Screen Size Calculator

Display dimensions are fundamentally governed by geometry and the Pythagorean theorem. Given a screen's diagonal length ($d$) and its aspect ratio ($A_1:A_2$), the physical width ($W$) and height ($H$) can be derived using trigonometric ratios and scaling factors. First, we determine the relative scaling factor from the aspect ratio. The diagonal is calculated as the hypotenuse of the width and height: $d = \sqrt{W^2 + H^2}$. For curved displays, additional parameters like radius ($R$) and arc length ($L$) account for the depth of the curve using circular segment formulas: $W_{curved} = 2R \sin(L / 2R)$ and $D_{curved} = R(1 - \cos(L / 2R))$.

Let us calculate the physical width and height of a standard widescreen 120-inch television with a 16:9 aspect ratio. First, we identify our inputs: Diagonal ($d$) = 120 inches, Aspect Ratio = 16:9. Using the proportion formula where height is scaled against the ratio, we determine the height ($H$) is approximately 58.88 inches. Next, we calculate the width ($W$) by multiplying the height by the width-to-height ratio (16/9 or 1.7778), yielding approximately 104.68 inches. Finally, the total screen area is found by multiplying width by height, giving us roughly 6,163 square inches of viewing space.

Always measure the actual panel rather than the outer plastic bezel when evaluating physical space constraints for mounting. Remember that aspect ratios dictate screen geometry completely; a 16:9 monitor will always have a different physical height than a 21:9 ultrawide monitor sharing the same diagonal measurement. When dealing with curved monitors, account for the extra desk depth required by the radius of the curvature.