How many lumens does my projector need?

The lumen number matters less than two things it depends on: how much light you can keep out of the room, and how big an image you are spreading that light across.

A dark, dedicated room needs far less brightness than a living room with a west-facing window and a marble floor that bounces every photon back at the screen. Double the screen area and the same projector puts half the light on each square metre; the picture goes grey before it goes dim, and grey is what kills contrast. So the sequence is: fix light control first, decide screen size second, and only then ask how many lumens.

Now the manufacturer's number. Lumen ratings are measured under ideal conditions, in a mode you would never watch in, and the measurement method differs between brands. Is the claim plausible? Usually, in that mode. Is it what you will get in your calibrated picture preset with the lamp or laser at a sensible level? Rarely. Treat the figure as a within-brand comparison, not an absolute. Two projectors from different companies with the same rating can look visibly different in brightness on the same wall. Nobody has been sued yet, which tells you how much room the standard leaves.

The other variable is the screen. In a room with light you cannot control, an ambient-light-rejecting screen changes the equation more than an extra few hundred rated lumens would, because it throws the room's stray light away instead of adding it to the picture. In a blacked-out room an ALR screen is money that should have gone into the projector.

What I would do before buying anything: tell us the room's light situation (curtains, direction of windows, when you watch), the screen size you have in mind and what you mostly watch. We will shortlist projectors that are actually bright enough for that combination and tell you plainly whether an ALR screen belongs in your budget or not. Chasing the biggest lumen number is how people end up with a bright projector and a washed-out picture.