How bright projector do I need?

I am doing a show at a very small stage, around a small school size. I need to project onto a screen around 3m away and there will be other coloured lights such as par cans in operation. So how bright does the projector need to be to just be seen over the lights? Thanks
 
Front or rear?

How many pars?

Are they pointed at the screen?

What's your budget?

Renting or purchasing?
 
5k if your low budget

10-12k if your high budget.

Point of reference this is 3k with no ambient light.

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There's actually a few more questions that need to be asked. How large is the image going to be? The larger your image, the brighter you will need. If you are front projecting, what are you projecting on and from where? What kind of content are you projecting? If it is anything more than a bright image, you probably won't see much. The more light that is on your screen, then the less contrast ratio that you will have in your image. This means that if your content is dependent on contrast (like an action movie where details are in the shadows) then you will need to come up with another plan.

If your PAR cans are going to be directly hitting the screen, forget about projection. If it is bounce, then you have a chance, as seen above.
 
PARs are notorious for spill. Use ellipsoidals, barn doors, snoots, whatever you have to keep direct light from hitting the screen. Controlling the light is easier and cheaper than getting a high horsepower projector.
 

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