What Is the Screen Ratio Calculator?
This tool converts a screen's diagonal measurement and aspect ratio into its actual physical width and height. Manufacturers advertise displays by diagonal size (e.g. a "55-inch TV"), but to know whether a screen fits a space, a mount, or a media console, you need the real width and height. This calculator does that math instantly for any aspect ratio — 16:9 widescreen, 4:3 standard, 21:9 ultrawide, 16:10 monitors, and more.
How to Use It
Enter the diagonal size in inches, then enter the aspect ratio as two numbers (for a 16:9 TV, put 16 in the width box and 9 in the height box). Press calculate to get the exact width and height plus the screen's surface area.
The Formula Explained
Let r be the aspect ratio (width ÷ height). A screen forms a right triangle where the diagonal is the hypotenuse. Since width = \(r \times \text{height}\), the Pythagorean theorem gives \(D^{2} = W^{2} + H^{2}\). Substituting yields:
$$W = \sqrt{\frac{D^{2} \cdot r^{2}}{1 + r^{2}}} \quad\text{and}\quad H = \frac{W}{r}.$$
Worked Example
For a 55-inch 16:9 TV: \(r = 16/9 \approx 1.7778\).
$$W = \sqrt{\frac{55^{2} \times 1.7778^{2}}{1 + 1.7778^{2}}} = \sqrt{\frac{3025 \times 3.1605}{4.1605}} \approx \sqrt{2297.5} \approx 47.94 \text{ in wide}.$$
$$H = \frac{47.94}{1.7778} \approx 26.96 \text{ in tall}.$$
FAQ
Does this work for any aspect ratio? Yes — enter any width:height pair, such as 21:9, 4:3, or 16:10.
Are the results in inches? They use the same unit as the diagonal you enter. Enter the diagonal in inches and you get inches; enter centimeters and you get centimeters.
Why is a 55-inch TV not 55 inches wide? The 55 inches refers to the diagonal corner-to-corner; the width is always smaller than the diagonal.
