Help!

Hi Everyone! Happy New Year! I’m knitting a hat for my granddaughter, age 7 1/2. The pattern calls for yarn with a gauge of 20 sts and 26 rows=4" in St st. And size 7 circular needles.
Now, the yarn I want to use has a gauge of 9 stitches + 14 rows = 4" using 10.5 needles.
How do I know how to adjust the pattern? I would like to use the 10.5 needles…Obviously I need to cast on a lot less stitches since I already had to undo to starts already since the hat was much too big for her! I’m a fairly new knitter…not quite a newbie, but close! And I’m not good at the math stuff…:??

If 20 stitches =4" then 5 stitches=1". Divide the number of stitches the pattern says to cast on by 5.

Example, if it says to cast on 80 stitches, then 80/5=16. So you know you are shooting for 16"

Knit a swatch to see how many stitches/inch you actually get. Multiply that by 16 and you’ll know how many stitches you need to cast on.

What you need to do for the yarn you have chosen is use a needle size that will give you the gauge the pattern calls for. Do not change the number of stitches but the size of needle you use. Knit a gauge swatch and go up or down a needle size until your gauge swatch is the same as the patterns calls for you to have. You may have to knit a couple of gauge swatches until you get the pattern gauge but in the long run you will finish the pattern exactly as it was written and you won’t have to remember how many stitches you subtracted off the pattern.:knitting:
If you want to use the 10.5 needles then there isn’t enough information given to tell you how many stitches to cast on. Are you a tight knitter or loose knitter? This will affect your knitting. I really say a gauge swatch is the best way to go.

Well no, that won’t work because the yarn is a really thick one and the pattern calls for a worsted weight. She’d have to go way down in needle size and the hat would be really stiff. Doing the math as Mason says is really the best way to go and for a hat, not all that difficult. And yes, it’s good to knit up a swatch to see how many sts/inch she’s going to get with the thicker yarn.

Thanks to all who were so kind to respond to my problem!!!