Atmospheric extinction magnitude calculator
With an extinction coefficient of 0.2 magnitudes per airmass, a star seen through 1.5 airmasses loses 0.3 magnitudes to Earth's atmosphere. Enter the coefficient and the airmass to get the total extinction in magnitudes. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Extinction coefficient
- 0.2
- Airmass
- 1.5
- Extinction magnitude
- 0.3 mag
- Precision
- 10
This atmospheric extinction magnitude calculator finds how many astronomical magnitudes are lost while light passes through Earth’s atmosphere. Enter an extinction coefficient in magnitudes per airmass and an optical airmass of at least one. The calculator applies the standard linear approximation A = k × X, where k is the coefficient and X is the airmass. It returns the total atmospheric extinction A in magnitudes, making quick observing estimates, calibration checks, lesson examples, and repeatable software tests straightforward.
What atmospheric extinction magnitude means
Atmospheric extinction describes the reduction in light from a star, planet, or other source as that light travels through Earth’s atmosphere. In magnitude notation, a larger positive extinction means more light has been removed and the source appears fainter than it would above the atmosphere. This calculator uses the common first-order relation A = k × X.
The extinction coefficient k states the magnitude loss for one unit of airmass, while X represents the relative atmospheric path length along the line of sight. At an airmass of one, usually associated with a target near the zenith under the simple plane-parallel model, the magnitude loss equals the coefficient. At an airmass of two, the model predicts twice that loss.
For example, a coefficient of 0.20 magnitudes per airmass and an airmass of 1.5 produce 0.30 magnitudes lost. To estimate an above-atmosphere magnitude from an observed magnitude under this convention, the extinction amount is commonly subtracted from the observed value, but that separate correction is intentionally not performed here. Keeping the result as magnitudes lost makes the value easy to inspect, reuse in calibration equations, and compare across filters or observing conditions.
How to enter the coefficient and airmass
Coefficients depend on passband, site, weather, aerosols, and the night being characterized, so the calculator does not invent a default or infer one from a location. Use a coefficient measured for your filter and conditions, or a value supplied by the exercise or observing plan you are following. Provide airmass as a finite dimensionless number greater than or equal to one.
An optional precision from zero to fifteen selects the decimal places used in returned numeric fields; it defaults to ten. Inputs that are missing, non-finite, negative where prohibited, outside the declared ceilings, or formatted as ambiguous text are rejected.
When the linear extinction model is useful
The A = k × X model is useful when you already have a suitable extinction coefficient and need a transparent estimate of atmospheric dimming. Amateur and professional observers can use it while planning exposure comparisons at different elevations, checking whether a calibration worksheet applied the expected correction, or recording the atmospheric contribution beside an observation. Teachers can build exercises that show why a target becomes fainter toward the horizon and can verify student arithmetic without hiding the formula inside a large photometry package.
The model is deliberately narrow. It does not derive airmass from altitude or zenith angle, fit extinction coefficients from standard stars, distinguish molecular scattering from aerosols, calculate color terms, convert magnitude loss into flux transmission, or model strong curvature and refraction near the horizon. A single coefficient also should not be assumed to apply equally across different filters or changing weather.
Those tasks need additional measurements and richer models. Within its stated scope, however, the calculator gives a direct and auditable answer: the supplied loss per airmass multiplied by the supplied number of airmasses.
What you can do with it
Plan an observing comparison
Estimate the magnitude loss for targets observed through different airmasses using a coefficient appropriate to the same filter and night.
Check a photometry worksheet
Verify that a spreadsheet or reduction lesson multiplied the stated extinction coefficient by the recorded optical airmass correctly.
FAQ
What formula does the calculator use?
It uses A = k × X, where A is atmospheric extinction in magnitudes, k is magnitudes lost per airmass, and X is dimensionless airmass.
Why must airmass be at least one?
This calculator uses the conventional ground-based model in which one is the minimum supported atmospheric path.
Does the result give the corrected magnitude of my target?
No. It returns only the atmospheric dimming in magnitudes. Apply that value according to the sign convention of your separate photometric correction workflow.
Can it determine the extinction coefficient for my site?
No. Supply a coefficient measured or adopted for the relevant site, filter, and conditions; this calculator does not fit coefficients or fetch weather data.
How much dimmer does a star get at higher airmass?
The loss grows in step with the airmass. At airmass one it equals the coefficient, at airmass two it doubles, and with a coefficient of 0.2 an airmass of 1.5 costs 0.3 magnitudes.
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/astro/extinction-magnitude \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"extinction_coefficient":0.2,"airmass":1.5}'const res = await fetch("https://api.kit.forhosting.com/astro/extinction-magnitude", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"extinction_coefficient": 0.2,
"airmass": 1.5
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/astro/extinction-magnitude",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"extinction_coefficient": 0.2,
"airmass": 1.5
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/astro/extinction-magnitude", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"extinction_coefficient":0.2,"airmass":1.5}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"extinction_coefficient":0.2,"airmass":1.5}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/astro/extinction-magnitude", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"extinction_coefficient": 0.2,
"airmass": 1.5
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "astro.extinction_magnitude",
"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_extinction_coefficient | 1000 |
max_airmass | 1000 |
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 calculation is free, while each successful API request costs $0.002.
What atmospheric extinction magnitude means
The returned extinction_magnitude is therefore a dimming correction expressed in magnitudes, not an observed apparent magnitude, a percentage transmission, or an intrinsic property of the target.
How to enter the coefficient and airmass
Provide extinction_coefficient as a finite, non-negative number measured in magnitudes per airmass. The lower bound matters: in the conventional ground-based approximation used here, one represents the minimum supported atmospheric path, so an airmass below one is rejected with invalid_input instead of yielding a physically misleading result. Numeric strings and common aliases such as k for the coefficient and x for airmass are accepted for practical API use. There are no network calls, random values, stored observations, or date-dependent tables, so identical valid inputs always follow the same calculation and produce the same JSON result.
When the linear extinction model is useful
Run it free in the browser for interactive work, or use the identical deterministic API result for $0.002 per successful request when automation and reproducibility matter.
Integration use cases
Build deterministic test fixtures
Generate stable atmospheric-extinction values for unit tests, observing-log importers, educational apps, and astronomy calculation pipelines.
Technical questions
How much does the API calculation cost?
The calculation is free in the browser. Each successful API request costs $0.002; invalid input is rejected rather than calculated.