Stellar luminosity in solar units calculator
Compare a star's power output with the Sun's from two ratios: twice the Sun's radius and 1.5 times its temperature give 20.25 solar luminosities, because brightness grows with radius squared and temperature to the fourth power. Free in your browser.
- Free
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- Your data stays on your device
Run — free
Worked example
- Radius solar
- 2
- Temperature solar
- 1.5
- Luminosity solar
- 20.25
This stellar luminosity calculator estimates how much power a star radiates compared with the Sun when you know its radius and effective temperature as solar ratios. It applies the standard Stefan-Boltzmann scaling relation: luminosity grows with the square of radius and the fourth power of temperature. Enter 1 for a property equal to the Sun's, 2 for twice the Sun's value, or any other positive finite ratio. The result is returned directly in solar luminosities, making comparisons between stars straightforward.
Enter radius and temperature as solar ratios
Both inputs are dimensionless ratios, so you do not need to supply kilometers, meters, kelvin, or another physical unit. The radius value is the star's radius divided by the solar radius. If you start with a temperature in kelvin, divide it by the solar effective temperature adopted by your data source before using this calculator.
Keeping both values relative to the same solar reference is important because inconsistent reference constants introduce avoidable error. Each input must be a finite number greater than zero. Zero and negative ratios have no physical meaning in this scaling calculation, while non-finite values cannot produce a usable luminosity.
The calculator rejects such values explicitly instead of returning a misleading number.
Understand the squared-radius and fourth-power temperature law
Expressing the equation as ratios cancels the Stefan-Boltzmann constant and the absolute solar radius and temperature, leaving a compact comparison. Radius affects the radiating surface area, which is why doubling radius multiplies luminosity by four when temperature remains unchanged. Temperature has a much stronger influence because thermal emission scales with its fourth power.
A star at twice the Sun's effective temperature would have sixteen times the solar luminosity even if its radius matched the Sun's. When both properties change, the effects multiply rather than add. For example, a star with twice the solar radius and one and a half times the solar temperature receives both the area factor and the temperature factor.
Interpret the result and recognize the model's limits
A result of 1 means the modeled star has the Sun's luminosity. A result of 10 means ten solar luminosities, and 0.1 means one tenth of the solar luminosity. This relation is useful for quick checks of stellar parameters, classroom exercises, catalog comparisons, and estimates based on fitted radii and effective temperatures.
It is also valuable for sensitivity analysis: small temperature revisions can cause substantial luminosity revisions because the temperature ratio is raised to the fourth power. The calculation assumes the star can be represented by a single effective temperature and that its total emission follows the usual spherical blackbody-style scaling. It does not account separately for wavelength bands, extinction, distance, apparent brightness, rapid rotation, surface temperature variations, or uncertainty propagation.
It also does not infer radius or temperature from observations. Use values derived consistently from an appropriate stellar model or trusted catalog. For research reporting, retain the source values and their uncertainties, then propagate those uncertainties separately rather than treating this single ratio as a complete observational analysis.
What you can do with it
Compare a modeled star with the Sun
Convert relative radius and effective temperature into one direct luminosity ratio for an immediate physical comparison.
Check stellar catalog parameters
Recompute the implied luminosity from listed radius and temperature ratios to identify inconsistent or mistyped entries.
Explore temperature sensitivity
Change the temperature ratio while holding radius fixed to see how strongly the fourth-power term affects luminosity.
FAQ
What does the calculator cost?
The same deterministic calculation can run in the browser.
What does a luminosity result of 1 mean?
It means the calculated luminosity equals the Sun's luminosity under the scaling relation.
Should temperature be entered in kelvin?
No. Enter the star's effective temperature divided by the Sun's effective temperature.
Why does temperature have such a large effect?
Radiated luminosity scales with the fourth power of effective temperature, so even a modest temperature-ratio change is amplified.
Can either input be zero or negative?
No. Radius and effective-temperature ratios must both be finite and strictly greater than zero.
Does the result include distance or extinction?
No. It estimates intrinsic bolometric luminosity from radius and effective temperature only; it does not calculate observed brightness.
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/stellar-number-density \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"radius_solar":2,"temperature_solar":1.5}'const res = await fetch("https://api.kit.forhosting.com/astro/stellar-number-density", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"radius_solar": 2,
"temperature_solar": 1.5
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/astro/stellar-number-density",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"radius_solar": 2,
"temperature_solar": 1.5
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/astro/stellar-number-density", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"radius_solar":2,"temperature_solar":1.5}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"radius_solar":2,"temperature_solar":1.5}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/astro/stellar-number-density", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"radius_solar": 2,
"temperature_solar": 1.5
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "astro.stellar_number_density",
"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
Enter radius and temperature as solar ratios
A radius_solar value of 2 therefore describes a star with twice the Sun's radius, while 0.5 describes one with half the Sun's radius. The temperature value follows the same pattern: temperature_solar is the star's effective temperature divided by the Sun's effective temperature.
Understand the squared-radius and fourth-power temperature law
The calculation uses the ratio form of the Stefan-Boltzmann luminosity law: L divided by solar luminosity equals radius_solar squared, multiplied by temperature_solar raised to the fourth power. The returned luminosity_solar value is the combined ratio, not an absolute power in watts, and no rounding is imposed on the deterministic numeric result.