Screen Size Calculator: Width and Height from Diagonal
Screens are sold by diagonal, but what fits on your desk or wall is the width and height. Enter the diagonal and aspect ratio to get the real dimensions, area and pixel density.
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Formula
width = diagonal x W / sqrt(W^2 + H^2)
height = diagonal x H / sqrt(W^2 + H^2)
area = width x height
PPI = horizontal pixels / width (inches)
1 inch = 2.54 cm exactly. Pixels are assumed square, and the screen is measured on its visible area.
Worked example
A 27 inch 16:9 monitor with 1920 pixels across:
- sqrt(16^2 + 9^2) = sqrt(337) = 18.358
- width = 27 x 16 / 18.358 = 23.53 in (59.77 cm)
- height = 27 x 9 / 18.358 = 13.24 in (33.62 cm)
- area = 23.53 x 13.24 = 311.5 sq in
- PPI = 1920 / 23.53 = 81.6
Frequently asked questions
How do I find a screen's width and height from its diagonal?
Width = diagonal x W / sqrt(W^2 + H^2) and height = diagonal x H / sqrt(W^2 + H^2), where W:H is the aspect ratio. For a 27 inch 16:9 screen the width is 23.53 in and the height is 13.24 in.
How big is a 55 inch TV in centimetres?
A 55 inch diagonal is 139.7 cm. At 16:9 that is about 47.9 inches (121.7 cm) wide and 27.0 inches (68.5 cm) tall, so check your furniture against the width, not the diagonal.
Does a bigger diagonal always mean a bigger screen?
Not across aspect ratios. A 4:3 screen has more area than a 16:9 screen with the same diagonal: a 20 inch 4:3 panel is 16 x 12 inches (192 sq in), while a 20 inch 16:9 panel is about 17.4 x 9.8 inches (171 sq in).
How is PPI worked out here?
PPI is the horizontal pixel count divided by the screen width in inches, assuming square pixels. A 1920 pixel wide 27 inch 16:9 monitor gives 1920 / 23.53 = 81.6 PPI.