Light Intensity (Inverse Square Law) Calculator

The inverse square law of light states that the intensity of light (and other forms of radiation) decreases proportionally to the square of the distance from the source.

The formula:

I₂ = I₁ × (d₁ / d₂)²

Where:

• I₁ = intensity at original distance d₁
• I₂ = intensity at new distance d₂
• d₁ = original distance from source
• d₂ = new distance from source

Why the inverse square relationship?

As light radiates outward from a point source, it spreads over an ever-increasing spherical surface. The surface area of a sphere is 4πr², so as distance doubles, the area covered quadruples, meaning the intensity at any single point decreases to ¼.

Practical examples:

Double the distance: Intensity drops to 1/4 (25%)
Triple the distance: Intensity drops to 1/9 (~11%)
Half the distance: Intensity increases to 4× (400%)

Photography (the Exposure Effect):

In portrait photography, moving a studio light from 1m to 2m away cuts the light intensity by 75%. This is why portrait photographers must significantly increase power or use a wider aperture when backing the light away.

Lighting design:

When planning office or home lighting, understanding the inverse square law helps calculate how many fixtures are needed and at what heights. A light 2m above a desk illuminates with ¼ the intensity of the same light at 1m.

Units of light intensity:

• Lux (lx): SI unit of illuminance, lumens per square meter. Common reference: 500 lux for office work, 10,000 to 25,000 lux in open shade on a clear day, and around 100,000 in direct sun.
• Foot-candle (fc): US equivalent, 1 fc = 10.764 lux
• Candela (cd): Luminous intensity of a source in a given direction
• Lumens (lm): Total light output of a source

Important: The inverse square law applies to point sources in free space. Real-world lights with reflectors, diffusers, or walls modify this relationship.
A working rule from photometry: treat a light as a point once you are at least five times its largest dimension away. A 60 cm softbox behaves by the law from about 3 m out; at 1 m the light falls off more slowly than the formula says.