Planet equilibrium temperature calculator
A planet receiving 1,361 watts per square metre with a Bond albedo of 0.3 balances at 254.578140117 K. Enter the stellar flux and Bond albedo to get the blackbody temperature at which a world radiates what it absorbs. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Stellar flux
- 1,361
- Bond albedo
- 0.3
- Equilibrium temperature k
- 254.578140117
- Stellar flux w m2
- 1,361
- Absorbed stellar flux w m2
- 952.7
- Globally averaged absorbed flux w m2
- 238.175
This planet equilibrium temperature calculator estimates the blackbody temperature at which a world radiates as much energy as it absorbs from its star. Provide incident stellar flux in watts per square metre and a Bond albedo between zero and one. The result is reported in kelvin using the standard rapid-rotation assumption: absorbed energy is redistributed evenly over the entire planetary surface before thermal re-emission. The response also exposes absorbed and globally averaged fluxes, the physical constant, formula, and model assumptions, making it useful for astronomy lessons, exoplanet comparisons, and reproducible software checks.
What planetary equilibrium temperature represents
Equilibrium temperature is an energy-balance estimate, not a forecast of weather or surface conditions. A planet intercepts radiation across its circular cross-section, reflects a fraction described by its Bond albedo, and absorbs the remainder. In a steady state, the model requires the absorbed stellar power to equal the thermal power radiated to space.
Because this calculator assumes rapid rotation and efficient day-night redistribution, the absorbed power is averaged across the whole spherical surface. The sphere has four times the area of its projected disk, which produces the factor of four in the denominator. The outgoing radiation is then treated as ideal blackbody emission governed by the Stefan-Boltzmann law.
The answer is in kelvin when incident flux is supplied in watts per square metre. This temperature is especially helpful as a common baseline for comparing planets that receive different irradiation or reflect different fractions of it. It deliberately excludes atmospheric and geological effects, so it should be read as the temperature implied by radiative balance under the stated assumptions rather than as a direct thermometer reading at the ground, cloud tops, poles, or substellar point.
Interpreting the result and model limits
The calculated kelvin value is most informative when compared with other results produced under the same assumptions. Higher stellar flux raises temperature only through a fourth root, so multiplying flux by sixteen doubles equilibrium temperature. Increasing Bond albedo lowers the absorbed share and therefore lowers the estimate.
The model does not include greenhouse warming, wavelength-dependent emissivity, internal heating, tidal heating, seasonal storage, eccentric-orbit averaging, or inefficient circulation. Those omissions explain why a measured surface temperature can differ substantially from equilibrium temperature. Earth, for example, has a surface warmed above its basic radiative equilibrium by atmospheric greenhouse effects.
Tidally locked planets can also develop large day-night contrasts that a globally redistributed rapid-rotation model hides. Use this tool for a clean baseline, a classroom energy-balance calculation, or the first stage of a broader climate model; do not present it as a habitable-zone verdict or local surface prediction. For reproducibility, store the input flux and Bond albedo alongside the result and state that the redistribution factor was four and thermal emissivity was treated as one.
What you can do with it
Compare candidate exoplanets
Put planets with different orbital irradiation and assumed Bond albedos on one consistent rapid-redistribution temperature scale.
Check astronomy coursework
Verify a hand calculation and inspect absorbed flux, the factor-of-four surface average, and the final kelvin result.
FAQ
Why is stellar flux divided by four?
The planet intercepts light over a disk but, under rapid and uniform heat redistribution, emits over a sphere whose area is four times larger.
Can I enter geometric albedo?
Not directly. The formula requires Bond albedo, which accounts for reflected energy over all wavelengths and directions; geometric albedo measures a different quantity.
Why can equilibrium temperature differ from surface temperature?
This blackbody baseline excludes greenhouse warming, internal heat, nonuniform circulation, emissivity effects, and local or seasonal temperature variation.
What equilibrium temperature does sunlight at Earth's distance give?
With 1,361 watts per square metre and a Bond albedo of 0.3, the result is 254.578140117 K. Of that sunlight, 952.7 W/m² is absorbed, which averages to 238.175 W/m² over the whole sphere.
How does stellar flux affect the temperature?
Only through a fourth root: multiplying the flux by sixteen doubles the equilibrium temperature. A higher Bond albedo works the other way, because a larger reflected share leaves less energy to absorb and lowers the estimate.
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/equilibrium-temperature \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"stellar_flux":1361,"bond_albedo":0.3}'const res = await fetch("https://api.kit.forhosting.com/astro/equilibrium-temperature", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"stellar_flux": 1361,
"bond_albedo": 0.3
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/astro/equilibrium-temperature",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"stellar_flux": 1361,
"bond_albedo": 0.3
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/astro/equilibrium-temperature", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"stellar_flux":1361,"bond_albedo":0.3}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"stellar_flux":1361,"bond_albedo":0.3}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/astro/equilibrium-temperature", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"stellar_flux": 1361,
"bond_albedo": 0.3
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "astro.equilibrium_temperature",
"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_stellar_flux_w_m2 | 100000000000000000000 |
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 planetary equilibrium temperature represents
Solving that balance for temperature produces T_eq = [F_star × (1 − A_B) / (4 × sigma)]^(1/4).
Choosing stellar flux and Bond albedo inputs
For context, modern solar irradiance near Earth's orbit is roughly 1,361 watts per square metre, but you should use a value appropriate to the star, orbital distance, and orbital phase represented by your calculation. The solver accepts zero as a limiting case and rejects negative, non-finite, missing, or excessively large flux. Bond albedo is dimensionless and describes the fraction of incident energy reflected across all wavelengths and directions. It differs from geometric albedo, which measures brightness at a particular viewing geometry and cannot generally be substituted without a phase integral. A perfectly absorbing ideal body has Bond albedo zero; a perfectly reflecting ideal body has Bond albedo one. Use stellar_flux for the total incident irradiance at the planet's orbit, measured on a surface perpendicular to the incoming rays. Both endpoints are valid here, while any value outside zero through one returns invalid_input. Values may be JSON numbers or strict numeric strings, and documented aliases are accepted. On success, inspect equilibrium_temperature_k for the principal result. The absorbed_stellar_flux_w_m2 field is flux times one minus albedo, while globally_averaged_absorbed_flux_w_m2 divides that value by four before the Stefan-Boltzmann conversion. These intermediate values make unit mistakes and unexpected albedo choices easier to catch.
Interpreting the result and model limits
The API charges $0.002 for each successful item, while invalid inputs such as an albedo of 1.2 are rejected. Since the browser and API share the same deterministic solve function, repeated calls with identical inputs return the same rounded numeric fields.
Integration use cases
Build deterministic simulation fixtures
Generate stable baseline values and invalid-albedo cases for orbital, climate, or radiative-balance software tests.
Technical questions
What formula does the calculator use?
It uses T_eq = [F_star × (1 − A_B) / (4 × sigma)]^(1/4), where sigma is the Stefan-Boltzmann constant.
What happens if albedo is outside zero to one?
The request returns invalid_input because a reflected fraction below zero or above one is outside the physical and declared input domain.