Inverse Square Brightness Calculator Formula
Understand the math behind the inverse square brightness calculator. Each variable explained with a worked example.
Formulas Used
Brightness Ratio (F2/F1)
brightness_ratio = pow(distance1 / distance2, 2)Magnitude Difference
magnitude_diff = 5 * log10(distance2 / distance1)Variables
| Variable | Description | Default |
|---|---|---|
distance1 | Distance 1(any) | 1 |
distance2 | Distance 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).
- 01F2/F1 = (1/2)² = 0.25
- 02At twice the distance, brightness is 25%.
- 03Magnitude diff = 5 log10(2) = 5 × 0.301 = 1.505 mag fainter.
Frequently Asked Questions
Why does the inverse square law work?
Light spreads uniformly over a sphere. The sphere's area grows as 4πr², so intensity per unit area decreases as 1/r².
Does this apply to all radiation?
Yes, for any point source of radiation in a vacuum, including light, radio, X-rays, and gravitational radiation.
How far away does a star need to be for its light to be negligible?
It depends on the star's luminosity and your detector sensitivity. The Sun would be invisible to the naked eye beyond about 20 parsecs.
Ready to run the numbers?
Open Inverse Square Brightness Calculator