Radiative Equilibrium Temperature Calculator

Calculator Inputs

Choose an input method *

All methods compute the same equilibrium temperature.

Stellar flux at target (W/m²) *

Earth near the Sun is about 1361 W/m².

Luminosity value *

Luminosity unit

Distance to target *

Flux is computed with inverse square dilution.

Star effective temperature (K) *

Sun is about 5772 K.

Star radius *

Used to compute flux at the target.

Distance to target *

Large distances reduce flux quickly.

Bond albedo A (0–1) *

Fraction of incident energy reflected.

Emissivity ε (0–1) *

Blackbody is 1. Many surfaces are lower.

Redistribution factor f *

Smaller values increase temperature.

Greenhouse offset ΔT (K)

Optional warming above equilibrium.

Results appear above this form after calculation.

Formula Used

Radiative equilibrium balances absorbed stellar power with thermal emission.

T_eq = \u221A\u221A\u221A\u221A( ((1 - A) \u22C5 S) / (f \u22C5 \u03B5 \u22C5 \u03C3) )

A is Bond albedo, S is incident flux, f is redistribution factor, \u03B5 is emissivity, and \u03C3 is the Stefan\u2013Boltzmann constant.

When you compute flux from a star, these options are available.

S = L / (4\u03C0d\u00B2) using luminosity L and distance d.
S = \u03C3T\u2217\u2074 (R\u2217 / d)\u00B2 using star temperature T\u2217 and radius R\u2217.

How to Use This Calculator

Select the input method that matches your data source.
Enter albedo, emissivity, and a redistribution option.
Add a greenhouse offset if you want a surface estimate.
Press Calculate to see flux and temperatures above.
Use CSV or PDF buttons to export your results.

Example Data Table

These examples assume \u03B5 = 1 and f = 4.

Body	Flux S (W/m²)	Albedo A	Emissivity ε	f	T_eq (K)
Earth	1361	0.30	1.00	4	254.58
Venus	2604	0.75	1.00	4	231.45
Mars	590	0.25	1.00	4	210.16
Mercury	9126	0.12	1.00	4	433.78
Jupiter	50.5	0.34	1.00	4	110.10

Article

1) Radiative Equilibrium in One Idea

Radiative equilibrium occurs when absorbed starlight equals emitted heat. A planet intercepts energy, reflects part using albedo, then reradiates infrared energy. The balance sets an equilibrium temperature, often written as T_eq. It is a baseline for climate comparisons across worlds.

2) Key Inputs That Control Temperature

Three inputs dominate: incident flux S, albedo A, and redistribution factor f. Increasing S raises temperature strongly because T scales with S^1/4. Higher albedo lowers absorbed energy. Smaller f concentrates heating, increasing temperatures. Emissivity ε adjusts how efficiently the surface radiates.

3) Interpreting Stellar Flux

Flux is power per square meter at the target distance. For the Sun near Earth, S is about 1361 W/m². If you know stellar luminosity L and distance d, flux follows inverse square dilution: S = L / (4πd²). Doubling distance reduces flux by four.

4) Choosing Redistribution Factor

The factor f represents how heat spreads over the surface. A global average uses f = 4, typical for fast rotation and strong winds. A dayside average uses f = 2 when nightside cooling is efficient. The extreme substellar point uses f = 1 for no redistribution.

5) Role of Emissivity and Surface Physics

Emissivity ε ranges from 0 to 1. A perfect blackbody has ε = 1. Many rocks, ices, and dusts are near 0.9–1.0, while some metals are lower. Lower emissivity reduces emitted power, raising the equilibrium temperature for the same absorbed flux.

6) Adding a Simple Greenhouse Offset

Real atmospheres trap heat through absorption bands. This tool includes a simple greenhouse offset ΔT to estimate a warmer surface temperature. For Earth, T_eq is about 255 K, while the mean surface is near 288 K, implying ΔT ≈ 33 K in a simple comparison.

7) Worked Scenario Comparisons

Try Earth-like settings: A = 0.30, ε = 1, f = 4, and S = 1361 W/m² to obtain ~255 K. Increase albedo to 0.60 and temperature drops noticeably. Keep albedo fixed but switch f from 4 to 2, and the dayside equilibrium rises by roughly 19%.

8) Common Modeling Limits

This calculator is an energy-balance baseline, not a full climate model. It ignores internal heat, wavelength-dependent albedo, clouds, and atmospheric circulation. It also assumes steady conditions and uniform emissivity. Still, it is excellent for quick habitability screening and mission planning comparisons.

FAQs

1) What is radiative equilibrium temperature?

It is the temperature where absorbed stellar energy equals emitted thermal radiation. It is a baseline estimate, not a full climate prediction.

2) Which albedo should I use?

Use Bond albedo, which averages reflection over all wavelengths and angles. If unknown, try 0.3 for Earth-like or compare a range, like 0.1 to 0.8.

3) What does the redistribution factor mean?

It approximates how heat spreads. f = 4 assumes global averaging, f = 2 assumes only dayside averaging, and f = 1 represents heating near the substellar point.

4) Why does emissivity change the result?

Emissivity controls infrared radiation efficiency. Lower emissivity means less emitted power at the same temperature, so the equilibrium temperature must be higher to balance the absorbed energy.

5) Can I estimate flux from star properties?

Yes. Use luminosity and distance, or use star temperature and radius with distance. Both methods compute the same flux at the target location.

6) Is the greenhouse offset physically exact?

No. It is a simple add-on for quick comparisons. Real greenhouse warming depends on atmospheric composition, pressure, clouds, and vertical temperature structure.

7) Why do results differ from published surface temperatures?

Published surface temperatures include greenhouse effects, internal heat, seasons, and circulation. Equilibrium temperature is only the radiative baseline from stellar input.