools and Compton-scattering demos
Normalize user-entered rest mass into Compton wavelength for interactive lessons, lab notebooks, and quantum-mechanics demonstrations.
FAQ
What does the Compton wavelength calculator cost?
It is free in your browser on this page.
How is the Compton wavelength defined here?
The SI unit is metres. The response also reports the reduced Compton wavelength λ̄ = ħ/(m·c) = λ/(2π).
What happens if mass is zero or negative?
Compton wavelength λ = h/(m·c) is undefined for a non-positive rest mass.
Is this the same as a de Broglie wavelength or λ = v/f?
No. De Broglie wavelength is h/p from momentum, and a classical wave uses speed over frequency. This tool only returns the rest-mass Compton wavelength λ = h/(m·c).
What units should I use?
Enter rest mass in kilograms. The Compton wavelength and reduced Compton wavelength are returned in metres, with h and c in SI units.
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/compton-wavelength \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"mass":9.1093837015e-31}'const res = await fetch("https://api.kit.forhosting.com/phys/compton-wavelength", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"mass": 9.1093837015e-31
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/phys/compton-wavelength",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"mass": 9.1093837015e-31
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/phys/compton-wavelength", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"mass":9.1093837015e-31}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"mass":9.1093837015e-31}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/phys/compton-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
{
"mass": 9.1093837015e-31
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "phys.compton_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.
Limits
max_abs_mass | 1e+40 |
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
What the Compton wavelength means and what the response contains
The Compton wavelength of a particle is the wavelength of a photon whose energy equals the rest energy of that particle. Arthur Compton introduced the scale while explaining how X-rays scatter from electrons: a photon that transfers energy to a recoiling electron behaves as if it had a characteristic length λ equal to Planck's constant h divided by the product of the rest mass and the speed of light. In SI units that closed form is λ equals h over m c. This calculator returns the rest mass you supplied, the Compton wavelength in metres as both wavelength and wavelength_m, the reduced Compton wavelength ħ over m c as reduced_wavelength, the exact SI 2019 Planck constant h and speed of light c used in the product, a unit string m, the method tag compton_wavelength, and a short formula reminder. There is no Monte Carlo sampling of quantum states and no table lookup of named particles: you supply the rest mass in kilograms and the engine either builds exact floating-point λ inside the supported magnitude range or rejects the input with invalid_input. Rejected cases include missing mass, non-finite values, magnitudes above the documented ceiling, and any mass that is zero or negative, because Compton wavelength λ equals h over m c is undefined or non-physical for a non-positive rest mass.
How rest mass is read and how λ stays reproducible
Optional leading plus signs and scientific notation on numeric strings are allowed when they parse as finite decimals; embedded spaces, hex prefixes, and non-numeric tokens are rejected with a clear message so a bad cell does not become a wrong Compton length. Computation divides the precomputed factor h over c by mass, then forms the reduced Compton wavelength by dividing that result by two pi, using the exact SI 2019 Planck constant and the exact speed of light so two clients never disagree about which handbook digits were baked in. The preferred field is mass for the particle rest mass in kilograms, but aliases rest_mass, m, and mass_kg are accepted so spreadsheets, query strings, and typed forms can reuse the same contract. Mass must be strictly positive: if mass is zero, negative, or negative zero, the request fails with invalid_input because Compton wavelength λ equals h over m c is undefined for a non-positive rest mass. Pair the free browser run on this page with the priced API when you need the identical mathematical result inside an automated pipeline without re-implementing the Compton formula yourself, and keep rest mass in kilograms so the published wavelength fields stay in metres without a hidden unit conversion.
Where Compton wavelength fits in study, research, and software
On this page the work runs entirely in your browser; through the API each successful lookup costs $0.002, failed validation is not charged, and nothing is stored after the response returns. That split — free interactive exploration and a priced, identical API — matches the rest of the KIT tier-A catalog and lets you move from a classroom demo to an automated pipeline without changing the mathematical result. Pair it with photon-energy or wavelength-from-frequency tools when you need related wave steps, and with other physics endpoints when you are building a small lab of free, deterministic science helpers.
Integration use cases
Deterministic test fixtures
Generate reproducible Compton and reduced Compton wavelengths for unit tests, property checks, and CI assertions on quantum or particle modules.