Works out the width and height of a screen from its diagonal and its aspect ratio. A screen described as 27 inches is quoting the diagonal, which alone does not fix its size. Adding the pixel count gives the pixel density in ppi.
A screen is sold by its diagonal, which alone does not say how large it is. This works out the width and height from the diagonal and the aspect ratio.
is the diagonal and the aspect ratio. Treating the ratio as the sides of a right triangle, its hypotenuse scales the diagonal down to each side.
Aspect ratio changes what a diagonal means. A 27-inch screen at 16:9 is 59.8 by 33.6 cm with an area of 2010 cm², while the same 27 inches at 4:3 would be 54.9 by 41.1 cm and 2256 cm², a good deal more. The squarer the shape, the more area a given diagonal encloses.
Dividing the pixels across by the width in inches gives the density in ppi. A 27-inch screen 2560 pixels wide comes to 108.8 ppi. Around 100 ppi is ordinary and past 200 the pixels stop being visible at a normal viewing distance.
A 27-inch 16:9 screen with 2560 pixels across is 59.77 cm wide and 33.62 cm tall, 2010 cm² in area, at 108.8 ppi.
The diagonal quoted is the display area itself and excludes the bezel. Older televisions were sometimes quoted including it, which is why the figures did not match.