To figure out how many stitches to cast on for a hat:
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Measure around head of which hat is to fit. (If a surprise, measure around the wrist and wrap the measuring tape around twice.)
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Measure how many stitches per inch you get with the needles you will be using to make the hat. Or, in other words, knit up a swatch with the needles you plan to use.
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Multiply the # of inches around the head by the number of stitches per inch. For example, if I got a person with a head circumference of 20 inches and I got 3 stitches per inch, it would look like this:
20 [U]x 3[/U] 60
Hope the tip helps!
PS - For children, I usually use a 16" size 11 circular needle and worsted weight yarn, and I CO 48 stitches.
Hope this helps!