NOTE: This was originally written for a now-defunct Wiki on morgueFile.com
There is a common myth when it comes to digital photos, digital video, and image sizes. The myth is that "DPI" makes sense for digital photos stored or being transferred in a computer-readable format where there are no inches.
What Is DPI?
DPI means dots per inch. Simple, right? Yes... and no. DPI may be a "simple" acronym for "dots per inch" but what it really means depends on what "dots" are involved. In other words, the "dots" in one situation are not the same as "dots" in another situation.
When you're printing something, the "dots" are the dots of ink (or similar material) that the printer puts on the paper (or similar medium). Within an inch of paper, you can count the number of dots. Well, maybe you can't because they're very small, but the printer design engineers can.
When you're taking a picture with a digital camera or using a scanner, the "dots" are single-color pixels ("picture elements") that are created by analyzing the image. As a side note, PPI (pixels per inch) is a more specific term in this case. Sensors (CCD, CMOS, etc.) are generally smaller than an inch, but if you put the image capture surfaces together to have enough for one inch, you could count the number of "dots" (pixel-creating cells) in an inch. Again, this is better left to the design engineers unless you have superhuman eyes!
Keep this in mind: DPI is a measurement for a device, not an image. Scanners scan at the DPI (PPI) you select. Printers print at the DPI you select. Images on your computer, by themselves, do not have "DPI."
Why DPI Makes No Sense For Images On Disk
DPI does not make sense for digital photos once they are in the computer. Yes, the image still has the same pixels, but where is the inch? There is no "inch" of digital data.
That is the most important point here, so it's worth repeating: There is no "inch" of digital data.
Technically, you could measure the physical space used on the magnetic platter of a hard disk, but it would vary per disk. Even that much is not possible when you're talking about storing a photo on a memory card, sending a photo as an email attachment, uploading a photo to a Web site, etc. Regardless, when people talk about DPI, they aren't thinking of magnetic disk storage.
The only correct way to refer to the size of a photo in terms of "dots" alone, without also referencing inches, is by describing the pixel dimensions, such as 640x480, 1024x768, etc. And here is the key: Because "DPI" makes no sense for photos on disk...
...there is no difference between a 1024x768 image "at 72 dpi" versus a 1024x768 image "at 300 dpi."
Proof via Algebra
DPI is determined by dividing dots (for a digital image on disk this is just pixels) by inches. This can be expressed as DPI (x) = dots (d) / inch (i), i.e.: x=d/i.
Example: If there are 600 dots and 2 inches, what is the DPI? x=d/i -> x=600/2 -> x=300. In other words, 300 DPI.
For any value d > 0, you cannot calculate x without a value for i.
Example: If there are 600 dots and an unknown number of inches, what is the DPI? x=d/i -> x=600/i -> ? There is no answer (i.e., no simple numeric answer for x, the DPI value) because we have two variables with no way to determine a value for either one.
Don't believe it? These two images are both 100x100 pixels. Can you tell which one was created at 72dpi and which one was created at 300dpi?
So, which is which? Do they look identical? They are! One was created at 72dpi and the other at 300dpi, but both were at 100x100 pixels. They look the same, and they use the same amount of space on disk (each is 3121 bytes). Indeed, if you use the "FC" command-line tool provided with Microsoft operating systems to do a binary comparison of the files, they are perfectly identical:
If you don't believe it and think this is some sort of trickery, try it yourself -- create your own. Make two images at 100x100, one at 72dpi and one at 300dpi. However, if you make changes (as was done with the images above to make them more interesting to look at), you must make identical changes to both images, and be careful to avoid other differences such as file types, compression settings, etc.
(In case you're curious, the image on the left was created at 72dpi -- not that it matters!)
Here is an analogy that might help you understand why a measurement in one situation may not make sense in another situation:
What is the distance between New York and Los Angeles?
Would it make sense if I said 2,750 miles? What if I said 41 hours, or three days, or six hours? The answer is "yes" to all of them, but for different situations. If you want to know the raw geographic distance it can be measured in miles. If, however, you want to know how long it takes to travel, then all of the time-related "measurements" make sense, even though they're different, because each is for a different scenario (non-stop driving, driving with stops, and flying, respectively).
The time-based measurements only make sense when you're talking about travel between the two points. If you want to know the real distance, the only sensible measurement is in miles (or kilometers, etc.).
Similarly, using dots per inch to describe a digital photo only makes sense in certain situations like printing, scanning, etc. Those situations all require a physical inch for the measurement to make sense. If you are talking about image size as it is stored on disk, posted to a Web site, submitted electronically to a contest, or sent via email, there is no physical inch and therefore DPI makes no sense.
What About File Size?
The typical confusion is that DPI relates to the size of the file. Many situations require limiting the size of a file (setting a minimum and/or maximum). DPI does affect file size when you're dealing with physical inches -- printing, scanning, etc. -- but as you learned above, there is no such thing as DPI for a digital image that is only stored in a computer. So what does affect file size? The basic answers are pixel dimensions, compression, and color depth.
One basic factor in the size of a file is how many pixels are used. In a 640x480 image, there are 307,200 pixels (multiply 640 by 480, just as you would find how many squares are on a piece of graph paper without counting each one). If you have a 1024x768 image, you have 786,432 pixels, which is over twice as many pixels. Over twice as many pixels means over twice as much data, so an uncompressed image (assuming identical color depth) will be over twice as big in terms of disk space.
There are many ways that a computer can "compress" a digital photo to keep it looking the same (or almost the same) while reducing how much disk storage is used for the photo. Some of those ways preserve the photo exactly ("lossless") and some of those ways actually throw away parts of the photo that are "less necessary" than other parts ("lossy"). If you alter the compression of your photo (while being wary of your image being ruined by too much "lossy" compression), you can manage the disk storage requirements. This has no effect on the number of pixels in the photo.
Another way to manage the amount of data (file size) for a digital photo is to manage how much color information is stored for each pixel. If you use just a 0 or 1 to describe each pixel, you won't need much disk space, but each pixel can only be one of two colors (typically black or white). This doesn't give you what most photographers think of as a "black & white" photo, since that requires shades of gray. If you use every number between 0 and 255 to describe each pixel, you can have up to 256 colors (or 256 shades of gray). However, those bigger numbers require more disk space, due to the way computers handle numbers. Many images use over 16 million colors per pixel, to give you a more natural image, and that means each pixel requires even more disk storage. This has no effect on the number of pixels in the photo, it just relates to how much information is stored about each one of those pixels.
But I've Heard Computer Monitors Are 72 DPI!
Maybe this was true back in the days of green- or amber-screen terminals used with mainframes. If you look at the dot-pitch specs for modern monitors, you'll see that they have many more display "dots" per inch than 72, and the "dots" do not match up with the pixels in your photo. Modern displays have flexible settings for the pixel dimensions they show, but this does not affect the actual dots used to display images. If you set your .27mm dot-pitch monitor to show 640x480 pixels, it will show far fewer pixels per screen inch, but it will still be a .27mm dot-pitch monitor. If you then reset the monitor to show 1024x768 pixels, it will show many more pixels per inch, but, again, it's still a .27mm dot-pitch monitor.
If somebody tells you that a computer monitor is set to 72 DPI, tell them you're waiting for them in the 21st Century!
OK, But Everybody Refers To DPI...
Naturally, DPI itself is not a "myth." As described above, it is logical and correct to refer to it in some cases (i.e., where there are inches).
Image editing software, such as Corel PaintShop Pro X7 Ultimate, will let you adjust the DPI settings of an image, but this can lead to confusion (and some software is worse than others about being confusing). When you set the DPI setting in an image without doing anything else (e.g., scaling), it does not change the image itself. It only stores the value as metadata, meaning data about the image file. The metadata information can be used later in analog output (i.e., printing), but it does not change the size of the image on disk.
The "myth of DPI" is that it makes sense for digital photos on disk. This myth is very widespread, but that doesn't make it right. Many people thought the world was flat, and many thought that Earth was the center of the universe. Popularity of an idea is not a measure of the idea's correctness.
To summarize, the "size" of digital photos on a computer can mean one of two things. First is the amount of disk storage needed, and second is the pixel dimensions (width and height). Neither of them use inches, so DPI (dots per inch) can't describe a digital photo's size on a computer. Dots per inch only makes sense when printing, scanning, or other situations that have a physical component. As mentioned above, DPI describes the function of a device, not the size of a digital photo.
If somebody asks you to email them a 300dpi photo, ask them to show you an inch of email!
Edited for clarity and to add algebraic explanation. Most recent edit: 16 AUG 2015