(Edited and updated in 2022, but the technology changes so fast, there's no guarantee this info is still accurate.)
by Zimmerman Skyrat, 101Bananas.com
35mm Film
Not too many people still take photos with a camera using 35mm film, but a lot of people probably have old photos and 35mm negatives or slides in boxes in the back of their closet. The "35" in 35mm film refers to the width of the film, which includes the little holes that a camera's sprockets fit in to advance or rewind the film. Each individual exposed frame on a strip of 35mm film is 24 x 36 mm, a 1:1.5 aspect ratio — in horizontal format, the width is 1.5 times the height. (We're talking about still cameras here, NOT 35mm Hollywood movie cameras, which are another matter entirely.)
2.54 cm (or, 25.4 mm) = 1 inch
24 x 36 mm = .944 x 1.417 inches
Photographic Prints
A standard 4 x 6 inch print has a 1.5 aspect ratio; in horizontal format the width is 1.5 times the height. This is exactly the same ratio as a 24 x 36 mm negative. Thus the whole frame of the negative fits perfectly, when enlarged, on a 4 x 6 print.
Since the standard sizes for photographic enlargements larger than 4 x 6 have different aspect ratios than the original negative or slide, something has to be cropped somewhere. Assuming a horizontal format for the picture (width larger than height), and assuming you want the full height of the frame printed, it is one or both ends of the picture (the width) that are usually cropped slightly.
A 5 x 7 inch print has a 1.4 aspect ratio; in horizontal format the width is 1.4 times the height. That's slightly different than the 1.5 aspect ratio of the original negative. This is why when you get a 5 x 7 enlargement from a negative or slide, the ends of the picture must be cropped slightly. About 7% to be exact. You can only fit 33.6 of the 36 mm width of the negative image, when enlarged, on a 5 x 7 print.
An 8 x 10 inch print has only a 1.25 aspect ratio, a little closer to being square than a 4 x 6, so the ends must be cropped even more, about 16%. You can only fit 30 of the 36 mm width of the negative image, when enlarged, on an 8 x 10 print.
And of course, if you are printing out your own pictures, and the software you're using allows it, you can print your photos at any resolution and physical size you want. You don't need to consider how Walmart or CVS will crop an image to fit a standard print size.
TV Screens / Computer Monitors
As of 2022, I doubt there are very many people at all who do NOT have an HD (high definition) wide-screen (16x9, or 1:1.77 aspect ratio) LCD or LED or OLED TV with a native resolution of at least 1920x1080 pixels. And now UHD, or "4K," is becoming almost the standard default, with much higher resolutions. In the not-to-distant past the size/aspect ratio of most TVs and computer monitors was 4x3, or 1:1.33 — the width of the screen was 1.33 times the height. This was the same as old Hollywood black and white movies, which is why they fit the screen of old TVs perfectly. Although there are still some "square" (4x3) computer monitors in use, almost all new computer monitors you can buy anywhere are wide-screen 16x9 (1.77) units. If you fool around with graphics very much like me (complete amateur, but enjoy the fooling around), it's nice to have a computer monitor that matches the resolution of your TV exactly, even though your monitor may be physically smaller. I use an older HD wide-screen 37" TV as my computer monitor (1920x1080 pixels resolution), with a direct HDMI connection to an HD wide-screen 43" TV (also 1920x1080 pixels). Scanning pictures, making slideshows, editing video to put on a DVD, etc., is easier because you can see exactly how it will look on an HD TV.
Windows Wallpaper
There are many different standard screen resolutions for your Windows desktop, going way back to the ancient 640x480 on a small 4x3 screen. Then it jumped up to 800x600, 1024x768, 1152x846, and 1600x1200. If you do the calculations, you can see that these older resolutions have aspect ratios of 1.33, exactly the same as the physical measurements of a standard older TV screen or CRT computer monitor. This was obviously by design, because if the aspect ratio, in pixels, of the "virtual" screen that is being visually displayed does not match the aspect ratio of the actual physical dimensions of whatever display device you are using, pictures will be compressed either horizontally (they'll look taller and thinner) or vertically (they'll look shorter and fatter). Depending on how powerful the video card in your computer is, what version of Windows you're running, and what kind/size of monitor you're using (standard or wide-screen), you will have several screen resolutions available, including an HD 1280x720 or 1920x1080 (or larger) widescreen 1.77 aspect ratio resolution. Just remember your Windows desktop screen resolution should be set to an aspect ratio that matches the aspect ratio of the physical dimensions of your monitor.
Now that your screen resolution is set correctly so you know that Playmate of the Month you're going to scan won't be taller and thinner or shorter and fatter than she should be, actually scanning a picture to use as Windows desktop wallpaper is simple. With your scanner's software, you can scan it at exactly the resolution you want; or, you can scan it at a higher resolution, load it into a photo editing program for touch-up, and then re-size and/or crop it down to exactly the dimensions of your Windows desktop. When scanning a 4 x 6 print or a negative or slide, which have 1.5 aspect ratios, remember the ends will have to be cropped a little (just as if you were getting an 8 x 10 print enlargement) if you want it to completely and exactly fill a standard 1.33 screen. And the top and/or bottom will have to be cropped a little to exactly fit a wide-screen 1.77 screen.
Taking Digital Photos for Prints
For the moment, note that we are talking only about prints made optically on photographic paper at a photo shop or drug store. We are NOT talking about prints made on your color ink-jet printer at home; there is an important difference that will be explained later. The commonly accepted standard for the resolution required in a digital file that you want to have a print made from is 300 dpi (dots per inch) for whatever size print you are making. (More than 300 dpi is wasted and will not increase the quality of the final print. Normal photographic paper does not have a fine enough grain to resolve more than about 300 dpi.) The dpi on photographic paper is an exact representation of the number of pixels in a digital file, so if you want some 4 x 6 prints made at 300 dpi, you would need a digital file that is 1200 x 1800 pixels in size. (4 inches X 300 dpi = 1200; 6 inches X 300 dpi = 1800.) For an 8 x 10 print, you would need a digital file that is 2400 x 3000 pixels in size. HOWEVER, like all so-called "commonly accepted standards" there is wide variation in what standard is accepted and by whom, and for good reason. You can get excellent results with 250 or 200 or even 100 dpi, especially if the original image or scan is very sharp and clear. Anyone who disputes this and claims you need 300 dpi for best results doesn't know what they are talking about, and there are a lot of experts that don't know what they are talking about. The proof is always in the pudding (preferably banana), not in a theoretical abstract discussion. I have actually tested this, and I urge you to do the same to convince yourself. I scanned a very colorful 8 x 10 picture of a basket of many different vegetables at 300 dpi, sharpened it a bit, cropped it to exactly 2400 x 3000 pixels, and it looked perfect onscreen. Then using Paint Shop Pro (you can use PhotoShop or any other of the many photo editing programs) I resized the picture to 2000 x 2500 pixels (250 dpi when printed at 8 x 10) and saved it as a separate file. Beginning with the original scan again, I resized the picture to 1600 x 2000 pixels (200 dpi when printed at 8 x 10) and again saved it as a separate file. I repeated the same thing to get files of 1200 x 1500 pixels (150 dpi at 8 x 10) and 800 x 1000 pixels (100 dpi at 8 x 10). I put a small text identifier in the corner of each picture so I could tell which was which. I put the original 300 dpi file and the other four lower resolution files on a CD and took it to Walmart and had one 8 x 10 print made from each file. After years of reading the propaganda in photo and computer magazines about the 300 dpi requirement, I was quite surprised at the results. I could not tell the difference between any of the five prints at first glance, and only after very close examination could I tell a tiny difference in sharpness around edges between the 300 dpi and the 100 dpi print. I even looked at the prints with a magnifying glass, and only when you get down to 100 dpi is there an almost insignificant difference in sharpness or clarity. This obviously shows up more on some types of photos than on others, for instance if there is a sign in the photo with black text on a white background, you will be able to see a difference between the 300 and 100 dpi prints. But for most general snapshots that you're not going to have blown up very large and framed, you won't notice any difference. If you don't believe me, do a test yourself. The small cost of the prints to actually prove this for your own eyes will convince you that for anything 8 x 10 or smaller, you don't really need anything more than 200 dpi, assuming the original is fairly sharp and clear.
Now for the difference between "real" photographic prints and color ink-jet prints. The main difference can be explained simply in how the term "dpi" is used and what it refers to. A photographic print is made optically on a special kind of paper, so as noted above, the "dpi" (or resolution, or sharpness of detail), of a photo coincides exactly with the number of pixels in a digital file. If you want a high quality 300 dpi print, you need a digital file that contains 300 pixels per inch for whatever size the final print will be. A printer is a little different. An average consumer-grade color ink-jet printer today might be advertised as printing at a resolution of 2400 dpi or more, but this refers to the actual number of dots of ink per inch the printer is capable of printing on paper, NOT to the digital file it is printing. Since it takes several dots of ink to print each pixel of the digital file, the printer obviously needs to be able to print much more than just 300 dots of ink per inch. The various makes and models of color ink-jet printers vary widely, but they all require several dots of different colored ink to print one pixel. It may be 6, 8, 10 dots of ink per pixel, or whatever, depending on the quality of the printer and the number of different colors of ink it uses, but they all need to print several different individual dots in varying patterns to create different colors and densities of pixels. So don't make the mistake of trying to save ink by setting your printer via software to print at only 300 dpi, thinking that's all you need for high quality. Leave your printer set to print at its highest resolution if you want the highest quality of print.
The sales of cameras have been declining for years now, since nowadays most people have a cell phone that takes pictures with a megapixel resolution much higher than small point-and-shoot cameras of just a decade ago. It would probably be very hard to even find a cell phone or camera that doesn't take shots with way more than enough pixels to print an 8x10 photo at 300 dpi. It should also be noted that a snapshot's resolution in pixels is only one factor in the quality of the final print. The quality of the light sensors in the camera or cell phone, the quality of the lens used, whether a tripod was used if zooming (highly recommended), and the software that runs the camera or phone and saves the picture as a .jpeg or other format, all have a direct impact on the final quality of the print. It is not only the widely advertised megapixel resolution of a camera or phone that determines how the picture looks.
Scanning Photos or Negatives & Slides for Prints
Scanning an old photograph or a picture from a magazine follows the same principles. You should scan the original at a resolution that will give you the number of dpi you want for whatever size print you are planning on making from the scan. As an example let's say you have an old 4 x 6 family photo whose negative has long since disappeared, and you would like an 8 x 10 print of that photo. (Remember that enlarging a 4 x 6 to an 8 x 10 will require a little cropping before printing.) I'll use 200 dpi for this example, since if you've been paying attention you should now know that you don't need 300 dpi to get excellent prints. Since you need a 1600 x 2000 pixel digital file for a 200 dpi 8 x 10, divide 1600 (height of the digital file required, in pixels) by 4 (height of the photo, in inches) and you get 400. You would need to scan the photo at 400 dpi, which would give you a 1600 x 2400 pixel file (4 inches X 400 dpi = 1600; 6 inches X 400 dpi = 2400). Most scanner software would then allow you to crop the image to 1600 x 2000, or you can load it into a photo editing program to do it. If you are not printing the picture yourself, but taking the digital file to a photo finisher to be printed, then you definitely want to do the cropping yourself first, so the print you get will be exactly what you see on screen.
For scanning slides or negatives, you will of course need a very high resolution scanner if you want to have some 8 x 10s printed from your scans. If you're not going to buy an expensive dedicated film scanner, make sure the flatbed scanner you get includes negative and slide holders. As noted above, slides or negatives from 35mm film are .944 x 1.417 inches. Since an 8 x 10 print at 200 dpi requires a digital file of 1600 x 2000 pixels, you would need to scan a negative at about 1700 dpi which would give you a digital file of 1604 x 2408 pixels. (.944 inches X 1700 dpi = 1604; 1.417 inches X 1700 dpi = 2408.) The picture can then be resized and the ends cropped, down to 1600 x 2000 to fit the 1.25 aspect ratio of an 8 x 10 print. Most inexpensive flatbed scanners today have at least 2400 dpi scanning ability, which is more than enough to get excellent results. As with digital cameras, the quality of the scanner hardware itself, and the software that runs it, is critical to the quality of the final print, so read reviews in magazines and online from users who have actually used the specific scanner you're interested in.