Inverse Square Law Calculator

The inverse square law calculator will shed light on the propagation of radiating quantities and their peculiar relationship with distance.

Intensity at 4 m62.51,000 × (1/4)²

Intensity at 1 m1,000

Ratio0.0625×16× the distance squared

Change in decibels-12.041 dBintensity is a power quantity, so the factor is 10

Distance ratio4×

At 2× the reference distance25025% of the reference, and -6.02 dB down

At 3× the reference distance111.11111111.1111% of the reference, and -9.54 dB down

At 10× the reference distance101% of the reference, and -20 dB down

Distance for half the intensity1.414214 monly √2 further, not twice as far

The formula

I₂ = I₁ × (r₁ ÷ r₂)²

Geometry, not absorption

The inverse square law is not a property of light or sound or gravity — it is a property of three dimensional space. A point source spreads its output over a sphere, and a sphere's area grows as the square of its radius, so the same power crossing a larger surface gives a proportionally smaller intensity. Nothing is absorbed or lost.

The consequence that surprises people is how fast it bites close in and how slowly far out. Moving from one metre to two quarters the intensity; moving from ten metres to eleven changes it by under a fifth. In decibels the fall is a tidy 6 dB per doubling of distance.

Two caveats. It applies to point sources: a long fluorescent tube falls off closer to inversely with distance at short range, and a collimated beam barely falls off at all. And it describes geometric spreading only — real media also absorb, which adds an exponential decay on top and dominates over long paths.