Foot-lamberts, and why the unit has an area in it
A lumen is a quantity of light. A foot-lambert is a brightness — light per unit of area, as it comes back off a surface. That distinction is the whole page. A projector emits a fixed number of lumens and they land on whatever size rectangle you point them at, so the brightness of the picture is the output divided by the area, adjusted by how much of that light the screen sends back toward the seats.
The arithmetic is one line. Foot-lamberts equal lumens reaching the screen, multiplied by screen gain, divided by the screen area in square feet. Rearranged for planning, the lumens you need at the screen are the target foot-lamberts multiplied by the area and divided by the gain. A 120 inch 16:9 image is 104.6 by 58.8 inches, which is 42.7 square feet, so 16 foot-lamberts on a gain 1.0 screen asks for about 684 lumens actually arriving.
That number looks absurdly small next to a projector advertised at 2,500 lumens, and the gap between them is the real subject here.
Where the rated lumens go
Three things stand between the specification sheet and the screen, and they multiply rather than add.
| Stage | What it is | Where the number comes from |
|---|---|---|
| Picture mode | The rated figure is measured in the brightest mode the projector offers, which is usually a cool, oversaturated mode nobody watches films in. A calibrated mode gives up a substantial fraction of it. | A measurement of your unit, or a published review that measured one |
| Light source condition | Lamps dim steadily from the first hour. Laser and LED sources dim more slowly but they still dim, and the manufacturer publishes a curve. | The manufacturer specification for your model and your hours |
| Eco or low power mode | Quieter and longer lived, at a direct cost in output | The projector menu and the manual |
Multiply the three survival fractions together and you get what actually reaches the screen. Losing 35 percent to the picture mode and 20 percent to a half-used lamp leaves 52 percent, so a 2,500 lumen projector is putting about 1,300 lumens on the wall. On that 42.7 square foot screen at gain 1.0 that is 30 foot-lamberts, which is comfortable. Stretch the same projector to a 150 inch image and the area goes to 66.8 square feet, and the same 1,300 lumens now gives 19.5.
None of those percentages are published constants and none of them are supplied here as facts. They are fields because the honest answer differs by model, by mode and by how many hours the thing has run.
The square law, stated plainly
Screen area scales with the square of the diagonal for a fixed shape, so the brightness for a fixed output scales with the inverse square of the diagonal. The table the calculator prints makes this concrete, and it is the number people are most often surprised by.
| Diagonal change | Area change | Brightness change at fixed output |
|---|---|---|
| 100 to 110 in | +21% | -17% |
| 100 to 120 in | +44% | -31% |
| 100 to 135 in | +82% | -45% |
| 100 to 150 in | +125% | -56% |
Going from 100 to 150 inches more than halves the brightness. That is why a projector that looks spectacular on a demo screen can look flat and washed out on the wall it was bought for, and why the sequence that works is to fix the image size first, then work out the light budget, then choose the projector — rather than buying a projector and finding out what size it will tolerate.
Gain is a redistribution, not a gift
A screen with a gain of 1.4 is not producing 40 percent more light. It is reflecting light into a narrower cone, so an on-axis viewer sees more and an off-axis viewer sees less, and the total is roughly conserved. The specification that describes the cost is the half gain angle: the angle off the centreline at which the brightness has dropped to half the on-axis figure. A screen with high gain and a narrow half gain angle is fine for one seat on the centreline and visibly uneven across a three seat sofa.
High gain screens also tend to show hot spotting, where the centre of the picture is measurably brighter than the edges from a single seat, and they can amplify the texture of the screen surface. Grey and ambient light rejecting screens work the other way, deliberately giving up brightness to hold a darker black when the room is not fully dark, which raises contrast at the cost of the light budget on this page. All of it belongs in the screen data sheet, and the data sheet is the authority.
What this does not settle
Contrast is separate from brightness and often matters more to how a picture looks. A dark room with dark surfaces holds contrast that a white ceiling and pale walls throw away, because light bouncing off the room lands back on the screen and lifts the black level. Two projectors with identical output in the same room can look nothing alike.
Nor does a foot-lambert target settle anything on its own. The figures people quote for a fully darkened room and for a room with lamps on are far apart, they come from different bodies with different purposes, and they get repeated without their context. Pick a target, see what it costs in lumens, and then go and look at a real image at that size. The rest of the install geometry is on the projector throw distance calculator, the seating distance question is on the viewing distance calculator, and what the room itself does to sound rather than light is the acoustic treatment calculator.
Questions people ask
How many lumens do I need for a 120 inch screen?
It depends on three things the question leaves out: the target brightness, the screen gain, and how much of the rated output your projector still delivers in the mode you watch in. A 120 inch 16:9 image is 42.7 square feet, so at 16 foot-lamberts on a gain 1.0 screen it needs about 684 lumens actually landing on the screen. Getting 684 lumens onto the screen from a projector rated in a mode you do not use, with a light source that has been running for a year, commonly takes a rated figure two to three times higher. Enter your own loss estimates rather than trusting a single headline number, because that is where the whole spread lives.
Why does my projector look dimmer than the specification says?
Because the specification was measured in the brightest picture mode the projector has, and that mode is normally unusable for film — cool, oversaturated, and with the light source at full power. Switching to a calibrated or cinema mode gives up a large fraction of the output, running in eco mode gives up more, and the lamp or laser has been dimming since the first hour it ran. None of that is a fault. It is the difference between a laboratory measurement condition and a living room, and it is why this calculator asks you to state the losses rather than assuming them.
Does a higher gain screen let me use a smaller projector?
Partly, and with a cost that is easy to miss. Gain redirects light into a narrower cone rather than creating any, so the seat on the centreline gains and the seats to the side lose. The number to look for in the screen data sheet is the half gain angle, which tells you how far off axis the brightness falls to half. With one seat on the centreline a high gain screen genuinely buys you light. With three seats across a sofa it buys the middle seat light and charges the outer two for it, and it can also show hot spotting where the centre of the picture is brighter than the edges. In a room where blackout is achievable, a lower gain screen and more lumens is usually the more even result.
What foot-lambert figure should I aim for?
This calculator deliberately does not tell you, because the published targets come from different organisations for different purposes and get quoted out of context constantly. The figures discussed for a fully darkened dedicated room are considerably lower than the figures discussed for a room with ambient light, and neither is a rule anybody enforces on a home installation. What is worth doing is picking a number, seeing what it costs in rated lumens at your screen size, and then looking at an actual image at that size before committing. If you have access to a light meter, measuring what you already have and deciding whether you want more or less is far more useful than any published figure.
Is a brighter projector always better?
No, and past a point it works against you. Too much light in a fully darkened room is genuinely fatiguing to watch for two hours, and the projectors that produce it often do so by running the light source hard, which means more fan noise and a shorter service life. Brightness also does nothing for contrast: a very bright projector in a room with white walls and a white ceiling still produces a washed out picture, because the light bouncing around the room lands back on the screen and raises the black level. Sizing the output to the screen with some margin for the light source dimming is a better goal than buying the largest number available.