Total magnitude of equal stars calculator
One hundred stars of magnitude 5 seen together shine at magnitude 0, exactly five magnitudes brighter than one of them. Enter a single star's apparent magnitude and the number of stars to get the group's total and the change. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Star magnitude
- 5
- Star count
- 100
- Total magnitude
- 0
- Magnitude change
- -5
- Precision
- 10
This total magnitude of equal stars calculator finds how bright a group of identical stars appears when their light is observed together. Enter the apparent magnitude of one star and the number of stars, and it applies the logarithmic Pogson magnitude relation to the summed flux. The result is deterministic and suitable for astronomy exercises, observation planning, classroom demonstrations, and software tests.
Why identical stellar fluxes must be added before converting magnitude
Astronomical magnitude is logarithmic, so the magnitude numbers of several stars cannot be added directly. A smaller magnitude represents a brighter source, and a difference of five magnitudes corresponds to a factor of one hundred in received flux. When every star has the same apparent magnitude, each contributes the same flux.
The group therefore has N times the flux of one member, where N is the star count. The subtraction is important: adding light makes the unresolved group brighter, so its numerical magnitude decreases. One star is a useful identity check because log10(1) is zero and the total magnitude stays equal to the individual magnitude.
One hundred equal stars produce one hundred times the flux and are exactly five magnitudes brighter than one star. This calculator reports both the total magnitude and the magnitude change, making the direction and size of the brightness adjustment visible. It assumes the individual value is an apparent magnitude measured consistently in the same photometric band for every member.
It does not estimate distances, extinction, intrinsic luminosity, color corrections, or detector response. Those effects must already be reflected in the single-star magnitude if they matter to the intended comparison.
How to enter a star magnitude, count, and rounding precision
A fractional count is rejected rather than silently rounded, preventing an accidental unit or spreadsheet error from looking like a valid astronomical result. The optional precision field controls the number of decimal places in the returned magnitude values and may range from zero through fifteen; it defaults to ten for reproducible numeric output. Magnitude_change is negative whenever more than one star is combined because the group is brighter than one member.
Numeric strings in ordinary decimal or scientific notation are accepted by the calculation core, while blank strings, nonnumeric labels, infinities, arrays, and objects are rejected. No network request, random value, stored state, or current date affects the answer.
When the equal-star approximation is useful and when it is not
The equal-star formula is useful when a problem explicitly describes identical sources, when a synthetic cluster model assigns every member the same magnitude, or when a classroom exercise isolates the relationship between flux and the Pogson scale. It also provides quick checks for code that combines photometry: ten equal sources must brighten the result by 2.5 magnitudes, one hundred by 5 magnitudes, and ten thousand by 10 magnitudes.
Observers can use the calculation as an approximation for an unresolved group only when the members truly have similar measured fluxes in the selected band. Real star clusters usually contain stars with a broad luminosity distribution, and a few luminous giants can dominate the integrated light. In that case, calculate a flux equivalent for each different magnitude, sum those fluxes, and convert the total back to magnitude instead of using a single magnitude and count.
The calculator also does not turn apparent magnitude into absolute magnitude, infer how many stars are present from integrated light, account for stars hidden by dust, or predict whether a telescope will resolve the group. Its narrow contract is intentional: it answers one well-defined question with transparent arithmetic.
What you can do with it
Check astronomy homework
Verify the combined apparent magnitude of a stated number of identical stars without incorrectly adding logarithmic magnitude values.
Model a simplified cluster
Estimate the integrated magnitude of an idealized unresolved cluster whose members share one apparent magnitude.
FAQ
Why does the total magnitude become smaller as stars are added?
Smaller magnitude numbers indicate greater brightness. More equal stars contribute more total flux, so the combined magnitude decreases.
Can the stars have different magnitudes?
No. This calculator assumes identical magnitudes. For different stars, convert each magnitude to relative flux, sum the fluxes, and convert back.
What is the total magnitude of 100 stars of magnitude 5?
It is magnitude 0. One hundred equal stars send one hundred times the light of one star, which on the magnitude scale is exactly five magnitudes brighter, so the change shown is −5.
What does the calculator return for a single star?
With a count of one, the total magnitude equals the star's own magnitude and the change is zero, a handy check. The count must be a whole number: a fractional count is refused instead of being rounded.
Does it correct for distance or interstellar dust?
No. It does not estimate distance, extinction, intrinsic luminosity or color corrections. If those matter, they must already be included in the single-star magnitude, measured in the same photometric band for every star.
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/cluster-total-magnitude \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"star_magnitude":5,"star_count":100}'const res = await fetch("https://api.kit.forhosting.com/astro/cluster-total-magnitude", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"star_magnitude": 5,
"star_count": 100
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/astro/cluster-total-magnitude",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"star_magnitude": 5,
"star_count": 100
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/astro/cluster-total-magnitude", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"star_magnitude":5,"star_count":100}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"star_magnitude":5,"star_count":100}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/astro/cluster-total-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
{
"star_magnitude": 5,
"star_count": 100
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "astro.cluster_total_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.
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
Run it free in your browser, or use the API for $0.002 per successful request when you need the same calculation in an automated workflow.
Why identical stellar fluxes must be added before converting magnitude
Converting that flux ratio back to magnitude gives m_total = m_star - 2.5 log10(N).
How to enter a star magnitude, count, and rounding precision
Provide star_magnitude as any finite real magnitude, including zero or a negative value for a very bright source. Provide star_count as a strictly positive integer because a physical group contains a whole number of stars and the logarithm is undefined for zero or a negative count. The response repeats the normalized individual magnitude and count, then returns total_magnitude, magnitude_change, precision, a method identifier, and the formula used. Counts above JavaScript's safe integer range are also rejected so the request cannot imply an integer that the runtime cannot represent exactly.
When the equal-star approximation is useful and when it is not
Use the browser calculation for exploration and teaching, or call the API for $0.002 per successful request when generating exercises, validating catalog software, or processing repeated equal-source scenarios in an automated system.
Integration use cases
Test photometry software
Generate deterministic equal-flux reference cases for unit tests of source-combination and catalog-processing code.
Technical questions
What formula does the calculator use?
It uses m_total = m_star - 2.5·log10(N), where N is the positive integer number of identical stars.
What happens when the star count is zero or negative?
The request returns invalid_input because a non-positive source count has no valid logarithm or physical flux sum in this calculation.
How much does the API calculation cost?
A successful API request costs $0.002. The same deterministic calculation is also available free in your browser on this page.