Projector throw distance and screen size

What is a projector throw ratio?

It is the distance from the projector to the screen divided by the width of the image. NOAA's Science On a Sphere guide puts it as the throw distance divided by the width of the screen. A projector with a 1.5:1 ratio makes an image 1 foot wide for every 1.5 feet of distance. A short-throw lens has a small ratio and a long-throw lens a large one. The ratio refers to the width of the picture, not the diagonal, which is the number screens are sold by.

How far should the projector be from the screen?

Multiply the throw ratio by the image width. A 100-inch 16:9 screen is 87.2 inches wide and 49.0 inches high. A zoom lens of 1.2 to 1.5:1 (an example, not a model) puts the projector between 8.7 ft and 10.9 ft from the screen. NOAA's own example is a Sony projector with a 1.91 to 2.41:1 zoom and a 96-inch-wide image: the distance is 183.36 to 231.36 inches, and it advises mounting the projector as far back as the maximum allows. Always use the ratio in your own projector's manual.

What screen size can I get from my room?

Switch to the second mode and enter the distance from the lens to the screen: the image width is the distance divided by the throw ratio. At 12 feet, a zoom lens of 1.5 to 1.8:1 gives a 16:9 image between 92 and 110 inches diagonal, 80 to 96 inches wide. Measure the distance with the projector where it will stand, not the room length, and remember that the unit takes space behind the lens.

Does the aspect ratio change the distance?

Not for a given width: the distance depends only on the width of the image and the throw ratio. But for a given diagonal, a wider screen is wider and a narrower one is narrower. A 100-inch 16:9 image is 87.2 inches wide; a 100-inch 21:9 image is 91.9 inches wide, so the projector has to sit 5% farther back to fill it. Check whether your projector's throw ratio is stated for its native aspect ratio.

How bright should the picture be?

The brightness of the screen is lumens × the gain of the screen ÷ the screen area in square feet, in foot-lamberts; one lumen on a square foot of a gain-1 white screen gives one foot-lambert. For 2,000 lumens on a 100-inch 16:9 screen (29.7 square feet) that is 67 foot-lamberts (231 cd/m²) in a dark room. Cinema references we found are 16 foot-lamberts for film in SMPTE 196M and 14 foot-lamberts (48 cd/m²) for digital cinema, which would need only about 475 lumens on the same screen with no light loss. Those references come from vendor and trade pages, not from the standards themselves. A projector's lumens are often optimistic, and ambient light from windows takes away contrast, so a room that is not dark needs more.

What about lens shift and keystone?

Lens shift moves the image up, down or sideways without tilting the projector, and keystone correction squares up a picture from a tilted projector by processing it, which usually costs some sharpness and pixels. Neither changes the throw distance, which stays the ratio times the width, but shift sets where the picture lands, so it decides where the projector can sit. NOAA's page does not cover offset, and each maker gives its own offset range; use the manual of your model.

The two formulas

Throw distance = throw ratio × image width, and the other way round, image width = distance ÷ throw ratio. The image width comes from the screen you choose: for a diagonal d and an aspect ratio w:h, the width is d × w ÷ √(w² + h²), which for 16:9 is 0.872 × d. That is the same relationship as in the TV size calculator. Distance and width must be in the same unit; the calculator takes inches or centimetres for the screen and feet or metres for the distance. A fixed lens has one ratio; a zoom lens has two, and the projector can sit anywhere between the two distances.

Worked example: a 100-inch screen

A 100-inch diagonal at 16:9 measures 87.2 by 49.0 inches, which is 4,273 square inches or 29.7 square feet. With a lens of 1.2 to 1.5:1, the distance is 1.2 × 87.2 = 104.6 inches (8.7 ft) at the wide end and 1.5 × 87.2 = 130.7 inches (10.9 ft) at the far end. If the room only allows 9 feet, the image from this lens comes out between 83 and 103 inches diagonal, and the screen will be a size you can set with the zoom.

Limits of this method

The throw ratio in a catalog is a nominal figure for the lens, so leave a margin before you drill ceiling mounts and test the picture first. The ratio refers to the width of the projector's native picture. Some makers publish their throw distances as formulas with an offset rather than a plain ratio: a Christie manual we saw in search results gives a minimum distance of the form 1.4789 × width − 3.6096 for one lens, which is why you should use the maker's own table when one exists. NOAA's page, which gives the base formula, says nothing about lens shift or offset. The brightness estimate treats the screen as a perfect diffuser with a single gain figure and ignores ambient light, projector aging and the lens's light loss at the long end of the zoom.

Sources: NOAA Science On a Sphere, “Projector Throw Distance for SOS” (sos.noaa.gov; the definition of the throw ratio, the distance formula, the zoom-range example, read October 28, 2026; the page does not discuss lens shift); the foot-lambert is lumens per square foot by definition, and the cinema references of 16 and 14 foot-lamberts (SMPTE 196M and digital cinema, 48 cd/m²) come from vendor and trade pages seen in search results, such as ProjectorScreen.com and Acoustic Frontiers; the SMPTE standards were not opened. Related: TV size and viewing distance (use it for the angle and seat distance, which this page does not cover), PPI calculator and aspect ratio calculator. How we check our calculators.