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How far to put projector away from the screen? 

Every projector is made differently, some projector come with lens as a all in one unit, some come with interchangeable lens (commonly found in installation projector). Different lens have different throw ratio.  The way the lens is made (the optic's components inside the lens) determines it's throw ratio. Throw ratio come with a number like 1.3:1  What this mean is that for every 1m width of the screen, it needs to take back 1.3m away from the screen. The first number is the distance to the proportion to the second number which is the width of the screen. For 2m wide screen, it needs to be taken back 2.6m (1.3 x 2m) away, and for 3m wide screen, 3.9m (1.3 x 3m) away...etc

You may sometime see there is a number like 1.3 ~ 2.2:1 What this mean is that there is a optical zoom in the projector lens, where it can produce a smaller or a bigger picture at a fixed point, or you can install the projector at a range of distance. E.g for 1.3 ~ 2.2:1 for a 2m wide screen, you can either install the projector at the minimal distance of 2.6m (1.3 x2m) up to 4.4m (2.2 x 2m) away.

If you have plenty of space and can install the projector at any distance you like, throw ratio shouldn't be a problem to you. If you're replacing an old projector (old projector usually have large throw ratio number) and not wanting to move the mounting point, you may need a projector with big throw number and a big range of throw ratio.

Most of the short throw projector have a throw ratio e.g 0.5:1, it is easier to position, as its closer to the screen. 1m away will produce a 2m wide screen. The presenter will have less eye strain, as the projector will not project directly to the presenter.

Ultra Short Throw projector usually have a throw ratio of 0.25:1 You can position the projector even closer to the screen (50cm away will produce a 2m wide screen), twice as close compare to short throw projector or four or five times closer comparing to normal throw projector.

Drawback of above short throw projector is that, it needs to be project on a wall or a tensioned material like a fixed screen. 

Please checkout below Projector Distance Calculator:

Benq Projector

Epson Projector

Nec Projector

Optoma Projector

Panasonic Projector

Sony Projector

Viewsonic Projector