Lumens are about the lamp, lux is about the place
A lumen is total light output. A lux is one lumen landing on one square metre. Between the two sits a spreading cone, and the arithmetic that connects them is short enough to do by hand.
Take the defaults: 800 lumens over a 120 degree full cone. The solid angle of that cone is 2π(1 - cos 60°), which is 3.1416 steradians, so the average intensity inside it is 800 divided by 3.1416, or 254.6 candela. At 18 inches — 0.4572 metres — the illuminance directly underneath is 254.6 divided by 0.4572 squared, which is 1,218 lux, or 113.2 foot-candles. Convert with 1 foot-candle equals 10.764 lux.
The square is the whole story
Every distance in that calculation is squared, which is why height dominates everything else. The same lamp at 9 inches gives four times as much; at 36 inches, a quarter.
| Height above the surface | Lux underneath | Lux 15 in out | Edge over centre |
|---|---|---|---|
| 9 in | 4,873 | 664 | 0.136 |
| 13.5 in | 2,166 | 648 | 0.299 |
| 18 in | 1,218 | 552 | 0.453 |
| 27 in | 541 | 362 | 0.668 |
| 36 in | 305 | 240 | 0.787 |
Read the last two columns together. Dropping the lamp from 36 inches to 9 multiplies the light under it by sixteen and makes the pool nearly six times less even: at 9 inches the point 15 inches away gets 0.136 of what the centre gets, and at 36 inches it gets 0.787. There is no setting that maximises both. Which one you want depends on whether you are lighting a page or a desk.
Off to one side, two things happen at once
Move the task point sideways and it gets further away, which costs light to the square. It also gets lit at a slant, and light arriving at an angle spreads across more surface, which costs the cosine of that angle on top.
At 18 inches up and 15 inches across, the straight-line distance is 23.43 inches and the cosine term is 18 over 23.43, or 0.768. The result is 552 lux against 1,218 directly underneath — 45 percent, from a point that is only 15 inches away on a desk. That is the falloff people notice as one bright patch and a dim rest of the desk.
What the cone model gets wrong
Treating the beam as a cone of uniform intensity is a simplification and it fails in a predictable direction. Real reflectors are brightest on axis and taper toward the edge of the beam, so the true centre figure is higher than this page says and the true edge figure lower. The published beam angle is itself usually defined as where intensity has fallen to half, which means light continues past it — the hard cut-off in this model does not exist in the room.
None of that makes the arithmetic useless; it makes it a scale rather than a measurement. If the number that comes out is 1,200 lux and your target is 500, the geometry has room. If it comes out at 520, the model is not precise enough to tell you whether you cleared it. A meter on the desk settles it in ten seconds and this page never will.
What this page does not tell you
It does not tell you how much light your desk should have. Recommended levels for office and detail work are published by several bodies, they differ, they depend on the task and on who is doing it, and asserting one as fact would be pretending to an authority this page has no claim to. The target field is empty of opinion on purpose: put your own number in and the arithmetic follows it.
Questions people ask
How many lux should a desk have?
This page does not say, and it is a deliberate omission rather than a gap. Recommended illuminance levels are published by standards bodies and lighting institutes, the figures differ between them, they vary by task and by the person doing it, and none of them is a fact this calculator is in a position to assert. What the page does is work out what a given fixture at a given geometry delivers to a given point, so that whatever target you bring can be checked against it. Where the light level is a workplace question, it belongs with the employer and whatever occupational rules apply to them.
Why is the calculated number so much higher than my light meter reads?
Three usual reasons, all of them real. First, the lumen figure on the box is often bare lamp output rather than what leaves the fixture after the shade and reflector have absorbed some. Second, the cone model assumes intensity is uniform across the beam, and a real fixture concentrates it on axis and tails off, so an off-axis reading falls short of the average. Third, the published beam angle is usually the half-intensity angle, which means the model draws a hard edge where the fixture has a soft one. Treat the arithmetic as a scale and the meter as the answer.
Does doubling the lamp height really quarter the light?
At the point directly underneath, yes, and it is the single most useful thing to know about task lighting. The illuminance goes as one over the distance squared, so twice the height is a quarter of the light. What you get back is a much more even pool: the same lumens are spread over four times the area, and the far edge of the desk is proportionally less far from the source than it was. The falloff table on the page shows both effects side by side, because choosing a height is choosing between them.
How do I handle two lamps?
Illuminance from separate sources adds directly, so run the page once for each fixture with its own height and its own offset from the point you care about, and add the lux figures. The fixture count the page prints is doing something cruder — it divides your target by what one fixture delivers at that exact geometry, which is fine as a sense of how far short you are and wrong as a plan, because two lamps cannot both sit in the same place.
Should I use foot-candles or lux?
Whichever your target is quoted in, since the page converts and reports both. One foot-candle is one lumen per square foot and one lux is one lumen per square metre, so a foot-candle is 10.764 lux — a square metre being that many square feet. American fixture literature and older lighting practice mostly use foot-candles; almost everything else, and most meters, use lux. The conversion is exact and neither is more correct.