Exoplanet Equilibrium Temperature Calculator

Estimate a planet's equilibrium temperature from its star's effective temperature and radius, orbital distance, Bond albedo, and heat-redistribution assumption via T_eq = T★√(R★/2a)(1-A)^(1/4) — in K and °C, with absorbed flux, a star-planet diagram, and a temperature gauge comparing it to solar-system planets.

Equilibrium temperature calculator

The temperature where absorbed starlight exactly balances emitted thermal radiation — ignoring internal heat and any atmospheric greenhouse effect: T_eq = T★√(R★/2a)(1−A)^(1/4) for full day-night heat redistribution. Earth's result (≈255 K, −18°C) sits noticeably below its real ≈288 K surface temperature — that gap is entirely the greenhouse effect, which this idealized model deliberately omits.

Star's effective temperature (T★)

Stellar radius (R★)

Orbital distance (a)

Bond albedo (A) — optional

T_eq ≈ 254.6 K = -18.5 °C

Absorbed stellar flux: 1362.3 W/m² (Earth receives ≈1361 W/m²)

Star colored by its actual effective temperature (hotter = bluer, in the real astronomical sense); planet colored by equilibrium temperature (colder = bluer, in the everyday "heat map" sense) — two different, deliberately distinct color scales.

Top row: familiar physical reference points. Bottom row: solar-system planets' own equilibrium temperatures (computed the same way, with the Sun) — fixed regardless of whatever star is entered above, for comparison.

Before anyone can say a planet is “habitable” or a gas giant is “scorching,” there’s a baseline number every such claim implicitly compares against: the temperature a bare rock at that distance from that star would settle to, with no atmosphere doing anything clever at all. That’s the equilibrium temperature — simple to compute, and precisely useful because of everything it deliberately leaves out.

The formula

T_{\rm eq} = T_\star \sqrt{\frac{R_\star}{2a}}\,(1-A)^{1/4}

This balances absorbed stellar power against thermal emission spread evenly across the whole planet (day and night sides equalized before radiating) — the “full redistribution” case. Plug in the Sun, Earth’s 1 AU, and a Bond albedo of 0.30, and you get T_eq ≈ 255 K (−18°C) — the number this calculator opens with.

Where the greenhouse effect lives

Earth’s actual mean surface temperature is about 288 K — roughly 33 K warmer than the equilibrium estimate. That gap isn’t an error in the formula; it’s the entire point of computing T_eq in the first place. The equilibrium model accounts for exactly two things — starlight in, thermal radiation out — and nothing about how a real atmosphere traps outgoing infrared radiation before it escapes. Every degree of that 33 K gap is greenhouse warming, by definition: it’s whatever the simple energy-balance model doesn’t explain.

Mars is a useful contrast: its thin atmosphere traps very little heat, so its equilibrium estimate (≈210 K) and its real average temperature sit close together. Venus is the opposite extreme — a very high albedo (0.75, mostly cloud reflection) actually gives it a cooler equilibrium temperature than Earth’s (≈232 K), even though its real surface, smothered under a runaway CO₂ greenhouse, is a scorching ≈735 K. The size of the gap between T_eq and reality is itself a measurement of how much greenhouse effect (or lack of one) a planet’s atmosphere provides.

The heat-redistribution assumption

Two idealized cases bracket real planets:

Full redistribution — winds efficiently move heat from the permanent dayside to the nightside before it radiates away, so the whole sphere (4πR_p²) does the emitting. This is roughly right for planets with thick, actively circulating atmospheres.
No redistribution (dayside-only) — the planet re-radiates only from its permanently sunlit hemisphere (2πR_p²), giving a T_eq about 2^(1/4) ≈ 19% higher for the same absorbed flux. This is closer to reality for many hot Jupiters, which are often tidally locked with circulation too sluggish to fully even out their scorching daysides.

Reading the visuals

The star-planet diagram colors the star by its real effective temperature (hotter genuinely means bluer here, the correct astronomical direction) and the planet by its equilibrium temperature using the opposite, more intuitive “heat map” convention (colder means bluer) — two deliberately different color scales for two different things.
The temperature gauge places the current result on a scale next to familiar physical reference points (water freezing and boiling, lava) and, on a second row, every solar-system planet’s own equilibrium temperature — all computed the same way, with the Sun’s real numbers, so the comparison is apples to apples.