Although today's TVs may deliver unparalleled image and sound quality when compared to sets of the past, you might consider a projector as an alternative to a TV for various reasons. A projector can give you more flexibility regarding screen size while also allowing you to design a home theater that truly resembles a movie theater. However, to leverage a projector to its full potential, you also need to consider how factors like where you sit when watching a movie or show can affect your overall experience. One way to optimize content viewed through a projector is to learn and apply the "4-6-8 rule."
This guideline defines the ideal viewing distance from the screen by accounting for the screen's height and the viewer's intention. Per the 4-6-8 rule, if someone wants to analyze content on the screen, the ideal maximum viewing distance from said screen is four times the screen height. This viewing distance is helpful, for example, when going over data in a PowerPoint or similar presentation.
In a general presentation context, such as during a classroom lecture or a videoconference, the best viewing distance is a maximum of six times the height of the screen. For pure entertainment purposes, a viewer can engage with the content best if they sit at a distance equal to approximately eight times the screen's height.
Here's a theoretical scenario to help you understand what the 4-6-8 rule might look like in practice. While it's a helpful guideline, because most home theaters are limited in size, it cannot be easily applied without making some concessions or adjustments.
For example, you might want your projector's screen height to be 50 inches tall. Per the 4-6-8 rule, for optimal relaxed viewing, you'd have to sit 400 inches (or almost 34 feet!) away from the screen to hit the sweet spot. That's obviously not realistic. The room where you plan on installing the projector might not be large enough to accommodate that kind of distance.
Again, that's why you might have to make some trade-offs. You might have to settle for a slightly smaller screen size, a slightly closer viewing distance, or, most likely, a little of both. Your goal is to sit as close to eight times the height of the screen away from the screen itself to get the best experience. Naturally, you probably won't be able to achieve the "perfect" distance, but the 4-6-8 guideline can nevertheless help you make reasonably effective room design choices.
Similar rules can also help with similar situations. For example, the 1-2-10 rule can help you determine the best distance to view a traditional non-projector screen from. If audio speakers are part of your home theater setup, you can also apply the 83% rule for ideal sound quality. Just remember, perfection isn't the goal. Your comfort and personal preferences are what matter most.