The pixels per inch of a display is what’s referred to as the pixel density or PPI. It’s a measure of how many pixels you would count if you counted the pixels, horizontal or vertical, that exist in a single inch on your display.

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.

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 centimeters in an inch (2.54) or 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-inch 4K television, for example, but 440.58 pixels per inch on a 5"-inch 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 Tables at the bottom of the page.

What you’ll need is the diagonal display size in inches and the resolution of the screen. Both of these numbers can be found on the technical specifications page of your display or device. See our page on 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 (3840x2160) screen:

  • Square the width pixels: 3840² = 14,745,600Square the height pixels: 2160² = 4,665,600Add those numbers together: 14,745,600 + 4,665,600 = 19,411,200Take the square root of that number: √(19,411,200) = 4,405.814Divide 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 your screen’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, most of the time, a device or display PPI is the first of two steps to ​getting to something much more practical.

Determine How Big an Image Will Look on Another Device

Now that you know your screen or device PPI, it’s time to put it to good use.

You may create or edit an image on your 17-inch laptop with an HD screen (129.584 PPI), but know that you’ll be displaying it on an 84-inch 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 950x375 pixels in size and the display you’re planning for is an 84-inch 4K (3840x2160) screen (52.45 PPI):

  • Divide the width by the PPI: 950 / 52.45 = 18.11 inchesDivide the height by the PPI: 375 / 52.45 = 7.15 inches

Here we showed that, no matter how “big” or “small” the image might appear to be on your screen, with pixel dimensions of 950x375, that image will appear to be 18.11" by 7.15" on that 84-inch 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-inch screen is roughly 73 inches across and 41 inches tall!

Determine the Size an Image Will Print at Full Resolution

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 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 the image itself.

Here’s how you do this if your image is 375x148 pixels in size and has a PPI of 72:

  • Divide the width by the PPI: 375 / 72 = 5.21 inchesDivide the height by the PPI: 148 / 72 = 2.06 inches

Assuming you don’t scale the image during the printing process, the image will be physically printed at the size of 5.21 inches by 2.06 inches. Do the math with an image you have and then print it out—it works every time!

The DPI resolution your printer is set at, be it 300, 600, 1200, etc., doesn’t impact the size at which the image is printed! This number is very similar to PPI and represents the “quality” by which the image sent to the printer is printed with, but shouldn’t be included as part of your image size calculations.

Pixels Per Inch Tables

As promised above, here’s our PPI “cheat sheet” which should save you the multistep math we demonstrated above.

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:

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.

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