Inverse Square Law Calculator

Inverse Square Law

Many physical quantities spread outward from a point source and fall off with the square of distance. Light intensity, sound pressure, and gravitational field strength all follow this pattern in ideal conditions. This calculator solves for any one variable when the other three are known.

Formula

$$I_2 = I_1 \left(\frac{d_1}{d_2}\right)^2$$

$I_1$ and $I_2$ are intensities at distances $d_1$ and $d_2$. Doubling the distance quarters the intensity. Rearrange to solve for any unknown.

Practical Notes

The law assumes a point source in free space with no absorption or reflection. Real rooms, lenses, and extended sources modify the result. Still, inverse-square scaling is the baseline for exposure, illumination, and radiation safety estimates.

Related tools: Lighting Calculator and Exposure Calculator.

Frequently Asked Questions

What quantities follow the inverse square law?

Intensity of light, sound, and ionizing radiation from a point source, as well as gravitational and electric field magnitudes in simple geometries.

Why is the exponent 2?

Flux from a point source spreads over a spherical surface whose area grows as 4πr². Fixed total power divided by growing area gives 1/r² intensity.

Can I solve for distance?

Yes. Select the unknown you need. For distance, use d = d_other × √(I_other / I_known).

Do units matter for intensity?

Distances must share the same unit. Intensities must share the same unit, but the ratio is unitless so W/m², lux, or dB SPL offsets work if consistent.

When does the law fail?

Near extended sources, inside waveguides, or where absorption and scattering dominate, intensity may not fall as 1/r².

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