Throw ratio times image width gives you the distance. The useful move is doing that arithmetic before you buy, because it tells you whether the projector you want physically works in the room you have.
Every projector publishes a throw ratio, which is the throw distance divided by the resulting image width.
A ratio of 1.5 means the projector sits 1.5 times the image width away. Want a 100 inch wide image? Place it 150 inches back, which is 12.5 feet.
Rearranged, throw distance equals throw ratio times image width. That is the whole calculation.
Most projectors have a zoom, so the ratio is a range rather than a single number, such as 1.2 to 1.6. That range is your installation flexibility, and a projector with a wide zoom range is considerably easier to place in a room you cannot rearrange.
Screens are sold by diagonal, throw ratios are calculated on width. On a 16:9 screen the width is roughly 0.87 times the diagonal. A 100 inch screen is about 87 inches wide, so using 100 in the calculation puts your projector over a foot too far back.
Three measurements decide what is possible.
The available throw distance, from the wall or ceiling position where the projector can actually mount, to the screen wall. Measure it rather than estimating, because this is the hard constraint.
The available screen width on the wall, allowing for whatever else is on it.
Ceiling height, which determines mounting options and whether a ceiling mount drops the projector into someone's eyeline.
With those, you can work backwards. Divide your available throw distance by your desired image width and you have the throw ratio you need, which is the number to shop with.
Throw ratio decides how far back. Vertical offset decides how high, and getting it wrong means an image that lands on the wrong part of the wall.
Most projectors do not project straight ahead. They throw the image upward or downward relative to the lens by a fixed percentage of the image height, which is what lets a ceiling-mounted unit put an image on a wall below it without tilting.
Tilting the projector to correct for bad placement introduces keystone distortion, and correcting that digitally costs image quality. Getting the geometry right physically is always better than fixing it in software.
Measure the intended screen top and bottom heights from the floor, and the intended lens height, and check those against the projector's offset specification.
This is a genuinely good application. Throw distances are often across a whole room, sometimes diagonally, and frequently to a ceiling mount point you cannot easily reach with a tape.
Shooting from the intended mount position to the screen wall takes seconds. Measuring the drop from ceiling to lens height, and the screen height off the floor, is the same tool without moving.
It is also the fastest way to test alternatives. If 12.5 feet is not available, measuring what you do have immediately tells you what image size is achievable, or what throw ratio to shop for instead.
If the room simply does not have the distance, the answer is a different lens class rather than a compromise.
Short throw projectors have ratios well below 1, producing a large image from a few feet. Ultra short throw units sit almost against the wall and throw upward at an extreme angle, which is why they are placed on furniture directly beneath the screen.
Ultra short throw is unforgiving of placement. Small errors in distance or squareness produce visible geometry problems, so precise measurement matters more with these than with a conventional projector, not less.
Measuring ceiling height is covered here, and the general room method here.
We cover laser measures and nothing else, and the front page is where the recommendations live.