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Each pixel takes up 3 bytes (which make up 3 values from 0-255 which are the values of Red, Green and Blue at that pixel) - so a 1 inch square image, at 96dpi, will contain 96x96x3 bytes = 27648 bytes = 27.65kb
That is for an uncompressed 24-bit image (because there's 8 bits in a byte they call them 24 bit images) with no header information in the file. Usually the file will have some extra bytes at the start which define the size and resolution (dpi) of the image, so your 27kb image will actually be 28kb.
Monitor resolution is the the number of pixels fit across and down your computer screen. You can increase your monitor resolution to fit more dots across your screen.
DPI resolution is a standard measure used in the real world to describe the number of Dots Per Inch
Simplest way I explain it is that INCHES only come into play when you are printing. So DPI has no importance for displayed images, only printed images.
"640x480 resolution" means 600 pixels wide, and 480 pixels high, ON THE SCREEN. What is the image's "DPI"? That is determined at print time, by your computer setup (software settngs, printer driver, printer settings, etc).
600dpi means 600 dots (like pixels) per INCH, so it must be referring to printouts. Eventually you come to nderstand that what you need as an image file is determined by what you intend to do with it (display or print). Many people don't accept that.
As for file size, that will depend on the file format (GIF, JPG, PNG, etc) other binary format if it is a printable document (Word doc, PDF, bitmap, etc)
the SIZE it will print is determined at print time, by the print resolution (dpi). So a 900x900 pixel image will print, at 300dpi, as a 3x3 printout. If you print it at 600dpi, it will be finer print BUT it will also be smaller (1.5 inches square). If you want it to still print as 3x3 inches, it will be grainy (lower resolution).
So you see if you want a certain SIZE printout and fine printed image (300dpi), then you have to define your image file accordingly. It will be a very large file.
For screen use, the same fine appearance for a 3x3 inch SCREEN size would be a relatively small file, for most monitors/settings.
The key to remember for screen display, if that's what you're after, is the image's dimensions -- how many pixels across, how many pixels down. That is, a 400-pixel-wide image will be 400 pixels wide on every monitor in existence, period, regardless of dpi, ppi, print size setting, or anything else.
Basics to know:
DPI=Dots per square inch
PPI=Pixels per square inch (same thing as DPI, just a different name)
The higher the DPI, the better quality print. The more dots there are per square inch, the more detail your eye will see.
As other people have pointed out, DPI (or PPI for that matter) doesn't matter on screen, only pixel dimensions matter. DPI only matters for print.
Text and vector graphics should be printed at the printers maximum. Offset presses often print text and vector graphics at 4,800 DPI and higher.
The standard DPI for a printed photograph if 300. There's a point of diminishing returns for high resolution photo printing because CMYK prints acheive their colors by offset, halftone screens. Those screens are made of dots that only get so small. 300 is the standard because most presses (and desktop printers) can't print any detail finer than 300 dpi because of their halftone screen's dot size.
Another thing to keep in mind. If you are going to use Photoshop's image size option to set an image's DPI, please remember that Photoshop can't invent detail that isn't there. What I mean is, that if you have an image that is 3"x3" @ 72 DPI, increasing it's resolution to be 3"x3" @ 300 DPI will NOT make the image look better. While your image will now be 300 DPI, it will be a fuzzy 300 DPI. Photoshop's default interpolation (interpolation means scaling up an image aka blowing up a photograph) method is bicubica interpolation. Bicubic interpolation samples the dots around it and adds the additional pixels as a mix of the colors next to it. What that means is that if you have a photograph of a leaf, increasing the resolution isn't going to suddenly put in detail that wasn't there before (like a ladybug that you couldn't see @ 72 DPI).
So if you want to have 300 DPI photos that will look good, you have to start with an image that is already the size you need at 300 DPI or larger (down sampling is ok for detail, just not the other way around).
Raster elements min. resolution = imagesetting liniature (lpi=lines per inch) x 2.
Namely. If you're going to output your jobs on a 2540 dpi/150 lpi imagesetter setup (general offset), you should use at least 150 lpi x 2 = 300 dpi raster element's resolution. At 175 lpi, you should use minimally 350 dpi.
On a rotooffset (web), at 90 lpi - 180 dpi images, 120 lpi - 240 dpi images.
All together to ensure smooth gradients without banding and smooth light- and dark- midtones and tonal transitions.