Android Central‘s Alex Dobie made this point to me in the buildup to Samsung’s Galaxy S8 launch yesterday: a 5.8-inch phone with the S8’s elongated 18.5:9 aspect ratio doesn’t have the same size screen as a 5.8-inch phone with the traditional 16:9. The two might share the same diagonal measurement, but in terms of area, the S8’s screen would be smaller. That’s because the change in aspect ratio breaks the linear scale by which we’ve compared almost all smartphones to date. If every rectangle has the same aspect ratio — the relationship between its height and width — then knowing its diagonal measurement gives us a rough way to compare or at least rank those rectangles by size.
Samsung and LG have broken from the industry convention with their new phones this spring — with the Galaxy S8 and the G6, respectively — and their renegade actions are wreaking havoc with our casual shorthand for comparing display dimensions. But never fear, there is still a way to bring them back into line and do direct comparisons. We’ll just need a little bit of Pythagorean mathematics to help us.
If you know the length of a right-angle triangle’s hypotenuse (a) and the ratio between its sides (b and c), you can work out the lengths of those sides and, consequently, the area of the rectangle within which that triangle resides.
Here’s my method of reverse-engineering a phone’s screen size from its diagonal measurement:
Convert from imperial to metric measurements, because everything’s simpler in metric form. For my example, let’s take the 5-inch / 127mm Google Pixel, which I could measure with a ruler to confirm my calculations were sensible.