Hi

I need to find the length of thread that is winded in a bobbin. I tried to find out with the rotation of the shaft. But as the diameter of the bobbin (with thread) increases the length winded is also increasing.

Say,
On the initial stage the thread winded for 10 rotation of shaft is 13 inches
After some stage for same 10 rotation of shaft thread winded is 21 inches
And in the final stage for 10 rotation of shaft thread winded is 30 inches.

Is there any formula I can use here?

I assume you want a formula that calculates the total length of thread wound for X number of revolutions of the bobbin, starting with an empty bobbin - correct? You will need to tell us how many revolutions it takes to get from the initial stage of 13 inches/10 revs to the 2nd stage of 21 inches/10 rev to the 3rd state of 30 inches/10 rev. With that data we can determine the rate of increase of the wrapping radius as a function of revolution of the bobbin.