Projector Throw Distance Calculator

Background.

Every projector's placement comes down to one published number: the throw ratio. BenQ defines it in one line — "Throw ratio is the width (W) of the image in relation to the throw distance (D)" — and gives the worked meaning: "If the throw ratio on a projector is 2.0, that means that for every 1ft of image width, the projector needs to be 2ft away." Everything on this page is that relationship, rearranged three ways.

The subtlety that trips people up is the word *width*. Throw ratio is measured against the image width, not the diagonal that screens are sold by, so a 120-inch screen does not put the projector 120 × the ratio away. A 16:9 image with a 120-inch diagonal is 104.59 inches wide, and at a 1.32 throw ratio the projector sits 138.06 inches — 11 ft 6 in — from the screen. Using the diagonal instead would have put it at 158 inches, over a foot and a half too far back, and the image would have overshot the screen.

You can check this against a manufacturer's own numbers. The Epson Home Cinema 3200/3800 user's guide prints a projection-distance table for 16:9 screens: 40 inches needs 46 to 74 inches of distance, 100 inches needs 116 to 188, 120 inches needs 139 to 226, and 200 inches needs 233 to 377. Dividing each of those by the corresponding image width gives 1.32 to 1.34 at the wide end of the zoom and 2.12 to 2.16 at the tele end — which is exactly the 1.32–2.15 throw ratio Epson publishes for the projector. The whole table is one multiplication.

That same guide contains a trap worth knowing about. Its 4:3 table lists 142 inches of distance for a 100-inch 4:3 image, and 142 divided by the 80-inch picture width is 1.775, nothing like 1.33. The reason is that the projector's imaging chip is 16:9: a 4:3 image 60 inches tall is inscribed in a 16:9 frame 106.67 inches wide, and 142 divided by 106.67 gives 1.331 — the real ratio. **The throw ratio is measured on the full projected frame, not on the part of it you can see.** If you are showing content in a shape the projector is not native to, work in the frame width.

The three modes cover the three ways this problem arrives. Distance mode is for when the screen is already chosen and you need to know where to drill the ceiling mount. Image mode is for when the mounting point is fixed — a shelf, an existing electrical box, a beam — and you need to know what size screen that gives you. Ratio mode is for when both the room and the screen are fixed and you are still shopping: it gives you the number to look for on the spec sheet, which is far more useful than a model name.

Aspect ratio is entered as two numbers rather than picked from a list, so 16:9 home cinema, 16:10 data-projector, 4:3 legacy and 2.35:1 cinemascope screens all work. What this page does not do is classify your ratio as "short throw" or "long throw". Epson's own projector guide defines those categories by distance — short throw as "between 3 to 8 feet away from projector to screen", ultra-short throw as "between 0 to 4 feet" — and no manufacturer or standards body publishes a throw-*ratio* threshold for them. Rather than invent a boundary, the page reports the geometry and leaves the label to the marketing department.

One last caveat on accuracy. Published throw ratios are rounded, usually to two decimal places, and that rounding is worth about a per cent of the distance: the 1.32 the calculation above uses is really nearer 1.329, which is why Epson prints 139 inches for the case that works out here at 138.06. Use this to plan and to shop; use the projector's own distance table for the final drill marks. Lens shift, keystone and vertical offset are separate numbers in that table and are not modelled here.

What is projector throw distance calculator?

Throw distance is the distance from a projector's lens to the screen surface — as Epson's projector guide puts it, "the distance between the projector and the image on the screen (i.e., the distance that the image is 'thrown')". Throw ratio is that distance divided by the width of the image it produces, and it is the single specification that determines where a given projector has to sit.

Because the relationship is a straight proportion, all three quantities follow from any two: distance = ratio × width, width = distance ÷ ratio, and ratio = distance ÷ width. The image width itself comes from the screen's diagonal and aspect ratio by Pythagoras, which is why the diagonal a screen is sold by is never the number to multiply. Projectors with zoom lenses publish a range of ratios rather than one value, and that range translates directly into a window of positions from which the same screen can be filled.

How to use this calculator.

1. 01Find the throw ratio on the projector's specification sheet. It is usually written as a range, such as 1.32–2.15, for a zoom lens.
2. 02Enter the screen's diagonal and its aspect ratio as two numbers — 16 and 9 for home cinema, 16 and 10 for a data-projector screen, 4 and 3 for a legacy screen, 2.35 and 1 for cinemascope.
3. 03Leave the mode on the first option to get the distance from lens to screen. Run it twice, once at each end of the zoom range, to get the window of usable positions.
4. 04If the mounting point is fixed instead, switch to the second mode and enter the distance to see what size image you get.
5. 05If you are still choosing a projector, switch to the third mode: enter your screen size and the distance the room allows, and the result is the throw ratio to shop for.
6. 06Measure from the front of the lens to the screen surface, not from the wall behind the projector or the back of the case.
7. 07Check the result against the projector's own distance table before drilling; published ratios are rounded and the table is authoritative.

The formula.

The throw ratio is a plain proportion: TR = d ÷ W, where d is the lens-to-screen distance and W is the width of the image. Rearranged, d = TR × W and W = d ÷ TR. A projector's optics fix TR (or a range of it, if the lens zooms), so distance and image width are locked together — you cannot change one without changing the other.

The work is in getting W. Screens are sold by their diagonal, so the width has to be recovered from the diagonal and the aspect ratio. For a screen whose sides are in the ratio a : b, both sides share a scale factor k with width a·k and height b·k, and Pythagoras gives D² = k²(a² + b²), so k = D ÷ √(a² + b²). The width is then W = a·D ÷ √(a² + b²). For the near-universal 16:9 shape, √337 = 18.3576, so W = 0.8716 D — a 120-inch screen is 104.59 inches wide and 58.83 inches tall.

Putting the two together: d = TR × a × D ÷ √(a² + b²). At TR = 1.32 on a 120-inch 16:9 screen that is 1.32 × 104.5891 = 138.06 inches, or 11.50 feet, or 3.51 metres. Because the relationship is linear in D, doubling the screen size doubles the distance — and the constant of proportionality, TR × 0.8716 for a 16:9 screen, is how far the projector moves per inch of diagonal.

The third mode inverts the whole chain. Given a screen you already own and a distance the room forces on you, TR = d ÷ W tells you the specification a projector must meet. This is the most practically useful of the three, because it converts an architectural constraint into a shopping filter: a room that only allows 8 feet in front of a 120-inch screen needs a throw ratio near 96 ÷ 104.59 = 0.92, which rules out every standard-throw projector on the market and points straight at the short-throw shelf.

One subtlety carries through all three modes. The width in the ratio is the width of the projector's full imaged frame. When the content's shape matches the projector's native shape, that is the same as the visible picture width. When it does not — a 4:3 image on a 16:9 chip, or a 2.35:1 film letterboxed inside a 16:9 frame — the frame is wider than the picture, and using the picture width will place the projector too close. The Epson tables demonstrate this exactly: the 4:3 distances only reconcile with the projector's 1.33 ratio once the surrounding 16:9 frame is taken as the width.

A worked example.

Frequently asked questions.

References& sources.

1. [1]BenQ Knowledge Center — 'What is a Good Throw Ratio and Why Does it Matter?': 'Throw ratio is the width (W) of the image in relation to the throw distance (D)', 'D/W = 2/1', and 'If the throw ratio on a projector is 2.0, that means that for every 1ft of image width, the projector needs to be 2ft away.'
2. [2]Epson — Home Cinema 3200/3800 User's Guide, 'Projection Distance': the 16:9 projection-distance table (40 in → 46 to 74 in; 100 in → 116 to 188 in; 120 in → 139 to 226 in; 200 in → 233 to 377 in, Wide to Tele), the 4:3 table, and the per-screen-size lens-shift offsets.
3. [3]Epson — Projector Guide: Throw Distance and Positioning: 'A projector's throw distance is the distance between the projector and the image on the screen (i.e., the distance that the image is "thrown")', with short throw given as 3 to 8 feet and ultra-short throw as 0 to 4 feet — distance ranges, not throw-ratio thresholds.
4. [4]Recommendation ITU-R BT.709-6 (06/2015), Table 1 — aspect ratio 16:9 with 1:1 (square) pixels, the default screen shape used here. International Telecommunication Union.
5. [5]National Institute of Standards and Technology, Office of Weights and Measures — SI Units: Length. 'The value for the inch, derived from the value of the Yard effective July 1, 1959, is exactly equivalent to 25.4 mm.' Used for the metre output.