What is the inverse square law?

The inverse square law states that a physical quantity (intensity) is inversely proportional to the square of the distance from the source. If you double the distance, intensity drops to one-quarter. Formula: I₂ = I₁ × (d₁/d₂)².

Does the inverse square law apply to sound?

Yes, for sound in a free field (no reflections). Every time you double the distance from a point source, sound intensity drops by 6 dB (factor of 4 in intensity). Rooms with reflective surfaces reduce this drop.

What units should I use?

The law is unit-agnostic for intensity ratios. Use any consistent unit for distance (meters, feet, etc.) and any power-per-area unit for intensity (lux, W/m², mR/hr). Just keep units consistent between I₁ and I₂, and between d₁ and d₂.

Why does intensity decrease with distance squared rather than linearly?

Because energy spreads over the surface area of an expanding sphere. Surface area grows as 4πr², so a fixed total power is spread over a larger and larger area as distance increases.

What if I get a negative or zero result?

All inputs must be positive numbers greater than zero. A distance of zero would imply infinite intensity, which is physically meaningless. The calculator rejects zero or negative values.

Inverse Square Law Calculator

Calculate how light, sound, or radiation intensity changes with distance. Enter any three values to solve for the fourth.

Solve For

Select the unknown variable, then fill in the other three.

I₂ = I₁ × (d₁ / d₂)²

Source Intensity (I₁)

Source Distance (d₁)

Target Distance (d₂)

Intensity at d₂ (I₂)

lux

Result

Fill in the fields and click Calculate.

Intensity vs Distance

How intensity changes at multiples of d₁ (shown when I₁ and d₁ are known).

Provide I₁ and d₁ to see the table.

Distance	Intensity	Ratio

Formula Reference

I₂ = I₁ × (d₁/d₂)²

I₁ = I₂ × (d₂/d₁)²

d₁ = d₂ × √(I₂/I₁)

d₂ = d₁ × √(I₁/I₂)

All distances and intensities must be positive and non-zero.

Summary

Calculate how light, sound, or radiation intensity changes with distance. Enter any three values to solve for the fourth.

How it works

Select which variable you want to solve for (I₂, I₁, d₁, or d₂).
Choose your distance and intensity units from the dropdown selectors.
Enter the known values in the three active input fields.
Click Calculate or press Enter to view the solved variable, step-by-step derivation, and distance table.

Use cases

Estimate light intensity at different distances from a lamp or LED.
Estimate sound intensity drop (W/m²) as distance from a point source increases.
Determine radiation dose rate at a safe distance from a radioactive source.
Plan stage lighting rigs to hit target lux levels at the audience.
Verify camera exposure settings across different flash-to-subject distances.
Solve physics homework problems involving inverse square relationships.

Frequently Asked Questions

Last updated: 2026-09-22 · Reviewed by Nham Vu