PPI Calculator (Pixels Per Inch)
This PPI calculator (pixels per inch calculator) finds the resolution of your display based on its dimensions and the pixel count. In this text, we will teach you what is PPI, and explore the differences between PPI vs DPI through the DPI definition. Also, you can find some comments on the dot pitch definition and its decline in usage. Of course, this is a calculator, so we'll show you how to calculate PPI and how to categorize resolution based on PPI.
PPI definition: What is PPI?
PPI is a widely used acronym in tech forums on the Internet, especially those focused on display technology and smartphones. The technical PPI definition is pixels per inch, and it represents a measurement of the pixel density of a screen or a digital image. The density is measured as the number of pixels that fit on a 1-inch line, hence the name.
This measurement is based on the fact that screens and images, despite being 2D, have generally the same density along any of the two main axes. There are other measurements of pixels density, such as pixel per square inch, that involve calculating the area of a rectangle that is the screen. Also worth mentioning is the fact that our pixel density calculator assumes square pixels.
It is important to note that for calculating PPI we need something that has a physical size, not a virtual file. For example, a screen or a printed picture has a fixed physical size, so it makes sense to calculate how many pixels per inch there are in such an object. However, when we're talking about a digital image in a computer, PPI cannot be computed since the digital image varies in size depending on the level of zoom, the size of the screen, etc. For purely virtual images, we have a calculator/converter that allows you to convert between different virtual sizes: the px to em calculator.
Formulas for calculating PPI
Now that we've established what is PPI and reviewed the PPI definition, let's see how you can calculate PPI. The most common one is to calculate it from the diagonal screen size (in inches or cm) and the number of pixels along the vertical and horizontal edges of the display.
First, you need to calculate the number of pixels that fit on the diagonal:
dₒ = √(w² + h²)
- w — Number of pixels along the horizontal line; and
- h — Number of pixels along the vertical line.
Then, you can calculate the PPI as the ratio between the number of pixels along the diagonal and the diagonal screen size:
PPI = dₒ/dᵢ
where dᵢ is the diagonal screen size in inches.
You probably noticed that you can also enter the width and height of the display into the PPI calculator. You can use these values instead of the diagonal size of the screen, and it will internally calculate the length of the diagonal using the Pythagorean theorem. Remember that the aspect ratio must be the same for both, that is the size of the screen and its resolution.
Our pixel density calculator also finds the total number of pixels on the display expressed in megapixels (millions of pixels, symbol: Mpx). This value is found as the product of the vertical and horizontal number of pixels, which is then divided by the total area to give another measure of the pixel density, in this case, how many pixels per square inch.
Dot pitch definition
The last number that you can find with our calculator is the dot pitch — the distance between two pixels' centers. This is calculated as the inverse of PPI. If PPI is a measure of the density of pixels in a given length, dot pitch is the exact opposite: it's the distance between two fixed pixels or dots. Note that we are using dots and pixels interchangeably, but this might not always be the case.
The dot pitch is somewhat forgotten, and its value is mostly not used due to the advancements of modern technology. Back in the days when smartphones (and even computer monitors) had resolutions of less than 100 pixels in both the vertical and horizontal direction, the usage of dot pitch was convenient and understandable.
Now that our devices have a couple of thousand pixels in less than 5 inches, this makes the dot pitch values ridiculously small and hard to understand intuitively. This was the doom of dot pitch and the rise of PPI as the new de facto standard. And that's the reason dot pitch is fading out of the mainstream scene, and why most people don't know what the dot pitch definition is anymore.
Before we move to an example of using the calculator, we must mention DPI. DPI or dots per inch is a similar measurement to PPI, as they both measure density. However, they do it in subtly different ways, or at least they used to.
DPI definition: dots per inch definition
The PPI definition and the DPI definition are almost the same. DPI, as we mentioned before, stands for "dots per inch" and it's analogous to PPI in the sense that they both measure how "grainy" an image is. As the name suggests, dots per inch measures the number of points that exist in the length, equivalent to
1 inch on average. This value is directly related to PPI for modern digital screens since each pixel corresponds to a dot in the image, but it doesn't always have to be a 1:1 correlation.
If you think of an ink printer, their settings usually include DPI, not PPI. This is because, in a printer, DPI means the number of ink dots per inch, and it's independent of the resolution of the image we want to print. Depending on the printer's characteristics, its DPI can be higher or lower than the PPI of the image. Let us illustrate it with an example.
Let's assume you have a printer capable of up to 300 dpi when printing. Imagine you have a
1800 × 2800 ~ 5 Mpx picture that you want to print on paper with an actual size of about
6 inches measured on the diagonal. The image's pixel density at this size is 554.8 ppi, way higher than the 300 dpi your printer is capable of. In this case, each ink dot printed will represent several pixels of the image so you will lose resolution in the printing process.
If you imagine the same scenario but with a better printer capable of 1000 dpi, the situation reverses. Now, each pixel will be composed of several dots of ink. A general recommendation is to set the DPI in the printer to an integer fraction or multiple of the original pixel density of the image to avoid the kinds of artifacts that appear when interpolating pixels and guessing color values.
Using the pixels per inch calculator: an example
Let's assume you want to calculate the PPI of your smartphone.
Check what the diagonal size of your smartphone is. Let's say it is equal to 5 inches.
Write down the vertical and horizontal pixel count. Let's assume they equal 640 and 480 pixels, respectively.
Calculate the number of pixels along the diagonal:
dₒ = √(w² + h²) = √(480² + 640²) = √640,000 = 800
Calculate the PPI according to the formula written above:
PPI = dₒ/dᵢ = 800/5 = 160
The total count of pixels is found as the product of w and h:
w × h = 480 × 640 = 307,200 = 0.307 Mpx
Calculate the dot pitch as the reciprocal of PPI:
dot pitch = 1/160 in = 0.00625 in = 0.1588 mm
PPI vs DPI: the differences
We have already seen the PPI definition as well as the DPI definition, so it's time to compare both values. DPI stands for dot per inch, while PPI is the same but with pixels instead of dots. There is no difference when talking about screens since the pixel is considered as the "dot" of a screen. Things are a bit more complicated when we compare PPI vs. DPI outside of screens or when we consider the comparison at a deeper level.
We mentioned the differences between PPI vs. DPI when we presented an example of printing an image on paper. This arises from the distinction between dot and pixel (which is the equivalent in digital form). If we stay in the purely virtual realm of digital technology, a pixel is the minimum unit of digital space, which is exactly the same as the dot.
However, in the physical-digital world, things become more complicated. A screen is a physical object that connects the virtual/digital world with our analogical/physical perception of reality. In a screen, a pixel is not actually one dot, but it is composed of three individual dots of different colors, namely red, green, and blue emitting the corresponding wavelength. This is where the similarities between pixel and dot start to break down, and it makes sense again to compare PPI vs. DPI.
This is especially noticeable when we encounter PenTile matrix screens. In these screens, the three subpixels that makeup one pixel are not the same size, and the perceived resolution ends up being smaller. In these cases, you make a distinction between PPI vs. DPI that really matters and that goes beyond pure semantics.
Does (PPI) size matter?
Oh, the age-old question! Is bigger better? Such a common question requires a similarly old and used answer:
HELL YES! it depends. Jokes aside, having a higher PPI or DPI is, in general, better since it means having a finer image that retains a greater amount of detail. However, there's always a trade-off, and there are certain scenarios in which having a higher PPI count might be detrimental.
If we have a small screen, such as those in our smartphones, or if we look at an image from far away (like a TV or a cinema projector), there's a point at which our eyes are not able to detect each individual pixel, and increasing the PPI has a smaller and smaller effect. This is the principle behind the so-called "Retina display" that Apple uses in its devices.
This threshold depends on the distance at which we typically look at the screen, as well as the size of the screen. For example, the iPhone XR PPI is 326, while the iMac with a 5K display has 218 ppi. The iPhone XR PPI count is clearly higher since we tend to look at our smartphones much closer than we (should) look at a computer monitor.
A second situation in which bigger might not be better is when we are mixing resolutions between the source and the display/printer. We already mentioned the printing problem, but we might encounter a similar issue when dealing with photos or videos online. The best-case scenario is to have the highest resolution possible, which is matched 1:1 between the source and the monitor we watch it on.
If that's not possible, then finding one resolution that is an integer multiple/fraction of the monitor is the second-best option since that would allow for direct mapping of pixels and avoid weird interpolations. If that's also not possible, the best option is to match aspect ratios. Notice that all those geometrical parameters are more important than raw resolution.
So, even though a bigger PPI is generally better, it really depends, as we saw when comparing the iPhone XR PPI vs. the iMac.
🔎 Try our resolution scale calculator to find the resized resolution values for your images, videos, or display resolution, while maintaining their aspect ratio.
You might be wondering, after all these calculations and definitions, whether your monitor/smartphone/… has a good density of pixels. If your phone or monitor was made in the last 3 years, we can almost guarantee that they have a respectable number of pixels per inch. However, if you want to have a more objective and precise reference, we will now give you a list of what is considered high, low, and medium pixels per inch. Just remember that as technology evolves, we see less of the lower end and more of the high end, and we will possibly get even higher values just for the sake of marketing.
How many pixels per inch is a good PPI value?
eXtra eXtra High
eXtra eXtra eXtra High
How do I calculate PPI from screen diagonal?
To calculate PPI from diagonal, use the formula:
PPI = √(w² + h²)/d
d– Diagonal screen size in inches;
w– Number of pixels along the horizontal line; and
h– Number of pixels along the vertical line.
How do I calculate PPI from screen width and height?
To calculate PPI, if you know your screen width and height (in inches!), follow these steps:
Write down the number of pixels along the horizontal and vertical lines: wₚ and hₚ. Square these numbers and add the results: wₚ² + hₚ².
Similarly, compute the sum of squares of the screen width wₛ and the screen height hₛ.
Divide the result from Step 1 by Step 2 and then take the square root.
That's it! You've just successfully applied the PPI formula:
PPI = √[(wₚ² + hₚ²)/(wₛ² + hₛ²)]
What is PPI for 1440p at 32 inches?
For a 32-in screen using the resolution of 2560p × 1440p, the PPI is 91.79. We get this result via the following calculation:
√(2560² + 1440²)/32 ≈ 91.79.