# How can two laptops have the same resolution and screen size but different pixel densities?

According to this comparison:

Lenovo's X250 and X260 have the same native resolution (1920x1080), the same screen size of 12.5" but different pixels-per-inch density values: 183 ppi vs 176 ppi. How is that possible? Rounding errors?

They can't, some parameters have been reported incorrectly. You can verify this yourself as follows.

There is a convenient pixel density calculator at this website. The calculation is trivial (from wikipedia)

Using this formula and/or the online calculator shows that for the X250 to have a ppi of 183 with a resolution of 1920x1080 it would need to be a 12" screen, not a 12.5" screen.

Using the value of 12" instead of 12.5" comes out to almost exactly 183 ppi while 12.5" comes to 176.

So either the manufacturer has redefined ppi, or they are not reporting the resolution or screen size accurately.

• By screen-size sometimes they mean the sized of the actual screen and sometimes the size of the laptop lid (LCD + surrounding bezel). It is just a a matter of whatever the marketeer that wrote the information thought what would sound better. Working backwards from PPI and resolution to screen-size is more reliable in my experience. – Tonny Dec 24 '16 at 15:45
• I believe the error is actually on the Specout web site. Lenovo's own site provides specs of 12.5" 1920x1080 for both units. Other sites providing specs for both units state 176 ppi for both models. – barbecue Dec 24 '16 at 16:17
• If your view or definite conclusion is that "You Cannot", then You should really write as the top sentence.. it's far clearer, that way the reader doesn't have to read through a mathematical formula before finding the simple answer. – barlop Dec 24 '16 at 22:34

I believe this is probably an error on the Specout site. The comparison at specout reports that the two models have identical resolutions and sizes, but different PPI densities. However I can't find this claim being made anywhere on the Lenovo site. Other laptop review sites don't reproduce this claim either. Notebookcheck.net reviews for the X250 and X260 give them the same graphics specs. The point is probably moot, since the X250 is actually a discontinued model, and the X260 is apparently its successor.

• The x250 is just gaining in popularity as a second-hand/refurbished item, so it won't be moot for another, say, 5-6 years at least. – einpoklum Dec 25 '16 at 0:19

The site correctly shows an aspect ratio of 16:10 for the X250, which is unusual compared to the far more common 16:9. However, it doesn't show any aspect ratio for the X260, so it probably assumes the far more common 16:9 as a default value.

A 12.5" diagonal with an aspect ratio of 16:9 means a screen area of 66.8 in^2. So, the square-pixels-per-square-inch is (1920 pixels * 1080 pixels) / (66.8 in^2). Take the square root of that to get pixels-per-inch (PPI), and it's 176, just like the website shows.

The math for the X260's PPI looks correct given that it's missing the aspect ratio and probably just defaulting to the common 16:9.

PS - Wikipedia's equation for PPI, as cited in the currently accepted answer, is simply wrong. PPI is the square root of the number of pixels over the area in which they're displayed. This doesn't reduce to the expression given on Wikipedia.

• Aspect ratio is a function of resolution (or vice-versa). 1920x1200 would be the closest resolution with a 16:10 aspect ratio. – Argonauts Dec 25 '16 at 12:57