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Illumination Calculator (Lux)

Light spreads out, so illuminance falls with the square of distance. If the surface is tilted away from the source, it also intercepts less light — the cosine law. Together they cover most lighting design questions.

Illumination — E = I·cosθ/d²

Illuminance (lux) on a surface from a point source of luminous intensity I (candela). θ is the angle from the surface normal; at θ = 0 this is the inverse-square law.

Illuminance E
If surface faces the source (θ=0)
  1. 1.Given: I = 100 cd, d = 2 m, θ = 0° (from the normal)
  2. 2.FormulaE = I · cos θ / d²SubstituteE = 100 × cos 0° ÷ 2²ResultE = 25 lux
Common trap: Doubling the distance quarters the illuminance (inverse-square), and tilting the surface away from the light cuts it by cos θ (Lambert's cosine law). Both effects are why a desk lamp must be close and aimed square-on to actually light the page.

The formula

E = I / d² ; tilted surface: E = (I / d²) × cos θ

E
illuminance on the surface (lux)
I
luminous intensity of the source (candela)
d
distance from source to surface (metres)
θ
angle between the light and the surface normal

Worked example

A 1200 cd lamp 2 m above a bench, and the same lamp lighting a surface tilted 30°.

  1. Directly below: E = 1200 / 2² = 1200 / 4 = 300 lux
  2. Tilted 30°: E = 300 × cos 30° = 300 × 0.866

300 lux head-on, dropping to 260 lux on the tilted surface.

Where you'll use it

Illumination engineering questions and practical lighting layout. The inverse square is brutal: doubling the mounting height quarters the light on the floor, which is why high bays need far more powerful lamps.

The laws behind it

Parts this applies to

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