How this calculator works
A screen diagonal is the hypotenuse of a right triangle whose legs are the width and height. If the aspect ratio is w : h, then the width is the diagonal times w divided by the square root of w squared plus h squared, and the height uses h in the numerator. For a 16:9 screen the ratio of width to diagonal is 16 / sqrt(337) = 0.8716, so a 55 inch television is about 47.9 inches wide. Area is width times height, which is why two screens with the same diagonal can have different usable areas: a 4:3 screen is closer to square and holds more area than a 16:9 screen of the same diagonal. The curved option reports the radius named in the marketing figure, where 1800R means a radius of 1800 millimetres.
Formula
For ratio w : h and diagonal D: width = D x w / sqrt(w^2 + h^2), height = D x h / sqrt(w^2 + h^2), area = width x height. From a known width W: height = W x h / w, diagonal = sqrt(W^2 + height^2).
Worked example
A 55 inch 16:9 television has a width of 55 x 16 / sqrt(337) = 47.94 inches and a height of 55 x 9 / sqrt(337) = 26.96 inches. The area is 1,292.6 square inches, or 8,339 square centimetres. The same 55 inch diagonal in 4:3 gives exactly 44 by 33 inches, an area of 1,452 square inches, because 3-4-5 triangles scale evenly. A 1800R curved panel has a radius of 1.8 metres.
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Frequently asked questions
Is a 55 inch screen 55 inches wide?
No. The figure is the diagonal, corner to corner. A 55 inch 16:9 television is about 48 inches wide and 27 inches high, while a 55 inch 4:3 screen is 44 inches wide and 33 inches high.
What does the R in 1800R mean?
It is the radius of the curve in millimetres. A smaller number means a tighter curve: 1500R bends more sharply than 4000R. A tighter curve can wrap the viewer more, but it also distorts reflections and is awkward for group viewing.
Do bezels count in the diagonal?
Manufacturers usually quote the panel diagonal, not the outside of the bezel. If you are fitting a television into a cabinet, add the bezel width to the width and height reported here.
Why does the area matter more than the diagonal?
The diagonal mixes width and height into one number that ignores shape. A 4:3 screen of the same diagonal has about 12 percent more area than a 16:9 screen, which is noticeable for documents and older games.