What is the Screen Size from Diagonal Calculator?
TVs, monitors, laptops and phones are almost always advertised by their diagonal measurement — a "55-inch TV" tells you the corner-to-corner distance, not how wide or tall the screen actually is. This calculator converts a diagonal size plus an aspect ratio into the real physical width and height of the display, and also reports the visible screen area.
How to use it
Enter the diagonal size in any unit (inches, centimetres — the output uses the same unit). Then enter the aspect ratio as two numbers, for example 16 and 9 for a standard widescreen TV, 21 and 9 for an ultrawide monitor, or 4 and 3 for an old display. Click calculate to see the width, height and area.
The formula explained
Let \(r = w/h\) be the aspect ratio. The diagonal forms the hypotenuse of a right triangle whose legs are the width and height. Since width = r × height, the Pythagorean theorem gives \(\text{diagonal}^2 = (r \cdot \text{height})^2 + \text{height}^2 = \text{height}^2 (r^2+1)\). Solving:
$$\text{height} = \frac{\text{diagonal}}{\sqrt{r^2+1}}$$ and $$\text{width} = \frac{\text{diagonal} \times r}{\sqrt{r^2+1}}$$. The area is simply \(\text{width} \times \text{height}\).
Worked example
For a 55-inch 16:9 TV, \(r = 16/9 \approx 1.7778\) and \(\sqrt{r^2+1} = \sqrt{3.1605+1} = \sqrt{4.1605} \approx 2.0397\). So $$\text{height} = \frac{55}{2.0397} \approx 26.96 \text{ in}$$ and $$\text{width} = \frac{55 \times 1.7778}{2.0397} \approx 47.94 \text{ in}.$$ Area = \(47.94 \times 26.96 \approx 1292.58\) square inches.
FAQ
Does the unit matter? No — output width, height and diagonal share the same unit; area is that unit squared.
Why is the width less than the diagonal? The diagonal is the longest line across the rectangle, so it always exceeds both the width and the height.
Can I use any aspect ratio? Yes. Try 16:10, 21:9, 32:9 or 3:2 — just enter the two numbers.
