To see this, let's start with a 1 inch square, at 10 dots per inch (dpi.) The total number of dots (pixels) is 10x10, or 100. If we create a larger square, say 5 inches on each side, we now have 25 square inches. At 10dpi, that's 2500 pixels (100 dots per square x 25 squares.) If we scanned a normal sheet of paper (8.5x11) we have a total of 93500 pixels.

Going back to the 1 inch square, say we double the dpi to 20. What does that do to the pixel count? You might initially say it doubles. If you calculate it, however, you find that you quadrupled the number (20x20 = 400.)

The total number of pixels can be found using the formula:

(horizontal dpi * image width in inches) * (vertical dpi * image height in inches) = total pixels

A normal sheet of paper, scanned at 100dpi

(100 * 8.5) * (100 * 11) = 935,000 pixels

The other item to consider is the bit depth of the image. For a bitonal image, each pixel is represented by 1 bit (black or white.) Color images, such as photos, are saved with RGB values for each pixel. This typically requires one byte per color, or three bytes per pixel

To calculate the total number of bytes per image:

total pixels * bytes per pixel = total bytes

A normal sheet of paper, again at 100dpi, scanned in 1 bit-per-pixel (bpp)

935000 * 0.125 = 116,875 bytes

That same page, scanned in 24bpp

935000 * 3 = 2,805,000 bytes (~2.5MB)

As you can see, scanning in full color without compression creates much larger images. Again with 24bit color, here are some common scanner dpi's with their resulting image sizes (in bytes.)

200 dpi = (200 * 8.5) * (200 * 11) * 3 = 11,220,000

300 dpi = (300 * 8.5) * (300 * 11) * 3 = 25,245,000

600 dpi = (600 * 8.5) * (600 * 11) * 3 = 100,980,000

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