The current iPhone 5 has about 730 thousand pixels and 326ppi pixel density. If the rumor is true, the next iPhone will have a screen with around 1.5 million pixels and 460ppi pixel density (that's assuming the screen size doesn’t change). If Apple decides to match current 5" 1080p droids at 440ppi, the screen size can be increased up to 4.2".
Of course, such a move will be difficult – going from the 3GS to the 4, Apple doubled the pixel count both horizontally and vertically, effectively quadrupling the pixel count. Apps that didn’t support the new resolution were easily upscaled.
From the 4 and 4S to the 5, Apple added an extra 176 pixel rows and apps that don't support the new resolution are just letterboxed with black bars (some still have them).
But to double the pixel count for the next iPhone, Apple will need to multiply the horizontal and the vertical pixel count by a square root of 2 (so the resulting resolution is something like 905 x 1606). Scaling apps to fit will be more difficult this time (or there will be black bars on the sides too), so it's unlikely Apple will go for this solution.
The rumored brand new look for iOS 7 might help somehow, but we'll have to wait and see.
The rumor also states that the next iPhone goes into production next month and will launch in September, meaning we might soon start seeing leaks.
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