The pixels per inch (PPI) of a display is what’s referred to as the pixel density and is quite literally how many pixels you would count if you counted the pixels, horizontal or vertical, that exist in a single inch on your display.
There are several reasons why knowing how many pixels there are in an inch of your display, but usually this is most helpful when you’re trying to imagine how an image on your screen might look on a different screen.
Another common assumption is that you need to know a display or printer’s PPI to understand how large or small an image might appear when printed out but you actually don’t in this case. More on that below.
There is No One Answer to Pixels per Inch
If all pixels were the same size, the pixels in an inch would be a known number like how many centimeters in an inch (2.54) or how many inches in a foot (12).
However, pixels are different sizes on different displays, so the answer is 58.74 pixels per inch on a 75″ 4K television and 440.58 pixels per inch on a 5″ Full HD smartphone screen.
In other words, how many pixels per inch depends on the size and resolution of the screen you’re talking about, so we’ll have to do some math to get the number you’re after for yours.
How to Calculate the Pixels in an Inch
Before we get into what looks like advanced math (it’s not, don’t worry), we’ve done the hard work for you for a number of displays in the Pixels Per Inch Table at the bottom of the page.
If you find your display’s PPI, move on to How to Use Your Pixels per Inch Numberbut if not, we’ll figure it out right here with a few simple mathematical steps.
What you’ll need in any case is the diagonal display size in inches as well as the resolution of the screen. Both of these numbers can be found on the technical specifications page of your display or device.
See How to Find Manufacturer Tech Support Information if you need help digging this up.
Here’s the full equation for you math savvy folks, but skip right past it for the step-by-step directions:
ppi = (√(w²+h²))/d
…where ppi is pixels per inch you’re trying to find, w is the width resolution in pixels, h is the height resolution in pixels, and d is the diagonal size of the screen in inches.
If you slept during the order of operations chapter in math class, here’s how you do this with an example of a 60″ 4K (3840×2160) screen:
- Square the width pixels: 3840² = 14,745,600
- Square the height pixels: 2160² = 4,665,600
- Add those numbers together: 14,745,600 + 4,665,600 = 19,411,200
- Take the square root of that number: √(19,411,200) = 4,405.814
- Divide that number by the diagonal screen measurement: 4,405,814 / 60 = 73.43
In five short steps, we figured the pixels in an inch on a 60″ 4K television to be 73.43 PPI. All you need to do now is repeat those five steps with your display, using yourscreen’s resolution and size.
So now you know your display’s PPI… but what good is it? If you were just curious, you’re done! However, as we alluded to in the introduction above, most of the time a device or display PPI is the first of two steps to getting to something much more practical.
How to Use Your Pixels per Inch Number
Now that you know your screen or device PPI, it’s time to put it to good use.
Determine How Big an Image Will Look on Another Device
You may create or edit an image on your 17″ laptop with an HD screen (129.584 PPI) but know that you’ll be displaying it on an 84″ 4K UHD display (52.45 PPI) in the office next week.
How can you be sure the image is being created large enough or has the right detail?
To answer this question, you’ll first need to know the PPI of the device or display that you’re curious about. We learned how to do that in the last section, or you found one or both numbers in the table below.
You’ll also need to know the horizontal and vertical pixel dimensions of your image. You’re creating or editing that so it should be easy enough to find in your graphics program.
Like before, here are the full equations if you’re so inclined, but the instructions are below:
hsize = w/ppi
vsize = h/ppi
…where hsize and vsize are the image’s horizontal and vertical sizes in inches, respectively, on the other display, w is the width of the image in pixels, h is the height of the image in pixels, and ppi is the PPI of the other display.
Here’s how you do this if your image is 950×375 pixels in size and the display you’re planning for is an 84″ 4K (3840×2160) screen (52.45 PPI):
- Divide the width by the PPI: 950 / 52.45 = 18.11″
- Divide the height by the PPI: 375 / 52.45 = 7.15″
Here we showed that, no matter how “big” or “small” the image might appear to be on your screen, with pixel dimensions of 950×375 that image will appear to be 18.11″ by 7.15″ on that 84″ 4K TV it’ll be shown on.
Now you can use that knowledge as you see fit… maybe that’s just what you were after, or maybe that’s not big enough considering that an 84″ screen is roughly 73″ across and 41″ tall!
Determine the Size an Image Will Print at Full Resolution
Fortunately, you don’t need to figure your device or display PPI to figure out how big an image you print will be on paper.
All you need to know is information that’s contained in the image itself – the horizontal pixel dimension, the vertical pixel dimension, and the image’s PPI. All three pieces of data are available in the image’s properties which you can find in your graphics editing program.
Here are the equations:
hsize = w/ppi
vsize = h/ppi
…where hsize and vsize are the image’s horizontal and vertical sizes in inches, respectively, as they’ll be printed, w is the width of the image in pixels, h is the height of the image in pixels, and ppi is the PPI of image itself.
Here’s how you do this if your image is 375×148 pixels in size and has a PPI of 72:
- Divide the width by the PPI: 375 / 72 = 5.21″
- Divide the height by the PPI: 148 / 72 = 2.06″
Assuming you don’t scale the image during the printing process, the image will be physically printed at the size of 5.21″ by 2.06″. Do the math with an image you have and then print it out – it works every time!
Note: The DPI resolution your printer is set at, be it 300, 600, 1200, etc., does not impact the size that the image is printed at! This number is very similar to PPI and represents the “quality” by which the image sent to the printer is printed with but should not be included as part of your image size calculations.
Pixels Per Inch Table
As promised above, here’s our PPI “cheat sheet” which should save you the multi-step math we demonstrated above.
|Size (in)||8K UHD (7680×4320)||4K UHD (3840×2160)||Full HD (1920×1080)|
Of course not every device or display out there is exactly 8K UHD, 4K UHD, or Full HD (1080p). Here’s another table with a number of popular devices with non-standard resolutions and their calculated PPI:
|Device||Size (in)||Resolution (x/y)||PPI|
|Dell Venue 8||8.4||1600×2560||359.390|
|Google Pixel XL||5.5||1440×2560||534.038|
|HTC One M8/M9||5||1080×1920||440.581|
|iPad Mini Retina||7.9||1536×2048||324.051|
|iPhone 6 Plus||5.5||1080×1920||400.529|
|MacBook Air 11||11.6||1366×768||135.094|
|MacBook Air 13||13.3||1440×900||127.678|
|MacBook Pro 13||13.3||2560×1600||226.983|
|MacBook Pro 15||15.4||2880×1800||220.535|
|Samsung Galaxy Note 4||5.7||1440×2560||515.300|
|Samsung Galaxy S5||5.1||1080×1920||431.943|
|Samsung Galaxy S6||5.1||1440×2560||575.923|
|Sony Xperia Z3 Tablet||8||1920×1200||283.019|
|Sony Xperia Z4 Tablet||10.1||2560×1600||298.898|
|Surface Pro 3||12||2160×1440||216.333|
|Surface Pro 4||12.4||2736×1824||265.182|
Don’t worry if you didn’t find your resolution or device. Remember, you can calculate how many pixels are in an inch for your device, no matter the size or resolution, using the math we described above.