How Screen Dimensions Are Calculated
Display manufacturers advertise screen size as the diagonal measurement in inches — but most people actually care about width and height. Given the diagonal and the aspect ratio, you can calculate both dimensions using basic trigonometry derived from the Pythagorean theorem.
For a screen with diagonal d and aspect ratio w:h, the width and height are:
- Width = d × w / √(w² + h²)
- Height = d × h / √(w² + h²)
- Area = Width × Height
For example, a 27-inch 16:9 monitor has a width of approximately 23.53 inches and a height of approximately 13.24 inches.
Pixels Per Inch (PPI)
PPI measures how densely pixels are packed on a display. A higher PPI means sharper text and images. To calculate PPI, you need the screen's resolution in addition to its diagonal size. Enter the horizontal resolution (e.g., 1920 for a 1080p display) and the calculator will derive the vertical resolution from the aspect ratio, then compute PPI using the formula:
- PPI = √(horizontal_px² + vertical_px²) / diagonal_inches
- A 27-inch 1080p (1920×1080) monitor has a PPI of about 82.
- A 27-inch 4K (3840×2160) monitor has a PPI of about 163.
Common Aspect Ratios Explained
- 16:9 — Standard widescreen, used by most TVs, monitors, and laptops.
- 16:10 — Slightly taller than 16:9, popular in older laptops and some productivity monitors.
- 4:3 — The "square-ish" ratio used by older monitors and some tablets.
- 21:9 — Ultra-wide, used in gaming and cinematic displays.
- 32:9 — Super-ultra-wide, essentially two 16:9 screens side by side.
- 1:1 — Perfect square, used in some specialty displays and older CRT monitors.
Frequently Asked Questions
Why is diagonal size used instead of width or height?
The diagonal measurement became the industry standard in the early days of television and has stuck ever since. It is a single number that summarises screen size regardless of aspect ratio, making it easy to compare screens in advertising. However, the width and height are more useful for practical purposes like desk space planning.
Does a larger screen always mean a better picture?
Not necessarily. A larger screen at the same resolution will have a lower PPI, meaning individual pixels are more visible. The ideal screen size depends on your viewing distance. For a typical desktop monitor at arm's length, a PPI of 90–120 is generally considered good. Laptop screens benefit from higher PPI (150+) because they are used closer to the face.
What is the difference between a 24-inch and 27-inch monitor?
At 16:9, a 24-inch monitor is approximately 20.9 × 11.8 inches, while a 27-inch monitor is approximately 23.5 × 13.2 inches. The 27-inch screen has about 26% more screen area, which is a meaningful difference for productivity tasks with multiple windows open side by side.