Max Screen Size for a Projector
The inverse of the projector-brightness tile: the largest screen a projector lights to a target brightness, max area = lumens x gain / target foot-lamberts, then the width, height, and diagonal at the aspect ratio. A 5,000-lumen projector on a unity-gain screen at 16 fL tops out near a 27 ft (16:9) diagonal; a lit room at 30-50 fL shrinks it. Size the projector 20-30% over the minimum for lamp aging. Sizes the screen from the brightness budget, not the throw geometry; the room and the projector's lens range govern.
Formula and source
Max screen area = lumens x gain / target foot-lamberts; width = sqrt(area x aspect_w / aspect_h), height = width x aspect_h / aspect_w, diagonal = sqrt(width^2 + height^2).
Standard AV screen-luminance identity (SMPTE-style targets, by name); foot-lamberts = lumens x gain / area, solved for the area.
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