Compton scattering calculator
A photon scattered at 90° by an electron at rest gains exactly one Compton wavelength, about 2.426 pm, and backscatter at 180° doubles that. Enter the angle in degrees, from 0 to 180, to get the shift in metres. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Angle
- 90
- Wavelength shift
- 0 m
- Compton wavelength
- 0
- One minus cos
- 1
The Compton effect is the inelastic scattering of a photon from a free electron: the photon gives up part of its energy and momentum, so the scattered wavelength is longer than the incident wavelength.
What Compton scattering computes from the scattering angle
When a photon collides with a free or loosely bound electron, conservation of energy and momentum require the photon to emerge with lower energy and therefore a longer wavelength. That inelastic process is Compton scattering. Forward scattering at θ = 0° produces no shift.
A right-angle scatter at 90° produces a shift of one Compton wavelength. Backscattering at 180° produces the maximum shift of two Compton wavelengths.
Where a Compton scattering calculator earns its keep
Classrooms and tutoring platforms use a Compton scattering calculator so learners can check Δλ for arbitrary angles without mixing degrees and radians or forgetting that the cosine of 90° is zero. First-year modern-physics labs that scatter X-rays from graphite or aluminium need a deterministic oracle for the expected wavelength shift at the detector angle they actually set on the goniometer. Gamma-spectroscopy notebooks and radiation-protection primers tabulate the maximum recoil at 180° when discussing shielding, detector response, and the energy a photon can lose in a single scatter.
Exam-prep generators and LMS plugins need an oracle that marks an angle of 200° as invalid instead of silently wrapping it or returning a negative cosine artefact from an out-of-range argument. Failed validation does not consume balance.
What you can do with it
Classroom and homework Compton-effect checks
Let students submit a scattering angle in degrees and verify the Compton wavelength shift in metres against the textbook identity Δλ = λ_C (1 − cos θ).
X-ray and gamma-spectroscopy labs
Predict the expected Δλ at a goniometer or detector angle for Compton-scattered X-rays or gamma rays without importing a nuclear-data library.
Exam and LMS auto-grading
Mark Compton-formula items with a deterministic oracle that rejects angles outside 0–180° and never invents a shift for an unphysical collision.
FAQ
How do I calculate Compton wavelength shift from the scattering angle?
Send a finite scattering angle in degrees between 0 and 180.
What Compton wavelength of the electron does this calculator use?
λ_C is computed from the exact SI Planck constant and speed of light with the CODATA 2018 electron mass, then rounded to twelve significant figures (about 2.42631023868×10⁻¹² m).
What happens if the angle is not between 0 and 180 degrees?
A single Compton collision cannot produce a scattering angle outside 0° (forward) to 180° (backscatter), and the failure is not billed.
Why does a 90° scatter shift the wavelength by one Compton wavelength?
Because 1 − cos 90° = 1, so Δλ = λ_C. Forward scatter (0°) gives Δλ = 0; backscatter (180°) gives the maximum shift 2 λ_C.
Does the shift depend on the wavelength of the incoming photon?
No. The shift depends only on the scattering angle, not on the incident wavelength, so X-rays and gamma rays scattered at the same angle are shifted by the same amount.
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-scattering \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"angle":90}'const res = await fetch("https://api.kit.forhosting.com/phys/compton-scattering", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"angle": 90
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/phys/compton-scattering",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"angle": 90
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/phys/compton-scattering", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"angle":90}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"angle":90}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/phys/compton-scattering", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"angle": 90
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "phys.compton_scattering",
"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
Arthur Compton’s 1923 formula isolates that wavelength shift from the scattering angle alone, Δλ = λ_C (1 − cos θ), where λ_C is the electron Compton wavelength h/(m_e c). This Compton scattering calculator accepts the photon scattering angle in degrees, applies the Compton formula, and returns the wavelength shift in metres. Angles outside the closed interval from 0° to 180° are rejected with invalid_input because they are not physical scattering angles for a single photon-electron collision.
What Compton scattering computes from the scattering angle
Treating the photon as a particle with energy hν and momentum h/λ, and the electron as initially at rest with rest energy m_e c², the algebra collapses to a compact kinematic result: the change in wavelength depends only on the scattering angle θ between the incident and scattered photon directions. The Compton formula is Δλ = λ′ − λ = (h / (m_e c)) (1 − cos θ), or equivalently Δλ = λ_C (1 − cos θ), where λ_C is the Compton wavelength of the electron. This calculator uses the exact SI Planck constant 6.62607015×10⁻³⁴ joule-second, the CODATA 2018 electron rest mass 9.1093837015×10⁻³¹ kilogram, and the exact speed of light 299792458 metres per second, so λ_C is 2.42631023868×10⁻¹² metres, about 2.43 picometres. The endpoint evaluates that closed form for one angle and always returns the shift in metres as the primary SI quantity. It does not ask for the incident wavelength, does not return the scattered photon energy, and does not treat bound-electron corrections, Klein–Nishina cross sections, or pair production; those are different search intents.
Input contract, response shape, and error behaviour
The value must be a finite number in the closed interval from 0 to 180 inclusive. POST a JSON body with one required field: angle, the photon scattering angle θ in degrees. Aliases theta, scattering_angle, angle_degrees, and deg are accepted and mean the same thing. JSON numbers and numeric strings such as "90" are valid; empty strings, non-numeric text, NaN, and infinities fail with invalid_input naming angle. Values below 0° or above 180° also fail with invalid_input, because a single Compton collision cannot produce a scattering angle outside that range—those failures are not billed. On success the body echoes the parsed angle; wavelength_shift, the Compton wavelength change Δλ in metres; compton_wavelength, the electron Compton wavelength λ_C used in the formula; one_minus_cos, the dimensionless factor (1 − cos θ); formula as a short ASCII identity; and unit set to m. Classic checks: 0° returns wavelength_shift 0; 90° returns one Compton wavelength, about 2.426×10⁻¹² m; 180° returns twice that. Pair the number with your own energy conversion if you also need the scattered photon energy; this endpoint solves the kinematic shift only and does not emit spectra, plots, or step-by-step prose beyond the formula field.
Where a Compton scattering calculator earns its keep
Keep the angle inside 0° to 180°, pin the rounded wavelength_shift in tests, and you get reproducible Compton kinematics for homework, grading pipelines, and edge workers without standing up a particle-physics toolkit of your own.
Technical questions
What does the Compton scattering calculator cost?
The browser tool is free. API requests use prepaid KIT balance at $0.002 per successful call; invalid input is not billed.