Solar Flux at Distance Calculator

Solar flux (irradiance) is the power per unit area received from the Sun at a given distance.

Formula:

F = L☉ / (4πd²)

Where:

• L☉ = solar luminosity = 3.828 × 10²⁶ W
• d = distance from the Sun (meters)
• F = irradiance (W/m²)

The inverse-square law:

Because light spreads out spherically, doubling the distance reduces flux by a factor of 4.
This is why Mercury gets about 15 times more flux than Mars despite being only 4 times closer: flux scales with the square of distance.

Simplified formula:

F = 1361 W/m² × (1 AU / d)²

where the solar constant (1,361 W/m² at 1 AU) is measured above Earth’s atmosphere.

Solar flux at each planet:

The solar constant is not quite constant, even for Earth. The orbit is slightly elliptical, so the figure swings from about 1,408 W/m² at perihelion in early January to about 1,317 at aphelion in early July. That is a 7% swing, and it barely registers in the weather, because the seasons come from the tilt of the axis rather than the distance. The Sun itself varies by only about 0.1% over the 11-year sunspot cycle.

Equilibrium temperature:

A body at distance d with albedo A reaches an equilibrium temperature:

T_eq = (F(1-A)/(4σ))^(1/4)

where σ = 5.67 × 10⁻⁸ W/m²/K⁴ (Stefan-Boltzmann constant).

The calculator uses an albedo of 0.3 for every distance, which is Earth’s. Put Earth in and it answers about 255 K, roughly −18 °C. The real average surface temperature is near 288 K, and that 33-degree gap is the greenhouse effect, which this formula knows nothing about.
Venus shows how far off the gap can get. At an albedo of 0.3 it comes out near 300 K, and with its real albedo of about 0.76 nearer 230 K. The surface is around 735 K.