With the iPhone 6 set to come in two separate display sizes — a 4.7-inch model, and a 5.5-model — Apple needs to increase the iPhone’s resolution to keep up. But what will the new resolutions be? Up until now, Apple has stuck with 326 pixels-per-inch for all Retina iPhones, but will larger iPhones require higher pixel densities.

Pulling out a spreadsheet, Daring Fireball’s John Gruber worked out the math for what he thinks the resolutions of the iPhone 6 will be. Using the Pythagorean Theorem, Gruber says that he thinks the 4.7-inch iPhone 6 will keep the current iPhone’s 326 pixels-per-inch, but the 5.5-inch model will have an astonishing 461 pixels-per-inch, making it practically Super Retina.

Although Gruber stresses he has no insider information, this is how he sees the exact resolutions breaking down:

• 4.7-inch display: 1334 × 750, 326 PPI

• 5.5-inch display: 2208 × 1242, 461 PPI

Gruber believes that these screens would allow Apple to easily upscale by doubling or tripling the pixels per inch of existing apps, similar to the way that non-Retina iPhone apps work on Retina iPhones. The 4.7-inch iPhone 6 would have a 1.38 times larger display, but the same pixels-per-inch as the iPhone 5, making upscaling UI elements a cinch. As for the 5.5-inch iPhone 6, UI elements would be upscaled by a factor of 3 when compared to non-Retina UI elements, but would still be backwards compatible with existing apps.

The bottom line? If Gruber’s right, the new iPhone 6 won’t just have a higher-resolution screen, but it won’t require developers to update their apps to work well on the new devices. And any fears that the bigger iPhones might be less “Retina” than the iPhone 5 have nothing to fear.

Make sure to read more of Gruber’s methodology at the link below. It’s a long but fascinating read, especially if you love math and detective work.

Source: Daring Fireball