The inverse square law says that light from a small source gets weaker with the square of the distance it travels. Move a light twice as far from your subject and only a quarter of the light arrives, two stops less. It matters because it is the reason a flash that is perfect at one distance is useless at another, the reason a lamp close to a face makes one cheek glow and the other fall into shadow, and the reason a background goes dark or stays bright depending on where you put the light.
Every artificial light you will use follows it: a flash, a studio strobe, an LED panel, a desk lamp, a candle, the torch on your phone. Once you can do the arithmetic in your head, you stop guessing where lights go.
Why light thins out with distance
A small light sends its output outward in every direction it points. The farther that light travels, the larger the area it has to cover. At 1 meter, a beam might cover one square. By 2 meters the same beam has spread twice as wide and twice as tall, so it covers four squares, and each square gets a quarter of the light. At 3 meters it covers nine squares, and each gets a ninth.
Written as a formula, the light arriving is proportional to 1 divided by the distance squared. You never need the formula on a shoot. What you need is what it means in stops, the unit your camera works in: a stop is a doubling or halving of light (see what a stop is if that word is new). Doubling the distance quarters the light, and a quarter is two halvings, so two stops. Tripling it leaves a ninth, which is about 3.2 stops.
Light is not being used up or absorbed on the way, at least not over the few meters a photographer works in. It is the same light, spread thinner. The science of light page covers the rest of how light behaves on its way to the camera.
The distance ladder: every 1.4 times farther costs one stop
If doubling the distance costs two stops, what costs one stop? Half the light needs the distance multiplied by the square root of 2, about 1.4. That gives a ladder you can climb in your head: 1, 1.4, 2, 2.8, 4, 5.6, 8 meters. Each rung is one stop less light than the one before. Those are the same numbers as the f-number scale, and that is not a coincidence: an aperture’s light-gathering area also goes with the square of its diameter. If you already know the f-stop sequence, you already know how distance works.
A worked example. A flash sits 1 meter from a subject at a fixed power and gives a good exposure at f/8. Move it to 2 meters and it delivers a quarter of the light, so you need f/4, or four times the flash power to stay at f/8. Move it to 4 meters and you are four stops down from the start, a sixteenth of the light, and you need f/2. Flash power settings run in stops too (full, 1/2, 1/4, 1/8), so one step on the power dial does the same job as one rung on the ladder.
The flash guide number packs this into one multiplication: guide number equals distance times f-number. A flash with a guide number of 36 (meters, ISO 100) at full power needs f/18 at 2 meters, f/12 at 3 meters and f/8 at 4.5 meters. Each of those is the inverse square law at work, and the numbers only stay simple because of it.
Want the aperture for your own flash and distance without the arithmetic? The flash guide number calculator works it out from guide number, ISO and distance.
It is the ratio, not the meters
The most useful thing to understand about this law is that what counts is how much the distance changes as a share of the distance, not by how many centimeters. Going from 1 meter to 1.1 meters costs exactly as much light as going from 10 meters to 11 meters: about 0.28 of a stop. Both are 10 percent farther.
That is why a light close to a subject is so touchy. Here is what a 10 centimeter move costs at different distances:
| Light to subject | Move 10 cm farther | Light lost |
|---|---|---|
| 0.5 m | 0.5 m to 0.6 m | 0.53 stop |
| 1 m | 1 m to 1.1 m | 0.28 stop |
| 2 m | 2 m to 2.1 m | 0.14 stop |
| 4 m | 4 m to 4.1 m | 0.07 stop |
With a light half a meter from a face, your subject leaning forward a hand’s width changes the exposure by half a stop. With the light 4 meters away, the same lean is invisible. The same idea explains group photos: with a light 3 meters from the front row and 4 meters from the back row, the back row is 0.83 stop darker. Pull the light back to 6 meters from the front row, 7 from the back, and the difference shrinks to 0.44 stop, because one meter is now a smaller share of the distance.
Falloff across a face or a body
The ratio rule works inside a single subject too. A head is roughly 20 centimeters across. With a light directly to one side, the far cheek is 20 centimeters farther from the light than the near cheek, and what that difference does depends on how far away the light is:
| Light to middle of head | Far side darker by | Far side gets |
|---|---|---|
| 0.5 m | 1.2 stops | 44% of the near side’s light |
| 1 m | 0.6 stop | 67% |
| 2 m | 0.3 stop | 82% |
| 4 m | 0.14 stop | 90% |
This is distance falloff alone, before any shadow from the nose or the turn of the cheek away from the light, which add more. Close light gives a face shape and drama because the brightness changes quickly across it. Far light gives even, flatter light. Moving a softbox closer also makes it larger relative to the face, so the light gets softer at the same time as the falloff gets steeper; hard light and soft light covers that other half of the story. Turning the light so the subject sits at the edge of its beam rather than the center, called feathering, is another way to even out a close light.
Want the shadow side of the face a set amount darker on purpose? Lighting ratios show how to measure and choose the difference between the key side and the fill side.
Subject and background: how distance decides the backdrop
The biggest practical use of the law is controlling the background. Put a light close to your subject and a wall some way behind, and the wall gets much less light than the subject because it is many times farther from the light. Put the light far away, and subject and wall are at nearly the same distance from it, so they come out nearly the same brightness. With light, subject and wall roughly in a line:
| Light to subject | Subject to wall | Wall darker than subject by |
|---|---|---|
| 1 m | 0.3 m | 0.8 stop |
| 1 m | 1 m | 2 stops |
| 1 m | 2 m | 3.2 stops |
| 1 m | 3 m | 4 stops |
| 0.5 m | 2 m | 4.6 stops |
| 3 m | 1 m | 0.8 stop |
| 3 m | 3 m | 2 stops |
Two settings stand out. Light close and wall far gives a near-black background from an ordinary room, which is how low-key portraits are often made without a black backdrop (high key and low key covers the look). Light far and wall close gives a bright, even background, the start of a white background. Notice also that the second and last rows give the same answer, 2 stops, with very different setups: in both, the wall is twice as far from the light as the subject. The ratio of the two distances is what matters, not the meters.
Drag the light and the wall here and watch the law work: the face stays correctly exposed while the wall goes darker the closer the light gets to the subject.
Flash on the camera at night is the extreme case. The flash lights whatever is nearest and almost nothing beyond it, so a subject at a few meters is bright and a street behind goes black. Weegee built a whole style on that: his single flash isolated people from the dark city behind them. When you want the background lit after all, you give it its own light (see hair light and background light) or you let a slower shutter collect the ambient light.
Background going black every time you use flash indoors? Balancing flash and ambient light explains why the room light does not follow the flash’s distance, and how to bring it back with a slower shutter.
Bounce flash: the distance counts twice
When you point a flash at the ceiling, the light travels up to the ceiling, and the patch of ceiling it lights then becomes a new, larger and dimmer light that shines down on your subject. Both legs of that trip lose light by distance, and for a rough estimate you can treat the whole path as the distance. If the direct path to your subject would be 2.5 meters and the bounced path is about 5 meters, distance alone costs two stops, and the ceiling scatters light in every direction and soaks some of it up, so the real loss is more than that. That is why bounce flash runs a flash at high power to match what direct flash does at a fraction of it, and why a high or dark ceiling can leave you short of light altogether.
Where the law bends
The law is exact for a point of light. Real lights are not points, and three cases matter.
Large sources, close up
A big softbox or a window is a wide surface, not a point. When the subject is close to it, light arrives from many parts of that surface at once, at different distances, and the brightness falls off more gently than the law predicts. Picture an evenly glowing round panel 1 meter across. Moving the subject from 0.25 to 0.5 meters away costs about 0.7 stop, not 2. From 0.5 to 1 meter, about 1.3 stops. From 1 to 2 meters, 1.8 stops. From 2 to 4 meters, 1.9. Past about five times the source’s width, the panel behaves like a point and the plain law holds to within about a hundredth of a stop. Real softboxes are a little brighter in the middle than at the edges, so treat these as a guide, not a measurement.
Window light follows the same pattern. Right at a large window the light is soft and fairly even. Walk a few meters into the room and the window starts to behave like a smaller source, and brightness falls away quickly, which is why window light portraits work best with the subject close to the glass.
The sun
The sun is so far away that a few meters, or a few kilometers, make no measurable difference to how much of its light arrives. A rock at your feet and a mountain on the horizon get the same sunlight. Outdoors in sun, distance from the light is not a control you have; direction, cloud and shade are. A flash used outdoors still obeys the law, which is why fill flash has a short reach in daylight and works best within a few meters.
Many lights at once
Each source obeys the law on its own, but several of them overlapping fill each other’s falloff. Street and parking lot lights are spaced so that wherever one fades, the next takes over.
Moving the camera does not change the exposure
A common mix-up is to think the law applies to the camera’s distance from the subject. It does not. Walk toward a lit subject and the subject’s light reaching your lens does fall with distance, but the subject also fills more of the frame by the same amount, so each part of the image gets just as much light as before. The correct exposure for a lit face is the same from 2 meters or 20. Only moving the light changes how bright the subject is.
This is why a flash on the camera seems to break the rule: when you step back with a flash on the hotshoe, you are moving the light, not just the camera. It is also why an incident light meter is held at the subject, pointed at the light: it measures the light arriving where it counts, at whatever distance the light happens to be.
Ready to take the flash off the camera so you can choose its distance yourself? Off-camera flash covers the triggers, stands and first setups.
Common mistakes with the inverse square law
- Expecting double the distance to halve the light. It quarters it. Two stops, not one. One stop needs the distance multiplied by 1.4.
- Thinking in meters instead of ratios. A 30 centimeter move matters a lot with the light at 0.5 meters and almost nothing at 5 meters. Think in percentages of the distance.
- Rounding a tripled distance to 3 or 4 stops. One ninth is about 3.2 stops. Close enough on a shoot, but know where the number comes from.
- Applying it to sunlight. The sun is effectively at infinite distance. Moving closer to a sunlit scene changes nothing about its brightness.
- Applying it to the camera. Moving the camera closer or farther does not change the exposure of a lit subject. Moving the light does.
- Using the point-source numbers for a big softbox at arm’s length. Close to a large source, falloff is gentler than the law predicts. The plain numbers return once the subject is several source widths away.
- Pushing the subject against the backdrop. With a light near the subject, a few meters of gap between subject and backdrop is what makes the background go darker. Against the wall, both get the same light.
Try this: watch two stops disappear
You need a single small light (a bare bulb, a desk lamp with its shade off, a flash on manual power, or a phone torch), a dark room, a tape measure, and a camera or phone you can set to manual exposure. It takes about ten minutes.
- Put a plain object, a mug or a cushion, on a table with a wall about 2 meters behind it. Turn off every other light.
- Place the light 1 meter from the object, level with it. Set the camera to manual, find an exposure where the object looks right, and take a frame. Write the settings down.
- Without touching the camera, move the light to 1.4 meters and take another frame, then 2 meters, then 2.8 meters.
- Now fix the exposure. At 2 meters, open the aperture two stops or slow the shutter two stops from your 1 meter settings and shoot again. It should match the first frame.
- Finally, put the light back at 0.5 meters from the object and take one more frame at an exposure that suits the object. Look at the wall.
How to judge it: in the first set, each frame should look about one stop darker than the one before (check the histogram if your camera shows one; it should shift left by about the same amount each time). The corrected 2 meter frame should match the 1 meter frame. In the last frame the wall should be far darker than in the 1 meter frame, even though the object looks the same, because the wall is now about five times as far from the light as the object.
Frequently asked questions
Why does doubling the distance cost two stops and not one?
Because the light spreads in two directions at once, wider and taller. Twice as far, it covers twice the width and twice the height, four times the area, so each part gets a quarter of the light. A quarter is two halvings, which is two stops.
Does the inverse square law apply to LED panels and continuous lights?
Yes. It applies to any light, whatever makes it, as long as the light is small compared with its distance from the subject. A small LED panel at 2 meters follows it closely. A large panel very close to the subject falls off more gently, the same way a big softbox does.
How far back should I put a light to light a group evenly?
Far enough that the depth of the group is a small share of the distance. With the front row 3 meters from the light and the back row 4 meters, the back row is about 0.8 stop darker. At 6 and 7 meters the gap is under half a stop. Raising the light so it shines down across the group also helps.
Does a bigger softbox fall off more slowly?
Only when it is close, within a few of its own widths of the subject. Beyond that, a big softbox and a small one at the same distance lose light with distance at the same rate. Size mainly changes how soft the shadows are, not how quickly the light drops away.
Why is my background black when I use flash indoors?
Your subject is probably much closer to the flash than the background is, so the background gets a small fraction of the flash’s light, and the shutter speed is too fast to record the dimmer room light. Move the subject closer to the background, bounce the flash, or slow the shutter to let the ambient light in.
Want to check how well the distance rules have stuck? The flash and ambient balance quiz asks about the inverse square law alongside flash compensation and the two exposures in every flash frame.
For where distance fits among all the other choices in lighting, from direction to the color of the light, see the photography lighting guide, and for flash itself from first principles, flash photography.