Is a 50-inch TV always the same size?

Only along the diagonal. At 4:3 you get 1,200 square inches, at 16:9 you get 1,068 and at 21:9 you get 905. The panel with the largest number can easily be the one with the least picture.

How do I compare two screens properly?

Convert both to area from the width and height, or from the aspect ratio and diagonal together. A 16:9 needs a 53-inch diagonal to match a 50-inch 4:3, and no amount of comparing diagonals alone will reveal that.

Rectangle Calculator

Rectangle

Calculate area, perimeter, and diagonal of a rectangle.

Rectangle Guide

A rectangle is a fundamental geometric figure in Euclidean geometry, consisting of four sides and four right angles.Opposite sides are equal and parallel, and all interior angles measure 90 degrees. A rectangle is a special case of a parallelogram where all angles are right angles.

The area of a rectangle is calculated by multiplying the lengths of two adjacent sides.If we denote the sides as a and b, the area is A = a × b.For example, a rectangle with sides of 5 and 8 units has an area of 5 × 8 = 40 square units.This formula is fundamental in many practical applications, from calculating room areas to land parcels.

The perimeter of a rectangle is the sum of the lengths of all its sides.The formula for perimeter is 2(a + b), which can also be written as 2a + 2b. For a rectangle measuring 5 by 8 units, the perimeter is 2(5 + 8) = 26 units. The perimeter is useful when determining the amount of material needed to border or enclose an area.

The diagonal of a rectangle connects two opposite vertices and divides the rectangle into two congruent right triangles.The length of the diagonal is calculated using the Pythagorean theorem: d = √(a² + b²).The diagonal is always longer than either side and represents the shortest route between opposite vertices.In practice, the diagonal is used to check if a rectangle will fit in a given space, such as when moving furniture.

Practical applications.The rectangle is one of the most common shapes in architecture and construction. All rooms, walls, windows, and doors are rectangular. In industry, rectangular sheets of metal, glass, and fabric are easier to produce and transport than elements of other shapes.

Three 50-inch screens, and one has 33% more picture than another

Screens are sold by diagonal, and the diagonal says nothing about area on its own. At 50 inches a 4:3 panel gives 1,200 square inches, a 16:9 gives 1,068 and a 21:9 ultrawide gives 905. Same headline number, a third less picture — because the diagonal fixes only one measurement of two.

How it works

Finds area, perimeter and diagonal from any two of them.
Works from an aspect ratio and a diagonal, which is how screens and displays are actually specified.
Makes the area comparison possible, since that is what the advertised number hides.

area = width × height
perimeter = 2 × (width + height)
diagonal = √(width² + height²)

from aspect ratio a:b and diagonal d:
  width  = d × a ÷ √(a² + b²)
  height = d × b ÷ √(a² + b²)

Worked example

The same 50-inch diagonal at three aspect ratios.

4:3 → 40.0 × 30.0 in → 1,200 sq in
16:10 → 42.4 × 26.5 in → 1,124 sq in
16:9 → 43.6 × 24.5 in → 1,068 sq in
21:9 → 46.0 × 19.7 in → 905 sq in

A 4:3 panel has 12.3% more area than a 16:9 at the same diagonal, and 32.6% more than a 21:9. To match a 50-inch 4:3 in area, a 16:9 screen must measure 53.0 inches — three inches larger just to draw level.

Reading the result

The wider the ratio, the more the diagonal flatters it. An ultrawide gains width fast and loses height faster, so the diagonal grows while the area shrinks — which is why ultrawides feel smaller than their number suggests when showing anything that is not a film.
The same trap applies to phones and tablets. A tall, narrow phone quoted at 6.7 inches has less screen area than an older, squarer 6.7-inch model, and comparing the two by diagonal alone gets the ranking wrong.
For a fixed perimeter, the square encloses the most area — 10 × 10 gives 100 while 15 × 5 gives 75 and 19.5 × 0.5 gives 9.75, all at a perimeter of 40. Fencing, framing and edging are priced by perimeter and used by area, so the shape decides the value.
Where you need area, ask for width and height. Every retailer publishes them, and two numbers settle in seconds a comparison that a single diagonal cannot settle at all.

Common questions

Is a 50-inch TV always the same size?: Only along the diagonal. At 4:3 you get 1,200 square inches, at 16:9 you get 1,068 and at 21:9 you get 905. The panel with the largest number can easily be the one with the least picture.
How do I compare two screens properly?: Convert both to area from the width and height, or from the aspect ratio and diagonal together. A 16:9 needs a 53-inch diagonal to match a 50-inch 4:3, and no amount of comparing diagonals alone will reveal that.