Inverse Square Law Calculator (Light Intensity)
Written by Thierno Sadou Diallo, formula verified per our methodology • Last checked on 9/9/2026
The inverse square law gives the intensity received at a distance r from a point source radiating uniformly in all directions: I = P ÷ (4πr²), where P is the total power radiated by the source. A 100 W source produces, at a distance of 2 m, an intensity of about 1.99 W/m².
Explanation
This law applies to any point source that radiates energy uniformly in all directions — a light bulb, a star, an omnidirectional radio antenna, or a sound source. It expresses a purely geometric principle: at a distance r, all the power emitted by the source spreads over the surface of an imaginary sphere of radius r, whose area is 4πr²; the larger this sphere, the more the same total energy is diluted over a larger surface, hence this 1/r² decrease. This same spherical geometry also explains why our Coulomb's law calculator and our gravitational force calculator both follow a 1/r² law: the three phenomena, although physically very different (electromagnetic radiation, electric field, gravitation), share this same geometric origin of dilution over a growing spherical surface. A well-known practical consequence of this law: doubling the distance to a light source doesn't halve its perceived intensity, but divides it by four — which is why a star twice as far as another, at equal intrinsic brightness, appears four times dimmer from Earth.
Example: a 100 W source, at a distance of 2 m
Inputs
Radiated power: 100 W. Distance: 2 m.
Calculation
I = 100 ÷ (4 × π × 2²) = 100 ÷ (4π × 4) = 100 ÷ 50.265 ≈ 1.9894 W/m².
Result
At 2 m from this source, the received intensity is about 1.99 W/m².
Frequently asked questions
Why does doubling the distance divide intensity by four, not by two?
Because the area of the sphere over which the energy spreads grows with the square of the radius, not proportionally to it: doubling the radius multiplies the sphere's area by four (2² = 4), so the same total power is diluted over a surface four times larger, and the intensity received at each point drops by a factor of four.
Does this law apply to all light sources?
It applies precisely to point sources radiating uniformly in all directions (or at a distance large enough that a finite-size source can be approximated as a point, like a distant star). A directional source like a laser or a focused spotlight, which only radiates in a specific direction, doesn't follow this same decay law.
Does this formula also apply to sound or other forms of radiation?
Yes, the same geometric principle applies to any form of energy that propagates uniformly from a point source in three-dimensional space: sound (sound intensity also decreases as 1/r² in free field), radio waves, or any other electromagnetic radiation emitted omnidirectionally.