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What does DPI mean?

I have a hard time understanding the concept of dots per inch. I've looked the wikipedia article and I am still unsure. Say I have a 4"x6" photograph at a resolution of 300 dots per inch. Say there are 20 bits of data per dot. What would be the file size of the image?

EDIT: From all your replies, this is what I figure. The file size of the image would be

4*6*(300^2)*20 = 43200000 bits = 5400 KB = 5.4 MB.

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pogo
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    Sorry but your edit shows more confusion. There is no simple relationship between bits and dots. – Itai Nov 03 '12 at 00:55
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    What exactly are you asking here? Is it: How much ink is used, how much data is needed,or something else entirely. There is no clear question that the whole post refers to. – damned truths Nov 03 '12 at 11:03
  • @pogo - In case it is not clear, compare the extremes: a 10-bit 4x6 image which is entirely white takes zero ink. One which is entirely black will take considerably more but only of the black ink. – Itai Nov 03 '12 at 12:57
  • The latest edit (#5, as of this writing) is still very strange. What units do you imagine the answer will be in for "size of the image"? – mattdm Nov 06 '12 at 00:20
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    Although I'm tempted to answer "It will be 4"×6"!" – mattdm Nov 06 '12 at 00:20
  • I'm going to second what @damnedtruths says above: because the question is confusing, we're only guessing at what you're trying to figure out. Can you take a step back and explain what prompted this question? – mattdm Nov 06 '12 at 00:25
  • Would this article help? It's a general overview of DPI and resolution I wrote a while ago. – Itai Nov 06 '12 at 01:13
  • That would be the raw data size. If you saved this in an uncompressed format you would have 5.4 MB (form your example) plus header and metadata. If you use most standard formats the size would be less because of compression (lossless or lossy). – Itai Nov 06 '12 at 04:08

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You are confused because dots on an image do not correspond to dots on a printer.

The recommended 300 DPI is for images where each dot is actually a pixel and can be of any number of colors, 16 millions for a JPEG, more for other formats.

A printer requires many dots to render a single image pixel, sometimes over 100. That is because a printer has between 3 to 12 colors possible for each dot. In order to simulate one of these millions of colors, printers make small patterns (called dithering) to make your eye see one of those colors.

That is why so see printers specified with resolution of 2400 to 9600 DPI but images in the 72 to 600 DPI range. You cannot calculate the volume of ink without knowing how the printer renders each dot in your image. That is because light colors require fewer dots than dark colors since the white of the paper provides the white component.

Some printers will apply a gloss coating over based on how much ink was used for each pixel in order for there not to be variations in glossiness on the print surface. Some printers will even mix differently to compensate for some cartridges being low.

Itai
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  • And even the pixel calculation is wrong: it would be (4 * 300) * (6 * 300) = 2,160,000 pixels. And along with the varying dot density, most printers can use variable dot sizes (to reduce the visibility of the dithering pattern). And that's why consumables are rated using an artificial "average" image with a known ink coverage (and why people with high-key and low-key styles report very different consumable costs). –  Nov 02 '12 at 18:03
  • "but images in the 72 to 600 DPI range" really should be "but images in the 72 to 600 PPI range". Pixels Per Inch is the correct term to use when describing picture elements, regardless of format. Dots Per Inch, or sometimes just "dots" is only correct when discussing the actual number of SUBPIXEL elements per inch. In the case of a computer screen (or even the LCD screen on a DSLR), DPI or "dots" is used to count each subpixel element, just like it is when counting individual ink droplets per inch (of which many may comprise a print "pixel"). – jrista Nov 06 '12 at 03:58
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The photograph and printer resolutions could be two quite different things. You have to find out what resolution the printer is actually using to calculate the total number of dots it prints. Even then your formula is incorrect. If the printer really emitted 300 dots per inch (DPI) in one dimension, then the number of dots in any one direction for a length in inches would be length * 300. To get the dots in a area, you multiply this value for both dimensions. In other words, the number of dots in a 4x6 inch area would be (4 x 300)(6 x 300) = 4 x 6 x 300² = 2.16M. I don't believe the printer actually would use 100 µg of ink per dot, but using your value that would mean if it printed every dot it would use (2.16 Mdots) * (100 µg/dot) = 216 grams of ink. That's a clearly absurd value, pointing out how unrealistic 100 µg/dot really is.

Then there is the issue of what exactly a "dot" is. Depending on how the printer does dithering, it could emit 0 to 3 droplets per dot depending on the color and dither pattern, and therefore which inks it used for that dot. Some printers lump a user-level "dot" into several internal microdots so that each "dot" can have several shades of each color, not just all or nothing for each of the 3 basic primaries or black.

Olin Lathrop
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  • The units doesn't match here. inch*inch * (dot/inch) * (dot/inch) * µg/dot = dot-µg and not µg – pogo Nov 03 '12 at 00:15
  • @pogo: I was trying to show where the numbers come from. Actually, the resolution would be 90,000 dots per square inch. Then (4 inches) * (6 inches) * (90,000 dots / square inch) = 2.16 Mdots as I said. I thought this was understood. However, in no way does it make sense to add the length and width as you did. – Olin Lathrop Nov 04 '12 at 00:20
  • how did you get 90,000 dots/square inch? If you multiplied 300 dpi * 300 dpi, isn't it 90,000 (dots/inch)^2 i.e 90,000 square dots / square inch ? Is this wrong? Thanks. – pogo Nov 06 '12 at 00:01
  • @pogo: it's not "square dots" because dots are counted, not measured. By analogy, when we measure people per square mile, we don't say "square people". – mattdm Nov 06 '12 at 00:43
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On edit six:

4*6*(300^2)*20 = 43200000 bits = 5400 KB = 5.4 MB.

Okay, so, you're right in the multiplication here (give or take a quibble about binary vs. decimal KB and MB). That is the uncompressed byte size of the data which makes up the image.

However, it's not necessarily the file size of the image, because most popular image file formats feature compression (either lossy, like JPEG, or lossless like PNG or many TIFF and RAW-type files), and because the image file will also carry some amount of metadata.

(Also, the bit depth is more likely to be 24, with three 8-bit channels.)

But, what are you trying to do with this result? You mentioned network transfer in an earlier edit, and amount of ink used before that.

Particularly, with digital files, you normally can just look at the height and width if that's what your concerned about, with no need to covert to inches and DPI and back again.

It's also worth mentioning that this usage is of "dots" is conceptually wrong, because we're really talking about image pixels, so PPI might be more appropriate. (See this other answer for more on that.) But the terms are often conflated, including in photography software.

I still think What does DPI mean? should cover everything you need to know here.

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mattdm
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