The projector throw distance calculator above turns two numbers you can look up — your projector's throw ratio and the image size you want — into the distance the lens has to sit from the screen. It also works the other way round, so if the mounting position is already fixed you can see what image size that position produces.
Arb Digital builds free calculators that keep the model-specific numbers as inputs rather than baking in assumptions. This page deliberately publishes no table of projector models, because throw ratios differ between units, between lens options on the same unit, and between firmware-limited zoom ranges. The only correct throw ratio for your room is the one printed on your own specification sheet.
What This Projector Throw Distance Calculator Does
Throw ratio is defined as the distance to the screen divided by the width of the image, as set out in the standard description of projector throw. A ratio of 1.5:1 means the lens sits 1.5 units back for every 1 unit of image width. That definition uses width, not diagonal — which is the single biggest source of error when people do this by hand, because screens are sold by diagonal.
So the calculator does the conversion for you. It takes the diagonal and the aspect ratio, resolves them into a true width and height, applies the throw ratio to the width, and returns the distance. Because most projectors have a zoom lens with a minimum and a maximum ratio, it returns a range rather than a single point, and that range is what tells you whether a given mounting position will actually work.
Our live screen size calculator handles the first half of that job on its own: it returns real width, height and area from a diagonal and an aspect ratio, for any screen at all. This page adds the projection geometry on top — the throw ratio, the distance, and the zoom range — and that is the boundary between the two. If you only need the dimensions of a display, that tool is the right one.
How to Use It
- Find the throw ratio on your projector's specification sheet. It is usually written as a range, such as 1.50 – 1.80:1.
- Enter the minimum and maximum. If the lens is fixed, put the same number in both boxes.
- Choose the aspect ratio of the image you are projecting, or enter a custom pair.
- Enter the screen diagonal in "image size I want" mode, or the distance you have in "distance I have" mode.
- Read the hero figure, then check the zoom range. If your intended mounting point falls outside that range, the projector physically cannot fill that screen from there.
The Formula and How It Is Calculated
Two steps. First, convert diagonal to width and height. For an aspect ratio of W : H and a diagonal D, the width is D × W / √(W² + H²) and the height is D × H / √(W² + H²). That is the Pythagorean relation rearranged, and our Pythagorean theorem calculator covers the same identity in its general form.
Second, apply the ratio: throw distance = throw ratio × image width.
Work the defaults. A 100 inch diagonal at 16:9 gives √(16² + 9²) = √337 = 18.3576. The width is 100 × 16 / 18.3576 = 87.16 inches and the height is 100 × 9 / 18.3576 = 49.03 inches. At a throw ratio of 1.50 the distance is 1.50 × 87.16 = 130.7 inches, which is 10 feet 10.7 inches, or 3.32 metres. At the maximum ratio of 1.80 the same image needs 1.80 × 87.16 = 156.9 inches. So a 100 inch 16:9 image from this projector is available anywhere between roughly 10.9 and 13.1 feet.
The reverse direction just divides. From a fixed 130 inch throw at a ratio of 1.50, the image width is 130 / 1.50 = 86.67 inches, and the diagonal is 86.67 × 18.3576 / 16 = 99.4 inches.
Why the Diagonal Trap Catches So Many People
A 100 inch screen is not 100 inches wide. At 16:9 it is 87.2 inches wide, and at 2.35:1 it is 92.0 inches wide. Multiplying the diagonal by the throw ratio instead of the width overstates the distance by about 15% at 16:9 — on a 1.5:1 lens that is nearly 20 inches of error, which is the difference between a bracket that works and one that has to be moved.
The error runs the other way too. People measuring an existing room often work out "I have 12 feet, so I can have a 12 foot image", which quietly assumes a throw ratio of 1.0. Very few standard-lens home projectors are anywhere near 1.0; short-throw and ultra-short-throw units are, and long-throw installation lenses are well above 2.0. The ratio is the whole game, and it is model-specific.
Aspect ratio is the third trap. Switching a 100 inch diagonal from 16:9 to 2.35:1 makes it wider and much shorter, so the required distance goes up even though the "size" number has not changed. Our aspect ratio calculator is the quickest way to sanity-check a ratio you have been given as two pixel dimensions.
What the Throw Distance Does Not Tell You
Distance alone does not make an installation work. Four other constraints sit alongside it.
The first is lens shift and offset. Most projectors do not put the image centred on the lens axis; they project it upwards (or downwards, ceiling-mounted) by a fixed offset, sometimes adjustable by a vertical or horizontal shift range. A correct throw distance with the wrong vertical offset puts the image on the wrong part of the wall, and correcting that with keystone processing throws away resolution. Offset is quoted separately on the same spec sheet and is not part of throw ratio.
The second is brightness. Image area grows with the square of the diagonal, so doubling the diagonal quarters the light per unit area. The 100 inch 16:9 image above is 4,273 square inches; a 120 inch one is 6,153 square inches, 44% more surface for the same lumens. The projection screen reference covers screen gain, which is the other half of that equation and varies by material.
The third is the room. Throw distance is measured from the lens to the screen surface, but the projector needs physical depth behind the lens, and a ceiling mount adds a drop. A 130 inch throw in a room with 132 inches of clear space is not a working plan.
The fourth is seating. A screen sized only by what fits the room is often too small or too large for where people actually sit. The DPI and PPI calculator is useful here in a roundabout way: it gives the pixel density of a display, which is the quantity that decides at what distance individual pixels stop being visible.
Short Throw, Standard and Long Throw
Throw ratios cluster into rough families, and knowing which family your projector belongs to prevents most planning errors. Ultra-short-throw units have ratios well below 0.5 and sit on furniture directly beneath the screen. Short-throw units run roughly from 0.5 to 1.0 and suit small rooms where a ceiling mount would be in the seating area. Standard home and business projectors mostly sit between 1.0 and 2.0, which is why a 1.5:1 default is a reasonable starting point for a first pass. Installation projectors with interchangeable lenses reach 4:1 and beyond, for auditoriums where the projector lives in a booth at the back.
Those are descriptions of where the market sits, not specifications. The point of stating them is that if your calculated distance looks absurd for your room, the likeliest explanation is that you have entered a ratio from the wrong family — a short-throw figure for a standard projector, or the other way round. Go back to the spec sheet before you move any furniture.
Measuring the Room Properly
Measure from the screen surface to where the front element of the lens will sit, along a line perpendicular to the screen. Not from the wall, not from the back of the chassis, and not diagonally. On a ceiling mount, remember that the lens is usually a few inches behind the mount point and offset from the centre line of the body.
Convert everything into one unit before you start. Mixing a screen quoted in inches with a room measured in metres is where most of the remaining errors come from, and our length converter and area converter handle both directions. Then leave yourself margin: aim for a distance in the middle of the zoom range rather than at either end, so a screen that arrives an inch off nominal does not force a remount.
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Browse the Free Tools Hub Talk to Arb DigitalCommon Mistakes to Avoid
- Multiplying the throw ratio by the diagonal. Throw ratio is defined against image width. At 16:9 the diagonal is about 15% larger than the width.
- Using one end of a zoom range as if it were fixed. The usable positions are the whole span between the minimum and maximum ratio, and planning at an extreme leaves no adjustment.
- Ignoring vertical offset. A correct distance still puts the image in the wrong place if the projector's fixed offset has not been accounted for.
- Measuring from the wall. The distance is lens to screen. A projector on a shelf can easily sit a foot forward of the wall behind it.
- Assuming a typical throw ratio. Ratios vary from under 0.3 to over 4.0 depending on the unit and lens. Only the spec sheet for your model is authoritative.
Related Free Tools From Arb Digital
Use the screen size calculator when you only need width, height and area from a diagonal, and the aspect ratio calculator to simplify or solve a ratio. The DPI and PPI calculator covers pixel density, the Pythagorean theorem calculator the underlying geometry, and the length converter and area converter keep your units consistent. Everything else is on the free online tools hub.
Frequently Asked Questions
Throw ratio is the distance from the lens to the screen divided by the width of the projected image. A ratio of 1.5:1 means the projector sits 1.5 metres back for every 1 metre of image width. It is a property of the specific projector and lens, and it is printed on the specification sheet.
It depends entirely on the throw ratio. A 100 inch 16:9 image is 87.2 inches wide, so a 1.5:1 lens needs about 131 inches, or 10 feet 10.7 inches, and a 1.8:1 lens needs about 157 inches. A short-throw unit at 0.5:1 would need only about 44 inches.
Because throw ratio is defined against image width, not diagonal. At 16:9 the diagonal is roughly 15% larger than the width, so multiplying by the diagonal overstates the required distance by about the same amount.
87.16 inches wide and 49.03 inches high. The diagonal of a 16 by 9 rectangle is the square root of 337, or 18.3576 units, so the width is 100 times 16 divided by 18.3576.
No. Throw distance sets how far back the projector goes; vertical and horizontal offset set where the image lands on the wall. Offset is quoted separately on the specification sheet and has to be planned alongside this figure.
Because throw ratios differ between models, between optional lenses on the same model, and between revisions. Publishing a table would guarantee that some readers use a figure that does not apply to their unit, so the ratio stays an input.
The screen size calculator returns the real width, height and area of any screen from its diagonal and aspect ratio. This page starts from the same geometry but then applies a throw ratio to produce a projection distance and a zoom range, which the screen tool does not do.
Yes, because the same light is spread over more area. Image area grows with the square of the diagonal, so a 120 inch image has about 44% more surface than a 100 inch one at the same aspect ratio, and looks correspondingly dimmer for the same lumen output.
This page is a geometry tool. It computes distance from the throw ratio and image size you supply and cannot verify either figure. Confirm the throw ratio, offset and minimum image size against your projector's own specification sheet before drilling any mount.
