Apparent Brightness Calculator
Enter a luminosity and a distance to get the apparent brightness in watts per square metre — and see how the inverse-square law dims a source with distance.
Flux from luminosity and distance
Enter the luminosity in watts and the distance in metres and the calculator returns the apparent brightness (radiant flux) in watts per square metre.
Use SI units
Watts for luminosity and metres for distance give the flux in W/m² — convert light-years or parsecs to metres before you start.
What is apparent brightness?
The radiant flux reaching you
The apparent brightness calculator turns a source's luminosity and your distance from it into the power that actually reaches you per square metre. Apparent brightness — also called the radiant flux — is what an observer measures, and it depends on two things: how much power the source radiates in total and how far away it is. A luminous but distant star can look fainter than a dim nearby one. The light spreads out over the surface of an expanding sphere, so the same power is shared across an ever-larger area, and the brightness you receive falls off with the square of distance. The result comes back in watts per square metre, the same unit used for the solar constant.
Enter a luminosity in watts and a distance in metres to get the apparent brightness in watts per square metre instantly.
Apparent brightness is the luminosity divided by the surface area of a sphere whose radius is the distance to the source.
b = L / (4π × d²)The distance is squared in the denominator, so it dominates: move twice as far away and the apparent brightness drops to a quarter. Suppose the source is the Sun, with a luminosity of 3.828×10²⁶ W, observed from one astronomical unit, 1.496×10¹¹ m. Squaring the distance gives 2.238×10²² m², multiplying by 4π gives a sphere area of about 2.812×10²³ m², and dividing the luminosity by that area yields roughly 1361 W/m² — the solar constant that defines how much sunlight reaches the top of Earth's atmosphere.
The formula is exact for an ideal point source, but a few practical points are worth keeping in mind.
Point sources, no absorption, consistent units
This calculator assumes a point source radiating equally in all directions into empty space. It does not account for interstellar dust or atmosphere that absorbs and scatters light, so real measurements of distant stars are often fainter than the geometry alone predicts. It also gives the total radiant flux, not the brightness in a single colour band. Keep your units consistent — watts for luminosity and metres for distance — or the W/m² will be wrong: convert parsecs or light-years to metres before you enter the distance.