I figured out the sizing for this hat by measuring a purchased fabric hat in size 18 months and comparing those measurements to a children's head size chart to estimate the measurements for the other baby and toddler hat sizes.
I used a self-striping sport weight yarn to crochet the example but wrote the directions in a way that will allow you to substitute any brand, weight and type of yarn that you choose. I used a basic increasing formula for the top circle of the hat.
Abbreviations: ch = chain, chs = chains, ea = each, sc = single crochet, st = stitch, sts = stitches
Materials: The beauty of this pattern is that you can use any weight of yarn because the size is determined by measuring each section as you go along and crocheting the number of rounds needed to get the size you want. Therefore, you can easily adapt this pattern to any type of yarn that you would like to make it with.
In the example, I used about 2 oz. Bernat Baby Coordinates Sweet Stripes sport weight yarn with US size G hook. This is a self-striping yarn that does the work of color changes for you.
If this will be a hat for summer wear in hot weather, a cotton or cotton blend yarn would be most comfortable for the wearer.
Measurements: Example - The top circle measures about 5 3/4 inches in diameter for size 18 months. Don't fuss too much about it if your measurements are off by 1/4 inch or so; there's leeway in the fitting of a hat. It's better to go a little bigger than a little smaller, though, to be sure that it won't end up being too small.
Top circle: 6 months - 5 1/4 inches, 12 months - 5 1/2 inches, 18 months to 2 years - 5 3/4 inches, 3 years - 6 inches
Center Band: 6 months - 2 inches, 12 months - 2 1/4 inches, 18 months to 2 years - 2 1/2 inches, 3 years - 2 3/4 inches
Bottom Brim: 6 months - 1 inch, 12 months - 1 1/4 inches, 18 months to 2 years - 1 1/2 inches, 3 years - 1 3/4 inches
Gauge: I am not including gauge because it is not needed. The size is determined by measuring each section ... so this pattern will work for any gauge.
Single Crochet - Instructions link, with photos: sc how-to
Pattern Note: You will work in continuous rounds. Be sure to mark the first stitch of each round and move the marker to the first stitch of the next round as you begin it. You could use a paper clip, safety pin or purchased stitch marker for this purpose.
Pattern begins at the center top of the hat.
Starting Chain: ch 5, join with a slip stitch to form a ring.
Hat Top, Rnd 1: 6 sc in ring.
Rnd 2: 2 sc in ea sc around (12 sc)
Rnd 3: sc in next sc, 2 sc in next sc (18 sc)
Rnd 4: sc in ea of next 2 sc, 2 sc in next sc (24 sc)
Rnd 5: sc in ea of next 3 sc, 2 sc in next sc (30 sc)
Rnd 6: sc in ea of next 4 sc, 2 sc in next sc (36 sc)
Rnd 7: sc in ea of next 5 sc, 2 sc in next sc (42 sc)
Rnd 8: sc in ea of next 6 sc, 2 sc in next sc (48 sc)
Note: When you reach the number of inches needed for the top circle for the size you are making, stop and skip to the Center Band directions. Otherwise, continue until you have the size you need.
Rnd 9: sc in ea of next 7 sc, 2 sc in next sc (54 sc)
Rnd 10: sc in ea of next 8 sc, 2 sc in next sc (60 sc)
Rnd 11: sc in ea of next 9 sc, 2 sc in next sc (66 sc)
Rnd 12: sc in ea of next 10 sc, 2 sc in next sc (72 sc)
Rnd 13: sc in ea of next 11 sc, 2 sc in next sc (78 sc)
Size 18 months (shown in the example), made with the materials listed, needed 13 rounds to reach 5 3/4 inches in my crochet gauge. Your gauge doesn't have to match mine as the size is determined by measuring the circle, using any number of rounds that will give you the correct number of inches for the Hat Top.
If you need to make further rounds, simply add one additional number of sc between increases for each new round (an increase is made by making 2 sc in one sc).
Center Band, Rnd 1: You will work in the back loop only of ea sc for this round only (makes the
piece fold downward easier). sc in back loop of ea sc (no increases).
Rnd 2 and additional rounds of center band: sc in ea sc of each round (no increases).
Make as many rounds for the center band as you need to reach the number of inches needed for the size you are making. Example: For size 18 months, the center band should be 2 1/2 inches wide.
Bottom Brim, Rnd 1: Work in the front loop only of ea sc for this round only (makes
the piece fold forward for the brim).
(2 sc in next sc, sc in next sc) as many times as needed to go around.
Rnd 2 and additional rounds of bottom brim: sc in ea sc of ea round (no increases).
Make as many rounds for the bottom brim as you need to reach the number of inches needed for the size you are making. Example: For size 18 months, the bottom brim should be 1 1/2 inches wide.
If desired, fold the bottom brim up in the front and sew on a few buttons or an applique to keep it in place. You could also use a strand of 1/8 inch wide satin ribbon by weaving the ribbon through both thicknesses (could use a yarn needle to pull the ribbon through) and tie the ribbon in a bow, if you only want to fold the bottom brim up temporarily.