Stellar flux at planet calculator

Enter the star's total luminosity in watts and the star-to-planet distance in metres. The calculator applies the inverse-square law and returns flux in watts per square metre. It is useful for comparing planetary irradiation, checking astronomy exercises, preparing simple climate estimates, and supplying a reproducible value to simulations or data pipelines without manually rearranging the equation.

Enter luminosity and orbital distance in SI units

Start with the star's bolometric luminosity, meaning the total radiant power emitted across all wavelengths, expressed in watts. Then provide the separation between the star and planet in metres. The separation should represent the distance for the instant or orbital position you want to study. For a nearly circular orbit, a representative orbital radius is often sufficient. For an eccentric orbit, calculate periapsis, apoapsis, or several points separately because the received flux changes continuously with distance. Do not enter an orbital period, a distance in astronomical units, or luminosity in solar luminosities unless you convert those values first. This capability deliberately uses explicit SI inputs so its output is unambiguous: watts divided by square metres. Luminosity may be zero, which produces zero flux, but it cannot be negative. Orbital distance must be greater than zero. A zero or negative separation has no physical meaning here and would make the inverse-square expression invalid, so the calculator returns an input error instead of an infinite or misleading result.

Understand the inverse-square calculation

The calculation uses F = L/(4πr²), where F is stellar flux, L is stellar luminosity, and r is orbital distance. Imagine the star's emitted power spreading uniformly over an ever-growing sphere. At radius r, that sphere has area 4πr², so dividing total power by the area gives power received per unit area. Doubling the distance makes the sphere four times larger and reduces the flux to one quarter. Tripling the distance reduces it to one ninth. The returned value is therefore an irradiance in watts per square metre, not the planet's total absorbed power and not its equilibrium temperature. The model assumes isotropic emission and uses the supplied distance directly. It does not account for stellar variability, directional emission, intervening dust, atmospheric transmission, planetary albedo, surface angle, eclipses, or heat redistribution. Those effects belong in later calculations. This result is best understood as the incident stellar power density at the orbital location before the planet modifies or redistributes that energy.

Use the result carefully in planetary studies

The flux result is a clean starting point for comparisons and downstream models. You can compare two planets around one star, examine how a changing orbit affects irradiation, or calculate the forcing associated with stars of different luminosities. If you need the total power intercepted by a planet, multiply this flux by the planet's cross-sectional area, πR², rather than its entire surface area. If you need globally averaged incident flux for a simple energy-balance model, a common next step is to divide by four, then apply the absorbed fraction using one minus the Bond albedo. Those operations are intentionally outside this capability so the stellar and planetary assumptions remain separate and auditable. Keep enough significant figures in the inputs for your purpose, but remember that an approximate luminosity or orbital distance limits the accuracy of the result. For automated work, the API returns both normalized inputs, the computed flux, its unit, and the formula. Each request costs $0.002, while the browser calculation can be used for quick interactive checks.