Inverse Square Law Calculator
How intensity falls with distance from a point source — light, sound, radiation, a radio signal or gravity — and the distance at which it reaches a level you choose.
Anything spreading evenly from a point covers a sphere whose area grows with the square of the radius, so the intensity per unit area falls with the square: double the distance, a quarter of the intensity.
How the inverse square law calculator works
Anything spreading evenly from a point covers a sphere whose area grows with the square of the radius, so the intensity per unit area falls with the square: double the distance, a quarter of the intensity. The same law governs illumination, radiation dose, sound pressure squared, and gravitational and electric force. The decibel row is 20 log₁₀ of the distance ratio.
Formula: I₂ = I₁ × (d₁ ÷ d₂)²; d = d₁ × √(I₁ ÷ I_target)
Worked examples
| Inputs | Intensity at the second distance | Note |
|---|---|---|
| 100 at 1 m → 5 m | 4 | 4 — a 25th |
| Halving the distance | 200 | 200 — four times |
| Sunlight at Mars (1.52 AU) | 589.0755 | 589 W/m² |
FAQFrequently asked questions
Why the square?
Because the surface of a sphere is 4πr². Whatever spreads evenly from a point is shared over that area, so each square meter gets a share that shrinks with r².
Does it apply to sound?
To sound intensity (power per area), yes — and sound pressure falls with plain distance, which is why the decibel drop is 6 dB per doubling either way. Indoors, reflections stop the fall-off within a few meters.
Does it apply to a beam or a long lamp?
Not exactly. A collimated laser hardly spreads, a long fluorescent tube falls off with distance rather than its square until you are far away, and a spotlight follows the law only within its beam.
How is this used in radiation safety?
Distance is the cheapest shield: stepping from 1 m to 3 m from a source cuts the dose rate to a ninth. Time, distance and shielding are the three rules.
Where these figures come from
- NIST — CODATA 2018 fundamental physical constants — G, g₀, R, c
- NIST Special Publication 811 — Guide for the use of the International System of Units — unit conversions
- The Engineering ToolBox — material properties — specific heats, expansion coefficients, densities
- National Institute of Standards and Technology — the US measurement authority
Last checked: September 2026. Constants are the CODATA 2018 values; formulas are the standard textbook forms.