How this instrument works
How far you should sit from a TV isn't just a matter of taste — it follows directly from trigonometry once you pick a target viewing angle, the horizontal angle the screen fills in your field of view from your seat. A wider viewing angle (sitting closer relative to screen size) feels more immersive and cinema-like, up to a point; too wide and you can't take in the whole screen without moving your eyes or head, which becomes fatiguing rather than immersive.
THX, the audio/video certification standard, recommends a 40-degree viewing angle as its "immersive" reference point for home theater — for a 16:9 screen, that works out to sitting at roughly 1.2 times the screen's diagonal measurement, a commonly cited practical rule of thumb this calculator's formula reproduces almost exactly. Other reference angles exist too: a narrower ~30-degree angle (closer to 1.6x diagonal) is a more relaxed viewing distance some enthusiasts and standards bodies like SMPTE reference, while the older, more conservative ~20-degree angle (2.5x diagonal) reflects more traditional retailer and manufacturer recommendations from the earlier HDTV era.
The constant in this formula, 8 divided by the square root of 337, isn't an arbitrary number — it's exactly the half-width-to-diagonal ratio for a standard 16:9 screen, derived directly from the 16:9 aspect ratio itself (16 divided by twice the square root of 16 squared plus 9 squared). For an ultra-wide or non-16:9 display, this exact constant wouldn't apply, though the same general trigonometric approach would, with a different width-to-diagonal ratio.
- Enter TV screen diagonal in inches — the screen size as commonly advertised.
- Enter Target horizontal viewing angle in degrees — 40 for THX's immersive reference, 30 for a more relaxed SMPTE-style viewing angle, or your own preferred angle.
- Read Optimal viewing distance in inches and feet — the recommended seating distance for your chosen viewing angle.
Worked example — a 65-inch TV at THX's 40-degree angle
A 65-inch TV at THX's 40-degree "immersive" reference angle: distance = (8/sqrt(337)) x 65 / tan(20 degrees) = 0.43579 x 65 / 0.36397 = 28.3262 / 0.36397 = 77.83 inches, or 6.49 feet. That matches THX's own commonly cited rule of thumb — roughly 1.2 times the diagonal for a 40-degree immersive field of view (1.2 x 65 = 78 inches) — almost exactly, confirming the exact trigonometric formula and the simplified rule of thumb agree.
The same 65-inch TV at a more relaxed 30-degree angle sits farther back, as expected for a narrower target angle: distance = 0.43579 x 65 / tan(15 degrees) = 28.3262 / 0.26795 = 105.71 inches, about 8.81 feet. And scaling up to an 85-inch TV at the same 40-degree angle: distance = 0.43579 x 85 / tan(20 degrees) = 37.042 / 0.36397 = 101.77 inches, or 8.48 feet — the distance scales exactly linearly with screen diagonal at a fixed viewing angle, as the formula's structure guarantees.
Questions
What viewing angle should I use?
40 degrees is THX's "immersive" reference angle, widely cited for a cinema-like home theater feel, and works out to roughly 1.2 times the screen's diagonal in viewing distance. A more relaxed, general-living-room viewing angle closer to 30 degrees (about 1.6x diagonal) is a common alternative some standards bodies and enthusiasts prefer for everyday, less immersive TV watching, where sitting quite that close for every viewing session feels excessive. There's no single "correct" answer — it's a preference trade-off between immersion and comfort.
Why does distance scale exactly linearly with screen diagonal?
Because at a fixed target viewing angle, the trigonometric formula reduces to distance = a constant times diagonal — the angle term (tan of half the viewing angle) doesn't change, so doubling the diagonal exactly doubles the required distance to maintain that same angle. That's why simplified rules of thumb like "1.2x diagonal" work as a quick shortcut once you've picked your target angle, without needing to redo the trigonometry each time.
Where does the 8/sqrt(337) constant come from?
It's the exact half-width-to-diagonal ratio for a standard 16:9 aspect-ratio screen, derived directly from the aspect ratio itself: for a 16:9 screen, width = 16 parts and height = 9 parts of a common unit, so the diagonal is sqrt(16 squared + 9 squared) = sqrt(337) of that same unit, and half the width is 8 of it. It isn't an arbitrary tuning constant — it falls straight out of the 16:9 geometry, which is why it reproduces the well-known 1.2x-diagonal-at-40-degrees rule of thumb so precisely.
Does this formula work for an ultra-wide or non-16:9 display?
Not with this exact constant — 8/sqrt(337) is specific to a 16:9 aspect ratio screen, which covers the overwhelming majority of consumer TVs. An ultra-wide monitor or a different aspect-ratio display would need the same general trigonometric approach but with a different half-width-to-diagonal ratio calculated from that display's actual aspect ratio.
Is a closer viewing distance always better for immersion?
Only up to a point. THX itself notes that a wider field of view increases the feeling of presence up to roughly an 80-degree plateau, but sitting so close that you can't comfortably take in the whole screen without moving your eyes or head becomes fatiguing rather than more immersive, and it also means you'll more easily notice pixel structure or compression artifacts on lower-resolution content. 40 degrees is specifically chosen as a strong-but-comfortable immersive target, not the theoretical maximum.