Screen Aspect Ratio Calculator (16:9, 21:9, 4:3 …)

Understanding the screen aspect ratio calculator — concept and principle

Monitors and TVs are sold by their diagonal in inches, but what you actually need to know is how wide and how tall the screen is: will it fit between the speakers, on the desk, in the TV cabinet? This calculator takes an aspect ratio such as 16:9, 16:10, 21:9 or 4:3 and a diagonal, and returns the width and height of the visible picture in centimetres and inches, plus the screen area.

How it is calculated

For a ratio a:b and a diagonal D:

• k = D ÷ √(a² + b²)
• Width W = a × k, height H = b × k (in inches, the same unit as D)
• Centimetres = inches × 2.54
• Area (cm²) = W × H × 6.4516

"21:9" is treated as 64:27 (about 2.37:1), the true shape of 2560 × 1080 and 3440 × 1440 ultrawide panels.

The principle

The width, the height and the diagonal of a rectangle form a right triangle, so by Pythagoras W² + H² = D². The ratio fixes the shape: W = a·k and H = b·k for some scale k. Putting those into Pythagoras gives k²(a² + b²) = D², so k = D/√(a² + b²). For 16:9, √(16² + 9²) = √337 ≈ 18.358, which means the width is about 87% of the diagonal and the height about 49%. Because area scales with the square of the size, a 32″ screen has (32/27)² ≈ 1.40 times the area of a 27″ screen of the same ratio.

Worked example

Default inputs: 16:9, 27 inches.

1. √(16² + 9²) = √337 ≈ 18.358.
2. k = 27 ÷ 18.358 ≈ 1.4708.
3. Width = 16 × 1.4708 ≈ 23.53 in; height = 9 × 1.4708 ≈ 13.24 in.
4. In centimetres: 23.53 × 2.54 ≈ 59.8 cm and 13.24 × 2.54 ≈ 33.6 cm (59.77 × 33.62 cm).
5. Area: 23.53 × 13.24 × 6.4516 ≈ 2,010 cm².

How to read the result

The numbers describe the active picture only. The real monitor is wider and taller because of the bezel and the stand, often by 1–3 cm on each side, so check the product's spec sheet for the outer dimensions. When comparing ratios at the same diagonal, the squarer screen has more area: a 27″ 4:3 screen is noticeably taller and larger in area than a 27″ 16:9 one. For ultrawides, compare the height: a 34″ 21:9 is about as tall as a 27″ 16:9.

Common mistakes

• Assuming the diagonal tells you the width; the ratio changes it a lot.
• Using 21:9 literally; most "21:9" panels are 64:27, and a few are 43:18 (2.39:1).
• Forgetting the bezel and stand when measuring a cabinet or a desk.
• Comparing screen area by diagonal alone: area grows with the square.

Frequently asked questions

How big is a 27-inch 16:9 monitor?

The picture is about 59.8 × 33.6 cm (23.5 × 13.2 in).

Is a 1920 × 1080 screen 16:9?

Yes. 1920/1080 reduces to 16/9. So do 1280 × 720, 2560 × 1440 and 3840 × 2160; 1920 × 1200 is 16:10.

Why does 21:9 use 64:27?

2560 × 1080 and 3440 × 1440 panels have a width-to-height ratio of about 2.37, which is 64:27; 21:9 is a marketing label.

How tall is a 34-inch ultrawide?

At 64:27, about 33.6 cm high and 79.6 cm wide, almost exactly the height of a 27-inch 16:9 screen.

Sources: Euclid, Elements, Book I, Proposition 47 (Pythagorean theorem) · NIST Special Publication 811 (2008), Appendix B (1 in = 2.54 cm exactly)