Projector Calculator

throwDistance = throwRatio × imageWidth

throwRatio

Throw ratio, from the projector's specification sheet

imageWidth

Width of the projected image (m)

throwDistance

Distance from the lens to the screen (m)

Rearranged, the same expression answers the other two questions: divide the distance by the throw ratio to find how wide an image fits in the room you have, or divide the distance by the image width to work out the throw ratio of a projector you already own. The image width itself comes from the screen size and the aspect ratio, because the diagonal and the two sides make a right triangle — a 100-inch 16:9 screen is 2.21 m wide and 1.25 m tall. Note that the throw ratio multiplies the width and not the diagonal, so two screens of the same diagonal but a different shape need different distances. The table below holds the screen fixed at 100 inches and 16:9, so that only the projector changes.

1. Where a 1.5 projector has to sit for a 100-inch screen

   1. Known: throw ratio 1.5, screen 100 inches at 16:9.
   2. One unit of the ratio: 2.54 × 100 = 254 cm of diagonal, ÷ √(16² + 9²) = ÷ 18.36 = 13.84 cm.
   3. Image width: 16 × 13.84 = 221.4 cm = 2.21 m. Height: 9 × 13.84 = 124.5 cm = 1.25 m.
   4. Throw distance: 1.5 × 2.21 = 3.32 m from the lens to the screen.
   5. So the room needs 3.32 m of depth plus the length of the projector itself. ✓

   3.32 m is also the 1.5 row of the table below — the same screen, the same machine, so the two have to agree to the centimetre, and they do.

2. What 3 metres of room buys at a throw ratio of 1.5

   1. Known: throw ratio 1.5, room depth 3 m, aspect ratio 16:9.
   2. Image width: 3 ÷ 1.5 = 2 m.
   3. Image height: 2 ÷ (16 ÷ 9) = 2 ÷ 1.778 = 1.125 m, which rounds to 1.13 m.
   4. Diagonal: √(2² + 1.125²) = 2.2947 m, and 2.2947 ÷ 0.0254 = 90.34 inches, so 90.3.
   5. The nearest real screen size below that is 90 inches; a 92-inch screen would need 3.06 m.

   The diagonal is the hypotenuse of the image, not its width. Writing it as the width times the ratio would give 118 inches — a screen that is two feet too wide for the wall.

3. What an already-mounted projector works out to

   1. Known: distance 2.5 m from the lens to the screen, screen 80 inches at 16:9.
   2. One unit: 2.54 × 80 = 203.2 cm, ÷ 18.36 = 11.07 cm.
   3. Image width: 16 × 11.07 = 177.1 cm = 1.77 m.
   4. Throw ratio: 2.5 ÷ 1.77 = 1.41.
   5. Height: 9 × 11.07 = 99.6 cm, which is a metre to two decimal places.

   This is the direction to use when the projector is already on the ceiling: measure the distance and the width of the picture, and the ratio tells you what the machine is. It is also the number to quote when you replace it, since a new projector at 1.2 would fill the same screen from 2.13 m.

4. An ultra short throw projector under a 120-inch screen

   1. Known: throw ratio 0.25, screen 120 inches at 16:9.
   2. One unit: 2.54 × 120 = 304.8 cm, ÷ 18.36 = 16.60 cm.
   3. Image width: 16 × 16.60 = 265.7 cm = 2.66 m. Height: 9 × 16.60 = 149.4 cm = 1.49 m.
   4. Throw distance: 0.25 × 2.66 = 0.66 m.
   5. For comparison, a 1.5 machine would need 1.5 × 2.66 = 3.99 m for the same picture.

   This is why ultra short throw machines sit on the cabinet below the screen rather than across the room. The trade is that the projector has to be very precisely placed: at this ratio, moving it 10 cm changes the image width by 40 cm.

Three things this page cannot know. A throw ratio on a specification sheet is nominal — a zoom lens has a range such as 1.5–1.8, and the printed figure is usually one end of it, so the distance calculated here is the distance for that end of the range. The distance is measured from the front of the lens rather than from the back of the projector, so a ceiling mount also needs the depth of the machine and some clearance behind it. And the geometry assumes the full panel is used with no keystone correction: tilting a projector to square up an image it is not aligned to costs resolution, and a screen with a black border is a little smaller inside than its quoted diagonal. Vertical lens shift does not change any of this — it moves the image without resizing it.

How far from the screen does my projector need to be?

Multiply the throw ratio by the width of the image you want. A 100-inch 16:9 screen is 2.21 m wide, so a 1.5 projector needs 3.32 m, a 1.3 one needs 2.88 m, and a long throw 2.0 needs 4.43 m. Measure from the front of the lens, and remember that the room has to be that deep plus the length of the projector and a little space behind it for cables.

What is a throw ratio, in plain terms?

It is the distance from the lens to the screen divided by the width of the picture: a 1.5 projector throwing a 2 m wide image sits 3 m away. The number describes the shape of the projection cone, and it is the single figure that decides whether a projector suits a room. Below about 1 it is sold as short throw, above 2 as long throw, and the very small ones — 0.25 or so — are ultra short throw machines that sit against the wall under the screen.

What is the difference between throw ratio and aspect ratio?

They describe different shapes and the similar names confuse people constantly. The aspect ratio is the shape of the image on the screen: 16:9 is the widescreen television shape, 4:3 is the older squarer one, 21:9 is ultrawide. The throw ratio is the shape of the light path between the projector and the screen: how far back it has to be for a given image width. Both are ratios of one length to another, and that is the whole of the resemblance.

My room is 3 metres deep — how big a picture can I get?

Divide the distance by the throw ratio to get the image width, then work out what diagonal that is. At 1.5 and 3 m the picture is 2 m wide and 1.125 m tall, which makes a 90.3-inch diagonal — so a 90-inch screen fits and a 92-inch one would need 3.06 m. Enter the distance and the ratio above with the screen box left empty and the calculator does the whole chain, sizing box included.

What does a short throw projector change?

It changes the distance for the same picture, and nothing else. A 100-inch 16:9 screen needs 3.32 m from a 1.5 projector, 0.89 m from a 0.4 short throw, and 0.66 m from a 0.25 ultra short throw showing 120 inches. The trade is placement precision: at a very low ratio a small movement of the projector moves the image a lot, and those machines are usually mounted below the screen, where the geometry puts them, rather than opposite it.

Do I measure the distance from the lens or from the back of the projector?

From the front of the lens, which is where the throw ratio is defined from. The difference matters for a ceiling mount: a projector 30 cm deep with 10 cm of clearance behind needs the calculated distance plus 40 cm of room. Some manufacturers quote a throw distance range rather than a ratio, and it is the same measurement expressed at the two ends of the zoom, so a quoted 3.0–3.6 m is simply the zoom range for that screen.

• Recommendation ITU-R BT.2020: Parameter values for ultra-high definition television systems — ITU-R
• The International System of Units (SI Brochure) — BIPM