Formula
Image width is the diagonal times the width part of the aspect, divided by the hypotenuse of the aspect. Height uses the height part. A 2.35:1 screen is wider and shorter than a 16:9 screen of the same diagonal, because more of that diagonal is width. Area is width times height. Throw ratio, on a spec sheet, is the distance to the screen divided by that image width, so distance is the ratio times the width.
W = diag × a / √(a² + b²)
H = diag × b / √(a² + b²)
D = throw ratio × W
What a projector throw calculator uses
A single throw ratio gives one distance. A zoom lens gives two ratios, and the same screen fits anywhere between them: the nearest seat of the lens is the smaller ratio, and the farthest is the larger one. Under about 1.0 is short throw. Under about 0.4 is ultra-short throw. Ratios outside about 0.15 to 10 still calculate, and the page says so, because that number is unusual on a spec sheet.
Manufacturers measure from the lens face or from the front or the back of the chassis. Ultra-short-throw sheets often quote the wall to the back of the projector. Add the chassis depth when the point you measure is farther from the screen than the lens, and subtract it when that point is closer. The drawing labels the distance this page is reporting.
Projector screen size from the distance
Run the same identity backwards. Width is the lens distance divided by the throw ratio, then height and diagonal come from the aspect. With a zoom range, the largest image is the smaller ratio and the smallest image is the larger ratio. This is the projector screen calculator and the projector screen size calculator on this page. A projector distance calculator is the same relationship, just starting from the room instead of the screen.
W = D / throw ratio
smallest image uses the larger ratio
Vertical lens shift, when the spec sheet lists it, moves the image centre up or down by that percent of the image height. This page uses the centre-of-lens convention. Makers do not all define the percentage the same way, so confirm the mount with the maker’s own calculator before drilling. Keystone correction is a different thing: it digitally squeezes the picture and costs resolution. Prefer lens shift, or moving the projector.
Seating uses the same viewing-angle idea as a television. SMPTE and THX publish angles for how much of your view the screen should fill. This page does not compute a seat row. The TV viewing distance calculator turns those angles into a seat distance, a screen size, and a mounting height, and the same angle guidance applies to projection.
Brightness, gain, and lens shift
Foot-lamberts are projector lumens times screen gain, divided by the screen area in square feet. Nits, in candelas per square metre, are foot-lamberts times 3.426. About 14 fL, or 48 nits, is the digital-cinema reference in SMPTE ST 431-1. About 16 fL was the classic film reference in SMPTE 196M. Both assume a dark room. A living room with ambient light needs much more, and an ambient-light-rejecting screen is a different trade than a higher gain number. Rated ANSI lumens are typically higher than the lumens left in a calibrated picture mode. Use a measured figure when you have one. The band on this page is guidance, not a guarantee, and the model’s spec sheet is the final word.
fL = lumens × gain / area(ft²)
nits = fL × 3.426
shift = (shift % / 100) × H
Worked examples
100 in, 16:9, throw ratio 1.50. Width 87.16 in, height 49.03 in. Distance 130.74 in, 10.89 ft (10 ft 10.7 in), 3.321 m.
120 in, 16:9, zoom 1.39–2.27. Width 104.59 in. Nearest 145.38 in (12.11 ft), farthest 237.42 in (19.78 ft).
12 ft at throw ratio 1.20, 16:9. Width 120.00 in, height 67.50 in, diagonal 137.68 in.
120 in, 2.35:1. Width 110.42 in, height 46.99 in.
100 in, 4:3, throw ratio 1.50. Width 80.00 in, height 60.00 in. Distance 120.00 in (10.00 ft).
2,000 lumens, 100 in 16:9, gain 1.0. Area 29.67 ft², 67.40 fL, 230.9 nits.
60% vertical shift, 100 in 16:9. The image centre can move 29.42 in above or below the lens axis.
Reference
The seven checks for this page. Distances are from the lens unless a chassis depth is set.
| Case | Result |
|---|---|
| 100 in 16:9, ratio 1.50 | 87.16 × 49.03 in · 130.74 in · 10 ft 10.7 in |
| 120 in 16:9, zoom 1.39–2.27 | 104.59 in wide · 12.11–19.78 ft |
| 12 ft, ratio 1.20, 16:9 | 120.00 × 67.50 in · 137.68 in diagonal |
| 120 in 2.35:1 | 110.42 × 46.99 in |
| 100 in 4:3, ratio 1.50 | 80.00 × 60.00 in · 10.00 ft |
| 2,000 lm, 100 in 16:9, gain 1 | 29.67 ft² · 67.40 fL · 230.9 nits |
| 60% shift, 100 in 16:9 | 29.42 in |
Questions
How far should a projector be from a 100-inch screen?
It depends on the throw ratio. A 100-inch 16:9 screen is 87.16 inches wide. At a throw ratio of 1.50 the lens sits 130.74 inches away, which is 10.89 feet, or 10 feet 10.7 inches. A different ratio, or a zoom range, moves that spot.
What is throw ratio?
Throw ratio is the distance from the lens to the screen divided by the image width. A ratio of 1.50 means the projector sits one and a half image-widths away. Under about 1.0 is short throw. Under about 0.4 is ultra-short throw.
How big a screen will my projector make at a given distance?
Divide the lens distance by the throw ratio. That is the image width. Height and diagonal follow the aspect ratio. With a zoom range, the largest image uses the smaller ratio and the smallest image uses the larger one. This projector distance calculator does that in the reverse mode.
What is the difference between short throw and long throw?
A short-throw lens makes a wide image from close to the screen, under about one image-width. A long-throw lens needs more room and is the usual living-room lens, often somewhere around 1.2 to 2.2. Ultra-short throw, under about 0.4, sits almost against the wall.
How many lumens do I need?
Divide lumens times screen gain by the screen area in square feet to get foot-lamberts. About 14 fL (48 nits) is the digital-cinema reference for a dark room, and about 16 fL was the classic film reference. A room with the lights on needs much more. Rated ANSI lumens are usually higher than a calibrated picture mode.
Can I use lens shift instead of keystone?
Yes, when the projector has it. Vertical lens shift moves the image centre up or down by a percentage of the image height without throwing away pixels. Keystone correction is a digital squeeze, and it costs resolution. Prefer lens shift, or moving the projector, and confirm the percentage with the maker’s own calculator before you drill a ceiling mount.
Does screen gain matter?
Gain multiplies the light the screen sends back. A gain of 1.0 is a matte reference. Higher gain looks brighter from the sweet spot and often narrower from the side. Ambient-light-rejecting screens trade some of that peak for a picture that holds up with the lights on. This page multiplies by the gain you type. It does not model the room.
Sources
- Throw ratio is distance divided by image width, the definition used on projector spec sheets. The sheet, and the maker’s own calculator, are the final word for a specific model, including where the distance is measured.
- SMPTE ST 431-1. Digital cinema reference luminance, 48 cd/m², about 14 fL, for a dark theatre.
- SMPTE 196M. The older film-projection reference, about 16 fL. A living room with ambient light is not either of these rooms.
- Nits on this page are foot-lamberts times 3.426. Screen gain is the number you enter. Neither one models the room, the lens, or a calibrated picture mode.