What throw ratio is, in one line of arithmetic
Throw ratio is the throw distance divided by the image width. Both in the same units. A projector at 1.5:1 placed 15 feet from the screen gives an image 10 feet wide, because 15 divided by 1.5 is 10. Rearranged, the image width is the distance divided by the ratio, and the distance you need for a given image is the width times the ratio. Every projector placement question is that one equation read in a different direction.
The catch is that almost no projector has a single ratio. A zoom lens is quoted as a range — 1.20:1 to 1.60:1 is a common home cinema spec — and the two ends produce very different images from the same seat. At 14 feet that example throws anywhere between 105 and 140 inches of image width, which is a 120 inch and a 160 inch diagonal. That spread is the reason a projector should be chosen after you know where it can physically go, not before.
The distance is measured from the lens, not from the front of the case, not from the ceiling plate, and not from the wall behind it. On a long-throw projector the difference is small enough to lose in the zoom range. On an ultra-short-throw sitting under the screen it is most of the measurement, and the manufacturer will publish the reference point for exactly that reason.
Turning image width into a screen you can buy
Screens are sold by diagonal, and the calculator converts for you, but the constant is worth knowing. For a 16:9 image, the diagonal is the width multiplied by 1.1473, because the diagonal of a 16 by 9 rectangle is the square root of 1 plus 0.5625 times the width. A 100 inch wide image is a 114.7 inch diagonal. Height is width times 0.5625.
| Image width | 16:9 height | 16:9 diagonal | Distance at 1.5:1 |
|---|---|---|---|
| 80 in | 45.0 in | 91.8 in | 10.0 ft |
| 92 in | 51.8 in | 105.6 in | 11.5 ft |
| 105 in | 59.1 in | 120.5 in | 13.1 ft |
| 122 in | 68.6 in | 140.0 in | 15.3 ft |
| 140 in | 78.8 in | 160.6 in | 17.5 ft |
Pick a screen near the middle of the zoom range rather than at an extreme. Zoom lenses are usually at their sharpest and brightest somewhere in the middle of travel, and more importantly a screen sized at the very edge of the range leaves you no adjustment when the mount ends up two inches off where you drew it.
Lens shift, offset, and why the projector is not level with the picture
A projector does not throw its image symmetrically around the lens axis unless it is designed to. Two related specifications describe where the picture lands relative to the lens.
Fixed offset is the amount, given as a percentage of image height, that the image centre sits above or below the lens axis when the optics are at neutral. A projector with a 100 percent offset throws an image whose bottom edge is level with the lens — that is the classic table-mounted arrangement, and inverted on a ceiling mount it throws the picture down instead.
Vertical lens shift is a range of movement around that neutral position, again as a percentage of image height. A projector quoted at plus or minus 60 percent can move the image up or down by 60 percent of its own height without tilting the body. That is what makes a ceiling mount work: the projector hangs at a sane height, the image sits where people can watch it, and nothing is tilted.
The calculator takes both, works out the window of heights the lens axis can occupy for the image position you asked for, and subtracts that from the ceiling to give the drop. If the window is empty — the number comes out negative — the geometry does not close, and no amount of keystone correction will rescue it. Something has to move: the image, the ceiling mount, or the projector choice.
The keystone temptation
Every projector has digital keystone correction and it is nearly always the wrong answer. Correcting a tilted projector in software means the panel renders a trapezoid inside its own rectangle, scales the source to fit, and blanks the rest. You lose resolution, the scaling softens fine text, brightness falls off across the corrected edges, and the focus plane is still tilted because optics do not care what the processor did. Physical placement and optical shift move the whole image without touching a pixel. Use keystone to clean up the last half degree after the mount is bolted, not as a placement strategy.
Ceiling mounting also puts a heavy object over the heads of the people watching. That fixing goes into structure — a joist, or blocking added between joists — and never into drywall with an anchor rated by optimism. If you cannot find structure where the geometry wants the mount, add blocking before you drill, or move the geometry. The stud wall calculator is the companion for laying out that blocking, and the TV mount height calculator covers the same argument for a flat panel.
What this page deliberately leaves out
Brightness is the specification that ruins more projector installs than geometry does, and it is not modelled here because it depends on screen gain, ambient light, and what you are watching. A projector that looks spectacular in a blacked-out room is a grey smear in a living room with two windows. Work out the geometry here, then have the light conversation separately, because a bigger image from the same projector is always a dimmer image — the same lumens are spread over more square feet.
Power for the projector is its own problem. An outlet at the ceiling for a mounted projector is new mains work and belongs with a licensed electrician; there is no version of that job that is a weekend fix. What you can plan for is the cable run from the rack to the ceiling and the heat the gear makes once it is all in a cabinet, which the equipment rack power and heat calculator handles.
Questions people ask
How do I find the throw ratio if the manual only gives a distance chart?
Take any row from the chart, divide the distance by the image width, and you have the ratio for that end of the zoom. Do it for the minimum and maximum distance columns at the same image size and you have both ends of the range. Watch the units — charts often list distance in feet and image width in inches, so convert one before dividing. A chart listing 10 to 13 feet for a 100 inch wide image gives 120 divided by 100, so 1.2:1 at the wide end, and 156 divided by 100, so 1.56:1 at the tight end. If the chart lists diagonals rather than widths, convert the diagonal to a width first by multiplying by 0.8716 for a 16:9 image.
Can I put the projector on a shelf behind the sofa instead of on the ceiling?
Often yes, and it is usually easier. The geometry is the same equation, but the offset works in the opposite direction: a projector sitting upright on a shelf throws its image upward relative to the lens, which suits a screen above head height. What you need to check is the shelf height against the lens axis window the calculator gives, and whether the throw distance still lands inside the zoom range from that wall. The practical downsides are noise and light — the fan and the light leak from the vents are right behind the seating — and heads passing through the beam. A rear shelf also has to be deep enough that the projector is not hanging off the front edge, which is more of a problem than people expect on a 15 inch shelf.
Does lens shift hurt image quality the way keystone does?
No, and that is the whole point of it. Optical lens shift physically moves the lens assembly relative to the imaging panel, so the projector is still drawing a full rectangle with every pixel used and the focus plane stays parallel to the screen. Nothing is scaled and nothing is discarded. At the far extremes of a shift range some projectors show slightly softer corners or a little more light falloff, because the image is using the outer edge of the lens, but that is a subtle effect and a completely different thing from the resolution loss keystone causes. Use all the shift you need before you touch keystone.
Where should the bottom of the screen sit?
High enough that the front row does not block it, low enough that the back row is not looking up. In a single-row living room a bottom edge around 24 to 36 inches from the floor usually works, because that clears a coffee table and puts the image centre near seated eye level. With two rows the constraint is the sight line over the heads in front, which pushes the whole image up and starts to strain necks in the front row — the point at which people build a riser for the back row instead of raising the screen. If you have a fixed screen position already, run the calculator in image-size mode with that bottom height entered and read off whether the lens axis window can reach it.
The calculator says the drop is negative. What went wrong?
Nothing broke — the geometry genuinely does not close. A negative drop means the lens would have to sit above your ceiling to put the image where you asked for it, which happens when the image is positioned high, the projector has little or no downward shift, or the ceiling is low. Three things fix it: lower the image bottom edge, choose a smaller image so its height shrinks, or use a projector with more vertical shift range. What does not fix it is tilting the projector down and correcting in software, because that trades a geometry problem for a picture quality problem and you still have the focus plane fighting you.