Home · Published 2026-08-12
The Inverse Square Law of Light, Explained
Why illuminance from a point-like source falls with distance, how to calculate the change, and where real luminaires depart from the simple rule.
7 min read
ICBy Imogen ClarkeEditorial contributor
TL;DR
What Is the Inverse Square Law?
The inverse square law describes how light from an ideal point source spreads over an area that grows with the square of the distance. As the same flux is distributed over a larger area, illuminance falls in proportion to one divided by distance squared. It is a relationship between distance and light per unit area, not a claim that the lamp itself emits fewer lumens.
The Formula
For two measurements on the same axis under comparable conditions, E₂ = E₁ × (d₁/d₂)², where E is illuminance and d is distance from the photometric centre. If a surface receives 800 lux at 0.5 m, the idealised prediction at 1 m is 800 × (0.5/1)² = 200 lux.
Doubling and Tripling Distance
At twice the distance, illuminance becomes one quarter of the reference value. At three times the distance, it becomes one ninth. At half the distance, the idealised value becomes four times as high. This non-linear change is why moving a task lamp a modest distance can change working illuminance much more than expected.
Why the Square Appears
Imagine light from a point spreading uniformly across an expanding sphere. The sphere's area is 4πr², so doubling its radius creates four times the area and tripling it creates nine times the area. The available light per unit area therefore falls by those same factors.
The Photometric Form
For a point source and a surface perpendicular to the ray, illuminance can be related to luminous intensity by E = I/d². When the receiving surface is tilted, the cosine of the incidence angle also matters. Luminous intensity in candela is directional, so the relevant value must correspond to the direction being evaluated.
When the Simple Rule Works Best
The model is most useful when the source is small compared with the measurement distance, the detector is in the far field, the direction and angle remain fixed, and stray light and reflections are controlled. Photometric laboratories determine a limiting distance beyond which deviation from point-source behaviour becomes acceptably small for the source being measured.
Why Real Rooms Differ
A large panel, linear strip, close diffuser, or complex luminaire is not a point source at short distances. Lenses and reflectors redistribute intensity, while walls and ceilings return light to the measurement plane. Daylight and other lamps add background illuminance. For these reasons, a phone meter in a furnished room should not be expected to reproduce an ideal curve exactly.
A Safe, Useful Demonstration
Use a cool-running LED source, a fixed target, and the same meter orientation in a darkened room. Record distance from a consistent reference point and subtract or at least note background light. Compare readings at one, two, and three units of distance. Do not touch hot lamps, stare into intense sources, or improvise around exposed electrical parts.
What the Law Does Not Tell You
The inverse square law does not tell you total lumens, colour quality, glare, visual comfort, beam uniformity, or whether a lighting layout complies with a standard. It predicts one distance relationship under stated assumptions. Real project decisions should use manufacturer photometric data or measurements and, where safety or compliance matters, competent lighting design.
Sources
- 1
- 2Realization of the candela
National Institute of Standards and Technology
- 3Measurement Services: Photometric Calibrations
National Institute of Standards and Technology
- 4International Lighting Vocabulary: Illuminance
International Commission on Illumination