Greetings All: I am new to the Board, and new to quilting. I am learning
to make hats. I wanted to know what the system is to find out measurements of a circle for the length of fabric to go around the circle.
As in the band size for a hat, to match the crown of the hat.

Also, is there an easy way to sew the band of a hat to the crown of the hat without making it pucker?

Cliff, welcome to the forum. I will attempt to answer and hope to be some help. Let's go back to math class and see if that will help. C=piRsquared. Does that sound familar? Yea it does to me too, but darn if I want to do it that way. An easier way for me would be to stand a tape measure on it's side and actually measure around. But if you are good at math, the above formula may be easier for you.
One trick I learned many years ago for sewing a band on a circle was to first fold the circle in half and then half again to find the quarters. Mark those with a pin or some method. Do the same with the band, folding twice to find quarters. One thing to note though, be sure to add seam allowance to the band and when you fold the second time only fold to the seam allowance. You can sew the seam first and use the seam as one of the quarter marks.
Now match your marks and pin the band to the circle. At this point, I will pin again in the opening at that center. Continue in this fashion until the band is secure enough to sew. After you have sewn the band to the circle, press the seam allowance in the direction it wants to go, which would probably be towards the circle.
Let me write out the formula for you, as I do not have math symbols on my keyboard.
Circumferance= pi x Radius squared

Boo and Cliff, I think you want c=2piR. The other is area. A shortcut is 6.28x radius=c or 3.14xdiameter=c. But be sure to allow for thickness fo material of hat, and any overlap required.
Also, a straight piece of band will pucker if the crown tapers any at all, and without making a complicated pattern for each one, I would recommend using bias cut fabric to make the band. It has some stretchability.

To avoid puckers I stay stitch the band with a 1/2" seam provided I am using 5/8" seams. I cut the seam allowance to the 1/2" point in about 1/2" intervals. Then I use lots of pins. I also divide both the crown and the brim into fourths as Boo does.

Judy

Norah, you are probably right. This getting old sure isn't for sissies. I don't think I have looked at these formulas since begining quilting. They were useful once, or maybe that was just what the teachers told me. :lol:
As far as using bias for the band, I have not ever done that. I have used straight grain for making sides on round pillows and making hats for babies and such. I think that bias would be too unstable.

Boo: Thanks for your help and suggestions. This is the first time I have used the message board and what a great response I got. I am really new to quilting and sewing in general. I work at a design company and have a really great access to lots of fabric, some very high end. I am using the fabric books that companys give us for samples, as they throw them away when discontinued. I am figureing ways to get around the paper backing on the fabric. I have been going to upholstery shops and getting their end bolts,so far I have gotten two truck loads. Last night I
stiched a half inch line on the band and then cut lots of slits to the stich and then sewed the cap to the band and it works out great. I just leave a
half inch on the start open and then sew to the end and close it up and cut off the excess fabric. Seems to be working really well. Thanks for all your help. Take care: Cliff

Judy: Thanks for this tip. Last night I did the 1/2" stich and then cut lots of slits to the stich mark and then just sewed it up. Worked great and lots faster, no puckers. Thanks for your help. Take care: Cliff