Screen Size Calculator

What is a screen size calculator?

Screens are almost always advertised by a single number: a 27-inch monitor, a 6.1-inch phone, a 65-inch television. That number is the length of the diagonal, the straight line from one corner of the picture to the opposite corner. On its own the diagonal tells you very little about how wide or how tall the panel actually is, because two screens with the same diagonal can have very different shapes.

This calculator fills in the missing dimensions. Give it the diagonal and the aspect ratio, and it returns the physical width, the physical height, and the total area of the active picture. If you also know the resolution in pixels, it reports the pixel density in pixels per inch (PPI), which is a good proxy for how sharp the screen will look.

Key concepts

• Diagonal (d) — the corner-to-corner measurement of the picture, the figure manufacturers quote.
• Aspect ratio (AR) — the ratio of width to height, written as two numbers such as 16:9. It fixes the shape of the rectangle.
• Width (W) — the horizontal size of the picture.
• Height (H) — the vertical size of the picture.
• Screen area (A) — the surface of the picture, useful when comparing how much you actually see.
• Pixel density (PPI) — how many pixels fall in one inch of screen; higher numbers mean finer detail.

How does the calculator work?

A screen is a rectangle, so the diagonal is the hypotenuse of a right triangle whose legs are the width and the height. The aspect ratio fixes the proportion between those legs, which is enough to solve the triangle completely.

Write the aspect ratio as a single number, $AR = a / b$, where the ratio is $a:b$ (for example $16/9$). Then the width and height share the diagonal as follows.

Formulas

Starting from the Pythagorean relation and the definition of the aspect ratio:

$$d^2 = W^2 + H^2, \qquad AR = \frac{W}{H}$$

the height and width work out to:

$$H = \frac{d}{\sqrt{AR^2 + 1}}, \qquad W = AR \cdot H$$

Equivalently, using the ratio numbers $a$ and $b$ directly:

$$W = d \cdot \frac{a}{\sqrt{a^2 + b^2}}, \qquad H = d \cdot \frac{b}{\sqrt{a^2 + b^2}}$$

The area is simply the product of the two sides:

$$A = W \cdot H$$

When a resolution of $p_w \times p_h$ pixels is supplied, the pixel density follows from the diagonal in pixels divided by the diagonal in inches:

$$PPI = \frac{\sqrt{p_w^2 + p_h^2}}{d}$$

Worked examples

Example 1: a 27-inch 16:9 monitor

With $d = 27$ in and aspect ratio $16:9$, so $a = 16$ and $b = 9$:

$$W = 27 \cdot \frac{16}{\sqrt{16^2 + 9^2}} = 27 \cdot \frac{16}{\sqrt{337}} \approx 23.53 \text{ in}$$ $$H = 27 \cdot \frac{9}{\sqrt{337}} \approx 13.24 \text{ in}$$ $$A = 23.53 \cdot 13.24 \approx 311.5 \text{ in}^2$$

Example 2: pixel density of that monitor

If the same 27-inch panel has a $2560 \times 1440$ resolution:

$$PPI = \frac{\sqrt{2560^2 + 1440^2}}{27} = \frac{\sqrt{8\,627\,200}}{27} \approx 108.79$$

Example 3: a 5.5-inch 16:9 phone

With $d = 5.5$ in and aspect ratio $16:9$:

$$W = 5.5 \cdot \frac{16}{\sqrt{337}} \approx 4.79 \text{ in}, \qquad H \approx 2.70 \text{ in}$$ $$A = 4.79 \cdot 2.70 \approx 12.93 \text{ in}^2$$

Example 4: a square 1:1 panel

For an unusual square display with $d = 10$ in and aspect ratio $1:1$, the width and height are equal:

$$W = H = \frac{10}{\sqrt{2}} \approx 7.07 \text{ in}$$

Practical uses

• Choosing a monitor or TV — compare two screens fairly by their actual width, height, and area rather than the diagonal alone.
• Planning a wall or desk — confirm a display physically fits the space before buying, since aspect ratio strongly affects width.
• Comparing sharpness — use the pixel density to judge whether a higher-resolution panel will look noticeably crisper at your viewing distance.
• Ultrawide versus standard — a 34-inch 21:9 monitor is far wider but shorter than a 34-inch 16:9 one would be; the calculator makes the trade-off explicit.
• Geometry practice — the diagonal of a screen is a direct application of the Pythagorean theorem, the same idea behind the diagonal of a rectangle.

Notes

• The diagonal and aspect ratio must both be positive for the result to be meaningful; a zero or empty diagonal leaves every output blank.
• Manufacturers usually quote the diagonal of the active picture, but a few quote the diagonal including the bezel, so a measured screen can come out slightly smaller than expected.
• The pixel density needs the diagonal in inches because PPI is defined per inch; switch the diagonal unit if you entered centimetres and the area will reconvert automatically, much like the area calculator.
• A custom aspect ratio accepts any two numbers, so you can model unusual panels such as 1:2.35 cinema displays or 32:9 super-ultrawides.