Inverse-Square Law Light Falloff Calculator

Frequently Asked Questions

What is the inverse-square law for light?

Intensity falls with the square of distance: I₂ = I₁ × (d₁ ÷ d₂)². Double the distance and light drops to one quarter - a 2-stop loss.

How many stops is a distance change?

Stops = 2 × log₂(d₂ ÷ d₁). Moving a subject from 2 m to 4 m loses 2 stops; 2 m to 3 m loses ~1.2 stops.

Why does moving the light closer increase falloff?

Near the source, the relative distance change between near and far parts of a subject is larger, so close lighting falls off fast (dramatic) and distant lighting is flat (even).

How is this different from a flash guide number?

Guide number sets correct exposure at one distance; this shows how exposure changes between distances - useful for feathering light and posing groups.

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How This Calculator Works

Light from a point or small source spreads over a sphere, so its intensity falls off with the square of distance: I₂ = I₁ × (d₁ ÷ d₂)². Double the distance and only one−quarter of the light remains - a two−stop loss, because stops of falloff = 2 × log₂(d₂ ÷ d₁). The tool also inverts this: given a target change in stops it solves for the distance that produces it, d = d₁ × 2^(−stops ÷ 2). This is the law that governs how quickly a subject darkens as it moves away from a window, lamp, or studio strobe.

Worked Example

A flash meters at intensity 100 with the subject 1 m away. Move them to 2 m: I₂ = 100 × (1 ÷ 2)² = 25 - a quarter of the light, a 2−stop loss. Move to 4 m and only 1⁄16 (about 6) remains: 4 stops down. Working the other way, to lose exactly 1 stop from a 1 m start you place the subject at 1 × 2^(1⁄2) ≈ 1.41 m. This is why a backdrop two steps behind the model goes several stops darker without touching a single light.

Real-World Use

Portrait and product photographers use inverse−square to control contrast rather than fight it. Place a key light close and small movements of the subject cause dramatic falloff - great for moody, fast−darkening backgrounds. Place it far away and the light is comparatively even across a group, because the relative distance change between the front and back rows is small. It also explains group−photo exposure problems, why a subject near a window blows out while the room stays dark, and how to feather or distance a light to balance a set.

Common Mistakes

Applying it to the sun or distant sources. Inverse−square assumes a point source at human distances; sunlight is effectively collimated, so moving a few metres changes nothing.

Confusing this with a guide−number tool. Guide number sets flash power vs. aperture; this tool models how existing light falls off over distance - a different question.

Forgetting modifiers change the effective source. A large softbox up close behaves less like a point source, so real falloff is gentler than the pure formula near the light.

Measuring to the modifier face vs. the bulb. Use a consistent reference point for d₁ and d₂ or the stop math drifts.

Limitations & Related Tools

The model is exact only for an idealized point source in open space. Reflective rooms add bounced fill that flattens falloff; very large modifiers, walls, and bare reflectors all soften the curve near the source. It also ignores atmospheric absorption (irrelevant at studio distances, real over long throws) and the source's own beam shaping. Treat the numbers as the physics baseline, then meter to confirm. Pair this with a flash guide−number calculator for power÷aperture, and an exposure−triangle tool to convert the calculated stop change into shutter, aperture, or ISO adjustments.

Inverse-Square Law Light Falloff Calculator

Frequently Asked Questions

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