*So how do you calculate the image size you need?
Decide what size you want your printed image to be, then multiply the height and width in inches by the PPI you need for the print resolution you’ll be using. So a 8”x10” printed image should be 1200x1500 pixels. 8x150=1200; 10x150=1500

PPI and DPI
The important point about resolution is the difference between PPI (pixels per inch) and DPI (dots per inch). Many software programs and scanner interfaces use these two terms interchangeably but that’s not exactly accurate. As a general rule, the term PPI should be used when referring to image resolution, and the term DPI should be used when referring to printing resolution.

A popular myth is that it’s necessary to scan an image at the same resolution that you will be using to print. In the case of color and grayscale images, this only results in excessive file sizes. A good general rule for inkjet and laser printing is that you need one-quarter to one-half the PPI of the printer’s DPI setting that you intend to use. So if you’re using your printer’s “normal” setting (600 DPI), your image needs to have at least 300 PPI for a laser printer and 150 PPI for an inkjet printer.

PPI and LPI
Printers can render many more dots per inch than the pixels per inch we call on them to print. This is good, because most printers, unlike monitors, can render very few colors, and so must average over many dots to render a particular color with reasonable accuracy. A 1440x1440 dpi printer can devote a 20x20 cell of dots to render a single pixel of a 72 dpi image. If the pixel is a light pink, a four-color printer will have a few of these 400 dots (20x20) red, while the remainder are white. Thus, someone speaking precisely would say that the image is 72 pixels per inch rendered on a 1440 dots per inch printer. Determining image resolution for offset printing (printing press) output is a little bit different because of the way an image gets printed. For an image to be printed on a printing press it must first be converted into a “halftone”. A halftone is expressed in terms of the “screen frequency” - the number of “Lines Per Inch” (LPI) of the screen used to prepare it. Halftones appearing in a typical newspaper range from 65 to 85 line screen. Halftones appearing in magazines, brochures and high quality catalogs typically vary between 133 and 150 line screen. There is a rule of thumb used in preparing images for printed output. Scan or size images at a resolution (PPI) of 1.5 to 2 times the screen frequency (LPI) of the finished halftone. For example, a 2 inch by 3 inch photo would be scanned or sized to a 2 inch by 3 inch image at 225 to 300 PPI for a finished halftone to be printed at 150 LPI (150 line screen). Were the same photo to be printed using a 120 line screen halftone, it would be scanned or sized to 2 inches by 3 inches at 180 to 240 PPI.