Every number in a generated hat pattern comes from two figures: stitches per inch and rounds per inch. A swatch is how you find them for your yarn and needles. Twenty minutes of knitting saves a hat that fits nobody.
Knit the swatch
Cast on about 30 stitches with the needles and yarn you plan to use. Work in stockinette (knit the right-side rows, purl the wrong-side rows) for about 4 inches. Bind off loosely. If the hat will be knit in the round and you want to be exact, knit the swatch in the round too, since many people purl at a slightly different tension than they knit.
Wash the swatch the way you will wash the hat and let it dry flat. Wool in particular relaxes after washing and the stitch count changes.
Measure it
Lay the swatch flat without stretching it. Put a ruler across the middle, away from the edges, and count the stitches in 4 inches. Do the same vertically for rows. Divide each by four.
A count of 18 stitches and 24 rows over 4 inches is 4.5 stitches and 6 rows per inch, which is the default gauge on the hat designer.
If the numbers are off
You do not have to hit a printed gauge. Enter your own figures on the designer or the hat calculator and the cast-on, length and crown are computed for them. Change needles only if you want a different fabric: a size up makes a softer, drapier hat; a size down makes it denser and warmer.
Half stitches matter
Over a 22 inch head, half a stitch per inch is 11 stitches of difference, about 2.5 inches of circumference. Measure over the full 4 inches, not 1 inch, and round to the nearest quarter stitch.