SOLVETUTORMATH SOLVER

Instrument MI-14-181 · Other

Screen Size Calculator

Enter a screen's physical width and height in inches and this instrument works out its diagonal size — the number normally advertised as a display's screen size.

Instrument MI-14-181
Sheet 1 OF 1
Rev A
Verified
Type 14 — Display & Aspect Ratio SER. 2026-14181

Diagonal (in)

14.341

diagonal = sqrt(width^2 + height^2)

The working Every figure verified twice
  1. diagonalIn = √(pow(12.5, 2) + pow(7.03, 2)) = 14.341
Worksheet log
  1. No entries yet — change an input to log a scenario.

How this instrument works

A screen's advertised 'size' — the number quoted for TVs, monitors and laptops — is almost always its diagonal measurement, the straight-line distance from one corner to the opposite corner, not its width or height. When that diagonal figure is missing, unclear, or you simply want to verify it yourself with a tape measure, you can recover it directly from the screen's physical width and height.

Because a rectangular screen's diagonal, width and height form a right triangle — the diagonal is the hypotenuse, and the width and height are the two legs — the Pythagorean theorem applies directly: diagonal squared equals width squared plus height squared. Squaring the width and height, adding them, and taking the square root gives the diagonal exactly.

This is genuinely useful beyond curiosity. Furniture and cabinet builders need a screen's real diagonal to size a mount or enclosure correctly; secondhand buyers can verify a seller's size claim with a tape measure and this formula instead of trusting an unverifiable listing; and it settles any doubt when a screen's spec sheet quotes size in centimetres or gives only width and height.

d=w2+h2d = \sqrt{w^2 + h^2}
widthIn, heightIn — the screen's physical width and height, measured across the visible display area in inches · diagonalIn — the resulting diagonal screen size.
  • Measure the screen's visible display area (not the outer bezel) width in inches and enter it into Screen width (in).
  • Measure the same visible display area's height in inches and enter it into Screen height (in).
  • Read Diagonal (in) for the resulting screen size — this is the number normally advertised or printed on the box, such as '14-inch laptop' or '55-inch TV'.
  • For the most accurate result, measure corner to corner of the actual glass or panel rather than relying on a printed spec if the display's borders or stand make direct width and height measurement awkward.

Worked example — a 12.5in x 7.03in laptop panel

Enter 12.5 into Screen width (in) and 7.03 into Screen height (in) — the physical display dimensions of a common 16:9 laptop panel. Diagonal (in) works out to √(12.5² + 7.03²) = √205.6709 = 14.341 inches.

That 14.341-inch result rounds to the '14-inch laptop' class advertised on most spec sheets and retail listings — display sizes are conventionally rounded to the nearest common marketing figure, so a measured diagonal of 14.341 inches reliably shows up in stores simply as '14-inch'.

Questions

Why is a screen's advertised size its diagonal, not its width or height?

Because diagonal is the single number that stays consistent regardless of aspect ratio, making it easy to compare screens of different shapes at a glance. A width-only or height-only figure would understate a screen bought in a different aspect ratio, while diagonal captures the full physical span corner to corner — a convention the display and television industry has used since the earliest CRT sets and never changed.

Should I measure the visible screen or the whole bezel including the frame?

Always measure the visible display area — the actual glass or panel that shows an image — not the outer plastic or metal bezel surrounding it. Advertised screen sizes universally refer to the visible area only; including the bezel in your width and height measurements will overstate the diagonal this calculator returns and won't match the manufacturer's quoted size.

Can I use this to check if a used TV or monitor listing is accurate?

Yes — measure the visible display's width and height with a tape measure, run them through this calculator, and compare the result against the size the seller claims. A genuine 55-inch TV should return a diagonal close to 55 inches; a meaningful mismatch, allowing for a small measuring margin of error, is a useful red flag before completing a private sale.

Does this formula work for any screen shape, including ultrawide monitors?

Yes — the Pythagorean relationship between diagonal, width and height holds for any rectangular screen regardless of aspect ratio, whether it's a squarish old 4:3 monitor, a standard 16:9 panel, or an unusually wide 32:9 ultrawide display. As long as the screen is a true rectangle, diagonal squared always equals width squared plus height squared.

Why do my measured inches not exactly match the advertised screen size number?

Small differences are normal and expected. Manufacturers round diagonal sizes to the nearest common marketing figure — a measured 14.34-inch panel is sold as '14-inch' — and manual tape-measure readings introduce their own small rounding or measurement error. A difference of a few hundredths or tenths of an inch from the advertised figure isn't cause for concern; a difference of a full inch or more suggests either a measuring mistake or a genuinely different size than advertised.

References