What is the Projector Screen Size Calculator?
Screen and TV sizes are advertised by their diagonal measurement, but what you really need to plan a room is the actual width and height of the picture. This calculator converts any diagonal size and aspect ratio into precise width, height, and surface area, in both inches and centimeters.
How to use it
Enter the diagonal size in inches, then set the aspect ratio as a width and height pair — for example 16 and 9 for a modern HD/4K screen, 4 and 3 for older standard format, or 21 and 9 for ultrawide cinema. The result shows the screen width times height, the metric equivalents, and the total screen area.
The formula explained
If the aspect ratio is \(AR = \text{width}/\text{height}\), then a diagonal \(D\) forms a right triangle whose sides are the width and height. By the Pythagorean theorem, \(\text{width}^2 + \text{height}^2 = D^2\). Substituting \(\text{width} = AR \cdot \text{height}\) gives the following:
$$\text{height} = \frac{D}{\sqrt{AR^2 + 1}}, \qquad \text{width} = \frac{D \cdot AR}{\sqrt{AR^2 + 1}}$$The area is simply \(\text{width} \times \text{height}\).
Worked example
For a 100-inch 16:9 screen, \(AR = 16/9 \approx 1.7778\), so \(\sqrt{AR^2+1} \approx 2.0396\).
$$\text{Width} = \frac{100 \times 1.7778}{2.0396} \approx 87.16 \text{ in}$$$$\text{Height} = \frac{100}{2.0396} \approx 49.03 \text{ in}$$The area is about \(87.16 \times 49.03 \approx 4{,}273\) square inches.
FAQ
Why isn't a 100-inch screen 100 inches wide? The 100 inches is the diagonal across the rectangle, so the width is always smaller than the diagonal.
What aspect ratio should I use? Most projectors and TVs are 16:9. Use 4:3 for legacy content and 21:9 for ultrawide/cinemascope setups.
How do I get centimeters? The calculator multiplies inches by 2.54 automatically and shows the metric width and height.
