The law, and the two-stop shock
Illuminance from a point source falls with the square of distance. Double the distance and you have a quarter of the light. A quarter is two stops, not one, and that gap between intuition and arithmetic is the single most useful thing a lighting calculator can teach. In formula terms, the stops lost moving from d₁ to d₂ is 2 × log₂(d₂ ÷ d₁), and the fraction of the original light remaining is (d₁ ÷ d₂)².
The reason is geometric rather than optical: light spreads over a sphere, the surface area of a sphere goes as the radius squared, so the same photons cover four times the area at twice the distance. Nothing about the lamp changes. This is why a lamp turned to half power and a lamp moved back by 41 percent produce the same one-stop drop, and why the second option also changes how hard the shadows look while the first does not.
Falloff is steep near the light and gentle far away
The consequence people feel on set is not the total drop but its unevenness. Consider a light at two feet from a subject. A step back of one foot, to three feet, costs 1.2 stops. Now put the light at ten feet: the same one-foot step back costs about a quarter of a stop. Same movement, wildly different penalty.
| Light distance | Subject steps back 1 ft | Exposure change | Practical effect |
|---|---|---|---|
| 2 ft | to 3 ft | −1.2 stops | Unusable for anyone who moves |
| 4 ft | to 5 ft | −0.6 stops | Noticeable, needs marks on the floor |
| 8 ft | to 9 ft | −0.3 stops | Tolerable for a moving subject |
| 15 ft | to 16 ft | −0.2 stops | Effectively flat |
So close lighting buys soft, wrapping quality and costs you positional tolerance. Far lighting buys tolerance and costs softness, since a modifier that is broad at three feet is a small hard point at twenty. Two people side by side under one close light will not be equally exposed, and the fix is either backing the light off or accepting the falloff as a lighting choice.
Feathering: using the edge on purpose
Feathering means aiming the light past the subject so the subject is lit by the edge of the beam rather than its centre. It works because the intensity across a beam falls off gradually toward the edge, and because the effective distance from the bright core of the source increases as you rotate away. The result is a softer transition across the subject, less spill onto whatever is behind, and a gentler falloff across a group than pointing straight at them delivers.
It is worth understanding that feathering does not repeal inverse square. It changes which part of the source is doing the work and how the spread is distributed, and inverse square still governs the distance term. The two tools stack: feather the light to control the spread, position it to control the falloff.
Backgrounds and the cheapest separation there is
The separation between a subject and its background is often assumed to require a second light. It rarely does. If the subject is six feet from the light and the background is twelve, the background receives two stops less, because it is at double the distance and the same square law applies. Move the subject forward and the light closer, and that gap opens further at no cost.
Running the numbers before you set anything up is faster than moving stands and re-metering. Pair this with the exposure calculator to convert the stops into a shutter and aperture you can actually dial in, and with the depth of field calculator if the aperture you land on turns out to change what is sharp.
Questions people ask
Does inverse square apply to softboxes and umbrellas?
It applies once you are far enough away for the modifier to behave like a point, which is roughly beyond twice its own width. Closer than that, the subject is being lit by a broad surface and different parts of that surface are at different distances, so the falloff measured in practice is gentler than the square law predicts. This is exactly the regime where large modifiers used close are prized, and it is why a big source close to a subject can wrap without dropping off as hard as the arithmetic threatens. Enter the source width and the calculator flags which regime you are in.
Does the sun follow the same rule?
In principle yes, in practice no, because the distances involved make the change unmeasurable. Moving your subject ten feet changes the distance to the sun by an amount so far below rounding error that daylight behaves as perfectly even illumination. What does change outdoors is atmospheric conditions, the angle of incidence and whatever is bouncing light back in, and none of those are inverse-square effects. The rule matters for lamps, flashes and any local source, which is where you have control anyway.
Is it better to move the light or change its power?
They are not interchangeable, even when the exposure change is identical. Moving the light changes the apparent size of the source relative to the subject, which changes shadow hardness and how the light wraps; it also redistributes the falloff across the subject and the background. Changing power leaves all of that alone and only changes brightness. So set the position for the look you want, then adjust power for the exposure. Reaching for the dimmer first tends to lock in a position you chose for the wrong reason.
Why do two people side by side never look equally lit?
If they are at different distances from the light — and they are, unless the light sits exactly on the axis between them — the square law puts them at different exposures. With the light close, six inches of difference is visible. The standard fixes are to back the light off so the ratio flattens, to feather it so the nearer person catches the weaker edge of the beam, or to move to a light source large enough and near enough that the point-source approximation stops applying. Which one you choose is a look, not just a correction.
How do I check this against a meter instead of trusting the math?
Meter at the subject position, move the light or the subject to the second distance, and meter again. The stop difference the meter reports should land close to the calculated figure whenever the point-source assumption holds. Where it disagrees, the usual culprits are a large modifier used close, bounced light from walls and ceilings adding a floor that the square law knows nothing about, or a fixture with a focusing optic that reshapes the beam. All three are real and none of them make the calculation useless — they make it the starting estimate rather than the answer.