The 40% figure is about area, not width
Both numbers are right, and they answer different questions. Going from a 55-inch to a 65-inch 16:9 panel, each side grows 18.2% — 47.94 in becomes 56.65 in wide, 26.96 in becomes 31.87 in tall. The area grows 39.7%. Neither figure is the other one with a rounding slip: area is the square of the linear change, 1.1818² = 1.3967, so a 18.2% longer side produces a 39.7% larger rectangle.
That is why "40% bigger" and "3 inches wider" can describe the same upgrade. If you are checking whether the set fits a wall or a cabinet, the number you need is the 18.2% one: 8.72 in (22.1 cm) more width and 4.90 in (12.5 cm) more height. If you are judging how much more picture you get for the money, it is the 39.7% one. Quoting either alone is where the argument usually goes wrong.
What the two screens measure
At 16:9 with both panels at 3840 × 2160, the numbers work out like this:
55 inch — 47.94 × 26.96 in (121.8 × 68.5 cm), area 1,292.6 sq in, 80.1 PPI
65 inch — 56.65 × 31.87 in (143.9 × 80.9 cm), area 1,805.3 sq in, 67.8 PPI
Difference — +8.72 in wide (+18.2%), +4.90 in tall (+18.2%), +512.8 sq in (+39.7%), −12.3 PPI (−15.4%)
Pixel density is the one row that moves against the upgrade. The same 4K pixel grid spread over a larger panel is less dense: 80.1 PPI at 55 inches, 67.8 PPI at 65 inches, a 15.4% drop. From a normal sofa distance that difference is hard to see, but it is real, and it is why a 65-inch 4K set is not simply "the same picture, bigger".
Single-size numbers live on how wide is a 65 inch tv, which gives the width, height and area of one diagonal, with a table for 43 to 85 inches. Where to put the seat is on tv viewing distance. The same step in monitors — 24 to 27 inches — is worked out on 24 inch vs 27 inch monitor. If you only need the 55 inch numbers — width, height, height with stand — they are on 55 inch tv dimensions.
How the numbers are calculated
Every value comes from the diagonal and the aspect ratio; the resolution is layered on top for pixel density:
height = diagonal ÷ √((a ÷ b)² + 1)
width = (a ÷ b) × height
viewable area = width × height
PPI = √(pixels wide² + pixels high²) ÷ diagonal
percent change = (B − A) ÷ A × 100
Because the area percentage is computed from the two areas, not from the width percentage, it comes out at the square of the linear change whenever the two screens share a shape. Change one screen to 21:9 and that relationship breaks, which is exactly when a single "40% bigger" sentence stops being usable.
What is rounded
Width and height are shown to 2 decimals in inches (1 decimal in centimetres), area to 1 decimal with a thousands separator, pixel density to 1 decimal, and every percentage to 1 decimal. The arithmetic keeps full floating-point precision and only the display is rounded, so a difference that reads as 0.00 means the two screens agree at the shown precision, not that they are identical.
What is measured
All measurements describe the active rectangular panel. Bezels, the stand, chassis depth and any curvature are excluded, so these are the glass dimensions, not the product footprint. A real 65-inch set measures wider than 56.65 in once the frame is counted. Pixel density stays in PPI in both unit modes, because PPI is a fixed unit and does not convert.
Questions this page answers
Is a 65-inch TV really that much bigger than a 55?
In area, yes — 39.7% more. Each side is only 18.2% longer, so it reads as a modest step on a wall but a big one once you sit down.
Why does everyone say 40% bigger?
Because that is the area figure, and area is what fills your view. The width figure for the same jump is 18.2%, which is the one that decides whether it fits.
So how much wider is it, exactly?
8.72 in, or 22.1 cm, at 16:9. Height goes up 4.90 in (12.5 cm). Those are the numbers to check against a cabinet or a wall.
Will a 65 fit where my 55 sits now?
You need 8.72 in more width and 4.90 in more height of clear space. Add the frame on each side, and check the stand depth if it is not wall-mounted.
Is 4K sharper on a 55 than on a 65?
Yes, by 15.4%: 80.1 PPI against 67.8 PPI for the same 3840 × 2160 grid. Switch either screen to 1920 × 1080 and the drop gets much larger.
What if I only have room for the width?
Type your real limit into the B diagonal until the width row fits. A 16:9 panel that is 56.65 in wide is a 65-inch set, so the width row is the constraint that picks the size.