Planetary Temperature Calculator
Estimate a planet's equilibrium temperature based on its host star's temperature, radius, and the planet's orbital distance. Useful for assessing whether exoplanets might fall within a habitable zone.
About this calculator
A planet's equilibrium temperature is the surface temperature it would reach if it absorbed and re-radiated all incoming stellar energy, assuming no greenhouse effect and a bond albedo of zero. The formula is derived from balancing the stellar flux intercepted by the planet with the thermal radiation it emits as a black body: T_planet = T_star × √(R_star / (2 × d)), where T_star is the stellar effective temperature in Kelvin, R_star is the stellar radius in meters, and d is the orbital distance in meters. In this calculator, stellar radius is entered in solar radii (R☉; 1 R☉ = 695,700 km) and orbital distance in AU (1 AU = 1.496×10⁸ km). This formula assumes the planet is a perfect black body; real planets are warmer due to greenhouse gases and cooler in reflective regions depending on their albedo.
How to use
Let's estimate Earth's equilibrium temperature. Enter the Sun's temperature (5778 K), radius (1 R☉), and Earth's orbital distance (1 AU). The calculator computes: R_star in km = 1 × 695,700 = 695,700 km. d in km = 1 × 1.496×10⁸ = 1.496×10⁸ km. T = 5778 × √(695,700 / (2 × 1.496×10⁸)) = 5778 × √(0.002324) = 5778 × 0.04820 ≈ 278.5 K (about 5.4°C). Earth's actual average surface temperature is ~288 K; the ~10 K difference is due to the greenhouse effect and Earth's albedo, confirming the formula gives a physically sensible baseline estimate.
Frequently asked questions
What does planetary equilibrium temperature tell us about whether a planet is habitable?
Equilibrium temperature provides a first-order estimate of how warm a planet would be based solely on stellar energy input, serving as a baseline before atmospheric effects are considered. For liquid water to exist on the surface — a key requirement for life as we know it — a planet's equilibrium temperature should roughly fall between about 200 K and 320 K, depending on its atmospheric properties. The habitable zone is typically defined as the range of orbital distances where this condition is plausible. However, equilibrium temperature ignores albedo, greenhouse gases, and internal heating from radioactive decay or tidal forces, all of which can shift a planet's actual surface temperature substantially above or below the equilibrium value.
Why does the equilibrium temperature formula ignore the greenhouse effect?
The equilibrium temperature formula assumes the planet behaves as a perfect black body — absorbing all incoming radiation and re-emitting it uniformly as thermal infrared radiation. This is the simplest physically meaningful baseline and requires no knowledge of the planet's atmosphere. Incorporating the greenhouse effect requires detailed modelling of atmospheric composition, pressure, and radiative transfer, which varies enormously between planets. For comparison, Earth's equilibrium temperature is about 255–278 K depending on albedo assumptions, but its actual surface temperature averages ~288 K due to greenhouse warming by water vapour, CO₂, and other gases. Venus has an even more dramatic discrepancy, with an equilibrium temperature near 230 K but a surface temperature of about 737 K.
How does orbital distance affect a planet's calculated equilibrium temperature?
Equilibrium temperature decreases with the square root of orbital distance, following the inverse-square law of stellar flux. If you double a planet's orbital distance from its star, the stellar flux it receives drops by a factor of four, and the equilibrium temperature drops by a factor of √2 ≈ 1.414. This means a planet at 4 AU receives only 1/16 the flux of one at 1 AU, and its equilibrium temperature is halved. For this reason, planets in the outer solar system are extremely cold — Jupiter's equilibrium temperature is around 110 K and Neptune's is near 47 K. Moving a planet closer to its star has the opposite effect, rapidly increasing temperature as the distance shrinks.