How this calculator works
How big a TV should be depends on how far you sit from it: too small at a given distance and detail is wasted; too large and the picture can feel overwhelming or reveal compression artifacts. This calculator uses two widely cited industry viewing-angle conventions to turn a distance into a recommended size range, or a size into a recommended distance range.
THX recommends a wider viewing angle (about 40 degrees) intended to fill more of the viewer's field of view for an immersive, cinema-like experience. SMPTE's more conservative convention (about 30 degrees) is often cited as the minimum for comfortable critical viewing. Between them they bracket a reasonable size or distance range rather than dictating one 'correct' answer.
The formulas
16:9 screen width from diagonal: width = diagonal × 16 ÷ √(16² + 9²) ≈ diagonal × 0.8716Screen width needed for a viewing angle θ at distance d: width = 2 × d × tan(θ ÷ 2)Distance needed for a viewing angle θ at width w: distance = w ÷ (2 × tan(θ ÷ 2))θ is the full angle the screen's width subtends at your eye. THX uses θ ≈ 40°; SMPTE uses θ ≈ 30°. The 0.8716 constant comes from the Pythagorean relationship between a 16:9 rectangle's width and its diagonal.
Worked example: sitting 8 feet from the screen
- Convert to inches: 8 feet = 96 inches.
- SMPTE width = 2 × 96 × tan(15°) ≈ 51.4 inches, giving a diagonal of 51.4 ÷ 0.8716 ≈ 59.0 inches.
- THX width = 2 × 96 × tan(20°) ≈ 69.9 inches, giving a diagonal of 69.9 ÷ 0.8716 ≈ 80.2 inches.
- So an 8-foot viewing distance suggests a screen somewhere between about 59 and 80 inches, depending on how immersive you want the picture to feel.
Frequently asked questions
Which convention should I actually use, THX or SMPTE?
Neither is officially 'correct' for a living room — SMPTE's 30° is a conservative, closer-to-traditional recommendation, while THX's 40° pushes toward the wider field of view used in commercial cinemas. Many buying guides suggest picking somewhere in between based on personal preference and room layout.
Does this apply to any screen shape?
The width-from-diagonal formula here assumes a 16:9 screen, which is standard for essentially all HDTVs, 4K and 8K TVs sold today. Movie projection or an ultrawide monitor would need a different width-to-diagonal ratio.
Why does a bigger screen need more distance?
The viewing angle formulas hold the angle constant, so a wider screen needs a proportionally greater distance to keep that same angle. It is the same reason you back away from a large cinema screen but sit close to a small phone screen.
Does 4K resolution change the ideal distance?
Higher resolution lets you sit closer without seeing individual pixels, which is why some 4K buying guides suggest distances below the SMPTE range calculated here. This calculator's ranges are based purely on viewing angle, not resolution or visual acuity.
What size TV should I get for a 10-foot viewing distance?
At a 10-foot (120-inch) viewing distance, the SMPTE convention (a 30-degree viewing angle) recommends about a 74-inch screen, while the THX convention (a 40-degree viewing angle) recommends about a 100-inch screen. Both come from the same width = 2 × distance × tan(angle ÷ 2) formula used throughout this calculator, converted to a diagonal using the 0.8716 constant for a standard 16:9 screen.