Inverse Square Brightness Calculator Formula

Understand the math behind the inverse square brightness calculator. Each variable explained with a worked example.

Use the Inverse Square Brightness Calculator

Formulas Used

Brightness Ratio (F2/F1)

brightness_ratio = pow(distance1 / distance2, 2)

Magnitude Difference

magnitude_diff = 5 * log10(distance2 / distance1)

Variables

VariableDescriptionDefault
distance1Distance 1(any)1
distance2Distance 2(any)2

How It Works

Inverse Square Law

Brightness (flux) decreases with the square of the distance from the source.

F2 / F1 = (d1 / d2)²

In magnitudes: m2 - m1 = 5 log10(d2 / d1)

Doubling the distance reduces brightness to 25% and increases magnitude by 1.505.

Worked Example

Compare brightness at distances 1 and 2 (same units).

distance1 = 1distance2 = 2
  1. 01F2/F1 = (1/2)² = 0.25
  2. 02At twice the distance, brightness is 25%.
  3. 03Magnitude diff = 5 log10(2) = 5 × 0.301 = 1.505 mag fainter.

Ready to run the numbers?

Open Inverse Square Brightness Calculator