How viewing distance recommendations work
Two main factors determine a comfortable viewing distance: the apparent size of the screen (how much of your field of view it fills) and the pixel density relative to your eye's resolving power. Sit too close and you can see individual pixels; sit too far and the screen fills too little of your field of view to be immersive.
THX recommends a viewing angle of about 40 degrees for a cinema-like experience in the home, which corresponds to a seating distance between 0.75 and 1.0 times the screen diagonal. SMPTE recommends a 30-degree viewing angle for a more conservative living room setting.
SMPTE distance = (Screen width / 2) / tan(15°)
A 30-degree total viewing angle means the screen edge subtends 15 degrees from the centre.
Pixel blur distance = Screen height × 3438 / Vertical pixels
The closest distance at which a typical human eye cannot resolve individual pixels, based on the 1 arcminute visual acuity limit.