There is one piece of physics that decides more about how a stage looks than any purchasing decision, and it fits on the back of an envelope: illuminance falls with the square of distance.
Double the throw and you get a quarter of the light. Move a fixture one metre and the difference is visible on camera. This is why truss height, riser position and stage depth matter more than fixture choice — and why two identical rigs at two venues can look like different budgets.
In this guide
Light from a point source spreads out as a cone. Move twice as far away and the same quantity of light is now spread over four times the area, because area grows with the square of the radius. Each square metre of that area therefore receives a quarter of the light.
Written as a formula: E = I ÷ d², where E is illuminance in lux, I is luminous intensity in candela, and d is the distance in metres. It is exact for a point source in a vacuum and a very good approximation for a stage fixture at any distance beyond a couple of metres.
The practical percentages are worth memorising, because they come up constantly in rigging conversations.
| Change in distance | Change in illuminance | What it means on stage |
|---|---|---|
| ×1.1 — 10% further | −17% | A truss raised half a metre on a 5 m throw |
| ×1.25 — a quarter further | −36% | Moving a fixture from the first to the second position on a boom |
| ×1.5 — half again as far | −56% | The difference between a 4 m front position and a 6 m one |
| ×2 — twice as far | −75% | Any doubling. The single most memorable number in lighting |
| ×3 — three times as far | −89% | A front-of-house position versus a downstage truss |
The square law assumes a point source. A large soft source — a 1 × 1 m panel, a big diffused wash — behaves differently at short range, because parts of the source are noticeably nearer than others. Close to a soft light the falloff is gentler than the square law predicts. By the time you are four or five source-widths away, the source behaves like a point again and the law takes over. This is why soft lights look forgiving at close range and why the law seems to “switch on” as you back away.
Take a real fixture with a published figure. The HUEWAVE MOVING HEAD 1915Z is quoted at 5,840 lux at 5 m — a measured illuminance, not a chip datasheet figure. Running that backwards: I = E × d² = 5,840 × 25 = 146,000 candela. That single number lets us predict the fixture at any distance.
Now the interesting part. At 3 m it delivers 146,000 ÷ 9 = about 16,222 lux. At 6 m it delivers 146,000 ÷ 36 = about 4,056 lux. Double the distance, exactly a quarter of the light — from 16,222 down to 4,056.
That step from 3 m to 6 m is the one people underestimate most often, because on a plan it looks like a modest move. A fixture on a low boom at the edge of a stage might be 3 m from a performer. The same fixture moved to a front truss position is now 6 m away. It has not become a worse fixture. It is delivering a quarter of the illumination, and the fix — more fixtures, a higher-output model, or moving it back — all cost money.
Here is where the square law stops being trivia and starts being a design constraint. A front light is usually rigged at the downstage edge and aimed at performers working upstage of it. The performer standing directly under the fixture is close; the performer at the back of the stage is far.
That creates an inherent brightness gradient across the acting area, and its steepness depends almost entirely on one thing: how high the truss is. Raise the truss and the near distance grows while the far distance grows more slowly, so the two ends converge.
A performer standing on the truss centre line, an 8 m deep stage, and a vertical receiving surface — a person standing up — which falls faster than a floor does. Both of those modelling choices are explained later in this article, and both matter if you want to reproduce these numbers on a real stage.
| Front truss height | Illuminance nearby | At 8 m upstage | Unevenness |
|---|---|---|---|
| 3 m | 16,222 lx | 702 lx | 23 : 1 |
| 4 m | 9,125 lx | 816 lx | 11 : 1 |
| 5 m | 5,840 lx | 869 lx | 6.7 : 1 |
| 5.66 m | 4,557 lx | 878 lx | 5.2 : 1 |
| 6 m | 4,056 lx | 876 lx | 4.6 : 1 |
| 7 m | 2,980 lx | 851 lx | 3.5 : 1 |
| 8 m | 2,281 lx | 807 lx | 2.8 : 1 |
| 10 m | 1,460 lx | 695 lx | 2.1 : 1 |
Read the top row against the bottom. At a 3 m truss the performer at the back of the stage receives 3% of what the performer at the front receives — a twenty-three to one ratio that no console can fix, because it is not a mixing problem, it is geometry. At an 8 m truss the ratio is 2.8 to one, which is workable. Same fixture, same rig, same budget: the truss height did all of it.
Notice the “at 8 m upstage” column. It barely moves — 702 to 878 lux across the entire height range, and it actually falls again above about 5.7 m. Raising the truss does not put more light on the back of the stage. What it does is reduce the amount of light on the front of the stage, and evening out the gradient is worth far more to a photograph than a brighter near position ever was.
There is a second effect layered on top of the square law, and it catches people out when they test a rig with a meter held flat. A light meter lying on the floor reads the illuminance on a horizontal surface. A performer is a vertical surface. These two do not fall off at the same rate.
For a fixture hanging at height H, a point on the floor directly below it is at distance H and receives the full perpendicular illuminance, I ÷ H². A performer standing further upstage is at a greater distance and at an angle, so their surface is no longer perpendicular to the beam. The illuminance they receive is reduced by the cosine of that angle, and because the cosine falls as the point moves away, the total falloff goes as H ÷ d³ rather than 1 ÷ d². Vertical surfaces lose light noticeably faster than floors do.
The practical consequence is that a rig can meter perfectly and still look flat and dim on the people. If you are checking a front light, do not measure it with the meter flat on the deck at the performer’s position — hold it vertically, facing the fixture, at the height and angle the performer will actually present. The two readings can differ by a large enough margin to change the whole fixture count.
Because the falloff is predictable, positioning becomes a calculation rather than a preference. There is even a clear optimum for the most common case: putting the most light on a performer standing at a known distance upstage.
Maximising H ÷ d³ for a fixed upstage distance y gives H = y ÷ √2, which works out to H being about 71% of the distance upstage. For a performer 8 m from the downstage edge that is a 5.7 m truss. And at that exact height the near-to-far ratio hits its floor of 3√3 ≈ 5.2 to 1 — you cannot do better by moving the truss up or down. Push the truss higher and the ratio keeps improving, but only because the near position is getting dimmer, which is a different and eventually self-defeating trade.
The square law does not only work front to back. A truss along the downstage edge is also further from a performer standing off centre than from one on the centre line, and that distance grows with the width you are trying to cover.
| Position across a 16 m stage | Distance from a 6 m truss | Illuminance | Versus centre |
|---|---|---|---|
| On the centre line | 6.00 m | 4,056 lx | 100% |
| 2 m off centre | 6.32 m | 3,650 lx | 90% |
| 4 m off centre | 7.21 m | 2,808 lx | 69% |
| 6 m off centre | 8.49 m | 2,028 lx | 50% |
| 8 m off centre | 10.00 m | 1,460 lx | 36% |
At the edge of a 16 m stage a performer receives about a third of what a performer on the centre line receives, from a front truss that is barely any further away in plan view. This is why wide stages get side positions and ladders rather than one heroic front truss: the geometry refuses to be solved from a single direction. Adding dedicated side light shortens the throw dramatically, and per the square law, shortening the throw is the most cost-effective brightness you can buy.
The fixtures below are chosen for the distance problem rather than for raw output. Every one of them has a motorised zoom, which means you can set the beam angle to the throw instead of accepting whatever angle the housing came with.
HUEWAVE MOVING HEAD 1915Z
$259
HUEWAVE 19Z PAR
$165
LIMONA PAR 2415IP
$299
LIMONA UPLIGHT 618
$2,099
One fixture delivers 4,056 lx on a performer directly below and 876 lx at the back of the stage. Aimed into the mid stage, one fixture covers the band from roughly 4 m to 8 m at between 2,336 and 876 lux on a vertical surface. Two fixtures overlapping across the width push the working area past 1,500 lx, and a third angled at the far position lifts the back of the stage out of the shadow. Three fixtures, positioned by geometry rather than by habit.
Illuminance falls in proportion to the square of the distance from the source. Double the distance and you receive a quarter of the light; triple it and you receive one ninth. It follows from pure geometry — the same output has to cover an area that grows with the square of the radius. It is the single most useful calculation in stage lighting because it explains the effect of fixture position, which is free to change, rather than fixture output, which costs money.
Because the light is spreading over an area, and area grows with the square of distance. At 3 m a fixture illuminates a circle of a certain size. At 6 m that same beam covers a circle four times the area, so each square metre of it receives a quarter of the light. Nothing has been lost — the same total output is simply spread thinner. The number is not a rule of thumb but an exact geometric consequence.
As a starting point, about 70% of the distance from the truss to the furthest working position on stage. For a performer 8 m upstage that is roughly 5.7 m, which is also the height that minimises the near-to-far unevenness at about 5 : 1. In practice truss height is often fixed by the venue, so treat the figure as a target rather than a requirement — but check the resulting ratio before you commit to a fixture count.
Almost certainly because you measured a horizontal surface and the performers are vertical. A meter flat on the deck reads the perpendicular illuminance; a performer is at an increasing angle to the beam and receives less, falling off as distance cubed rather than squared. Hold the meter vertically, facing the fixture, at the height and angle a performer will present. The reading will be lower and more honest.
Only up to a point, and it is usually the expensive way. Adding fixtures raises the whole curve including the already-hot near position, so a 20 : 1 gradient stays roughly 20 : 1 while getting brighter. Fix the ratio first, by moving positions or adding a second angle, then set the level. Ratio is a geometry problem; level is an output problem, and they are not interchangeable.
Because the near position gets further away while the far position gets slightly closer. In the worked example, going from a 3 m to an 8 m truss cut the near position from 16,222 to 2,281 lux while the far position moved only from 702 to 807. The average is lower and the coverage is far more even. Evenness is usually worth more than raw level, especially on camera, but it does mean the rig needs more fixtures to hit the same average.
Yes. It is geometry rather than a property of the lamp, so it applies to every source in the same way. Two caveats. First, the law assumes a point source, so a large soft panel behaves more gently at close range until you are several source-widths away. Second, some LED fixtures reduce output as they heat up, which adds a second, entirely separate cause of dimming that has nothing to do with distance.
Because a front truss cannot cover width efficiently. On a 16 m stage, a performer at the edge sits 10 m from a truss that is only 6 m from the centre line, and receives about a third of the light. Side positions put fixtures far closer to the performers they cover, and since illuminance rises with the square of reduced distance, shortening the throw is the cheapest brightness available. That is why wide stages are lit from several directions rather than one.
This article explains the inverse square law and its application to stage lighting positions. Worked figures derive from a single published measurement — 5,840 lux at 5 m for the HUEWAVE MOVING HEAD 1915Z — treated as a point source of 146,000 candela; real fixtures depart from point-source behaviour at short range and vary with zoom position, colour mix and operating temperature, so treat all derived values as planning estimates rather than specifications. Published figures for products sold on sanyilights.us are quoted from the current datasheet at the time of writing. Product availability and pricing are subject to change.
