How this calculator works
Throw distance is proportional to screen width: a throw ratio of 1.5 means the lens sits one and a half screen widths away. The screen shape turns a diagonal into width and height using the same right-triangle geometry as a television, so a 100 inch 16:9 screen is 87.18 inches wide. Brightness comes from the lumens reaching the screen spread over its area. One lumen per square foot is one foot-lambert at a screen gain of one, so a 3000 lumen projector on a 29.67 square foot screen gives about 101 foot-lamberts, provided all the light lands on the screen. Lamps dim with age, lens shift and zoom reduce light, and a high gain screen brightens the centre while narrowing the viewing cone.
Formula
screen width = diagonal x w / sqrt(w^2 + h^2) for a w:h screen. throw distance = throw ratio x screen width. brightness (foot-lamberts) = lumens x screen gain / screen area in square feet. Screen area in square feet = width x height in square metres / 0.09290304.
Worked example
A 100 inch 16:9 screen is 87.18 inches wide, or 2.214 metres, and 49.03 inches high, or 1.245 metres. With a throw ratio of 1.5 the projector sits 1.5 x 2.214 = 3.321 metres from the screen. Its area is 2.758 square metres, or 29.67 square feet, so a 3000 lumen projector with a gain of 1 gives 3000 / 29.67 = 101.1 foot-lamberts. Setting the projector 3 metres away instead gives a 2 by 1.125 metre screen, a 90.34 inch diagonal and about 123.9 foot-lamberts.
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Frequently asked questions
What is a good image brightness?
The cinema standard for a darkened room is around 16 foot-lamberts, and many home theatre guides suggest 16 to 30. Bright rooms need more, but too much brightness in a dark room tires the eyes and crushes shadow detail.
Does zoom change the throw ratio?
Yes. A zoom lens has a range of throw ratios, and the quoted model figure is often the widest or the midpoint. Use the value for the zoom setting you will actually use, or the picture will be a different size than planned.
How does screen gain work?
Gain compares the light reflected towards the viewer with a perfectly diffuse white surface. A gain of 1.0 is neutral, 1.3 is brighter on axis but narrower off axis, and grey screens below 1.0 trade brightness for better black levels in a bright room.
Why is the measured brightness lower than this figure?
Lamp ageing, lens losses, keystone correction and zoom all reduce light, and the lumen rating is usually a maximum in the brightest mode. Expect 70 to 90 percent of the calculated figure in a real installation.