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The saved projector calculator converts eight point five feet to one hundred two inches, then divides by one point two five for eighty-one point six inch diagonal. Bars compare throw distance and diagonal at five pixels per inch. Its throw coefficient is explicitly used against diagonal rather than screen width. Preserve this source convention; it is not independently validated optics or a verified manufacturer specification. The saved model, price and brightness values are illustrative inputs rather than current product testing. Width equals diagonal times sixteen divided by square root of three hundred thirty-seven, while height uses nine over the same root. For eighty-one point six diagonal this is about seventy-one point one two wide and forty point zero one high. Bars compare approximate dimensions at six pixels per inch. Dividing their product by one hundred forty-four gives square feet. Real projection can be limited by focus, installation and screen shape, none of which the arithmetic measures. At unchanged throw coefficient, doubling distance doubles both computed dimensions and multiplies screen area by four. Since its brightness expression is entered lumens divided by area, it then gives one quarter the brightness. Bars show normalized relative brightness four versus one at one hundred pixels per unit. This is the source inverse-area relation, not measured perceived image quality. Native generic preset, complete stable JSON export and reset preserve source canvas allocations. Room ratings and deal tiers are threshold labels, not verified suitability or current retail comparisons.