TV Size Calculator (inches → width, height, area)

Understanding the TV size calculator — concept and principle

TV and monitor sizes are sold by the diagonal of the visible picture in inches, which says little about how wide the screen really is. This calculator turns a diagonal into the actual width, height and area of a 16:9 screen in centimetres, and compares its area with a 55-inch set. Use it before buying to check whether a TV fits a cabinet, wall or alcove, and to see how much bigger a step up in size really is. Korean "형" sizes are the same inches (65형 = 65 inches).

How it is calculated

For a 16:9 screen with diagonal d (inches):

• width W = d × 16 ÷ √(16² + 9²) = d × 16 ÷ √337 ≈ d × 0.8716
• height H = d × 9 ÷ √337 ≈ d × 0.4903
• centimetres = inches × 2.54; area (cm²) = W × H × 6.4516
• area vs 55-inch = d² ÷ 55²

Widths, heights and the diagonal are rounded to 0.1 cm, the area to 1 cm² and the comparison to 1 %.

The principle

Width, height and diagonal form a right triangle, so Pythagoras' theorem applies: W² + H² = d². With the 16:9 aspect ratio fixed, the sides are 16 and 9 parts of a triangle whose hypotenuse is √337 ≈ 18.36 parts. Scaling that triangle to your diagonal gives the width and height. Because area grows with the square of the diagonal, a small increase in inches gives a much larger increase in picture: 10 % more diagonal means about 21 % more area.

Worked example

Default input: a 65-inch TV.

1. Diagonal in cm: 65 × 2.54 = 165.1 cm.
2. Width: 65 × 16 ÷ √337 = 56.65 in × 2.54 = 143.9 cm.
3. Height: 65 × 9 ÷ √337 = 31.87 in × 2.54 = 80.9 cm.
4. Area: 56.65 × 31.87 × 6.4516 ≈ 11,647 cm².
5. Versus 55-inch: 65² ÷ 55² = 1.397, shown as 140 %.

How to read the result

The numbers describe the visible screen only. The cabinet with its frame is usually a little larger, and stands or wall brackets add height and depth, so check the maker's product dimensions before you buy. Typical screen widths are about 122 cm for 55 inches, 144 cm for 65 inches and 166 cm for 75 inches.

Common mistakes

• Thinking a 65-inch TV is 65 inches wide; it is about 57 inches (144 cm) wide.
• Assuming 75 inches is "15 % bigger" than 65; the area is about 33 % larger.
• Using these 16:9 formulas for ultrawide (21:9) or 4:3 screens.

Frequently asked questions

How wide is a 65-inch TV?

About 143.9 cm of picture; the whole TV is usually a little wider.

How much bigger is a 75-inch TV than a 65-inch?

75² ÷ 65² ≈ 1.33, so about 33 % more screen area.

Does a 4K TV have a different size than a 1080p TV?

No. Resolution changes the pixel count, not the physical dimensions for the same diagonal.

Sources: ITU-R Recommendation BT.709 (HDTV parameters, 16:9 aspect ratio) · NIST Special Publication 811 (2008), Appendix B (1 inch = 2.54 cm exactly)