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Screen Diagonal to Width/Height Converter

Calculate a screen's actual width and height from its diagonal size and aspect ratio.

Result

Width
47.9 in / 121.8 cm
Height
27 in / 68.5 cm

Uses the Pythagorean theorem: for an aspect ratio of W:H, the diagonal splits proportionally so width and height can be solved from the diagonal length alone.

About the Screen Diagonal to Size

The Screen Diagonal to Width/Height Converter turns a single diagonal measurement, the number printed on every TV and monitor box, into the actual physical width and height of the screen. Retailers advertise displays only by diagonal inches, which leaves buyers unable to check whether a screen will fit a media cabinet, wall mount, or desk without doing the trigonometry themselves. This tool does that math instantly for any diagonal size and any of five common aspect ratios.

How It Works

Enter the diagonal size in inches and pick an aspect ratio (16:9, 16:10, 4:3, 21:9, or 1:1). The calculator treats the diagonal as the hypotenuse of a right triangle whose legs are the screen's width and height, solves for the shared scale factor implied by the ratio, and multiplies that factor by the ratio's two numbers to get width and height in both inches and centimeters.

k = diagonal / sqrt(ratioWidth^2 + ratioHeight^2); Width = k x ratioWidth; Height = k x ratioHeight. Centimeters = inches x 2.54.

Formula & Methodology

For a ratio expressed as W:H, the diagonal, width, and height form a right triangle where diagonal^2 = width^2 + height^2. Because width and height are always in the proportion W:H, they can be written as k*W and k*H for some scale factor k. Substituting into the Pythagorean relationship gives diagonal = k x sqrt(W^2 + H^2), so k = diagonal / sqrt(W^2 + H^2). Multiplying k back by W and H yields the actual width and height.

Examples

55-inch TV, 16:9

For a 55 inch diagonal at the default 16:9 ratio, k = 55 / sqrt(16^2 + 9^2) = 55 / 18.358 = 2.996. Width = 2.996 x 16 = 47.9 in (121.8 cm) and height = 2.996 x 9 = 27.0 in (68.5 cm).

27-inch monitor, 4:3

For a 27 inch diagonal at 4:3, k = 27 / sqrt(16 + 9) = 27 / 5 = 5.4. Width = 5.4 x 4 = 21.6 in (54.9 cm) and height = 5.4 x 3 = 16.2 in (41.1 cm).

Advantages

  • Converts a single spec sheet number into dimensions you can measure against real furniture, wall space, or a shipping box before buying.
  • Covers five aspect ratios in one tool, so the same calculator works for widescreen TVs, ultrawide monitors, and older 4:3 displays.
  • Returns results in both inches and centimeters, useful when comparing US retail listings to international product pages.

Common Mistakes

  • Assuming two screens with the same diagonal are the same size, when a different aspect ratio can shift several inches of the diagonal from width into height or vice versa.
  • Forgetting that a diagonal size typically refers to the visible screen area only, not the outer bezel or case, so the calculated dimensions won't match the product's total footprint.
  • Mixing up which number is the width ratio and which is the height ratio when a display uses an unusual or portrait-oriented ratio.

Edge Cases to Watch For

  • A 1:1 (square) ratio still uses the same square-root formula, it simply produces equal width and height values.
  • Manufacturer diagonal specs are sometimes rounded to the nearest half or full inch, so the computed width and height are a close approximation of the panel's visible area rather than a guaranteed exact match to a datasheet.
  • Ultrawide 21:9 and standard 16:9 screens of the same diagonal produce noticeably different widths, since a larger ratio spread pushes more of the diagonal into the width leg and less into the height leg.

Common Use Cases

  • Furniture shoppers checking whether a new TV's actual width fits an existing stand or entertainment center.
  • Video editors and photographers estimating the physical size of a proposed monitor or projector screen for a given aspect ratio.
  • Online sellers and installers who need to quote precise width and height dimensions from a diagonal-only spec sheet.
Written & fact-checked by the Calculateus TeamLast updated August 5, 2026How we verify our formulas

Frequently asked questions

Why do I need the aspect ratio, not just the diagonal, to know a screen's size?

The diagonal alone doesn't fix a unique width and height - a 55" 16:9 TV and a 55" 4:3 display would have very different actual dimensions, since the diagonal is the hypotenuse of a triangle whose legs (width and height) depend entirely on the aspect ratio.

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Conclusion

Because diagonal size alone cannot describe a rectangle, this calculator supplies the missing width and height using nothing more than the aspect ratio and the Pythagorean theorem. It gives a fast, consistent way to translate a marketing spec into real-world measurements.

References