How it works
Two common guidelines tie screen size to how much of your field of view it fills. SMPTE recommends the screen take up at least 30° for general viewing; THX recommends about 40° for a cinema-like experience.
For a 16:9 TV, the 30° guideline works out to sitting about 1.6 times the diagonal away, and 40° to about 1.2 times the diagonal.
Resolution matters too. With normal 20/20 vision you can resolve about one arcminute. The 4K and 1080p figures show where individual pixels become too small to see, so sitting farther than that means you are not getting the full benefit of the resolution.
Formula
Distance = screen width ÷ (2 × tan(angle ÷ 2)); width = diagonal × 16 ÷ √337
Questions people ask
What size TV for an 8 foot distance?
About 59 inches by the SMPTE 30° guideline and about 80 inches by THX 40°. A 65-inch TV is a popular middle ground.
Can a TV be too big?
If it fills much more than 40° of your view you may need to move your eyes or head to follow the action, which some people find tiring. Mounting height matters too: the center should be near eye level when seated.
Does 4K let me sit closer?
Yes. Because the pixels are a quarter the size of 1080p, you can sit about half as far away before the picture looks pixelated.