I can't be sure if my earlier post got buried, didn't go through, or nobody was interested, so I guess I'll try posting a second time!
I saw the thread you started on calculating turns ratio, and while it's not an "online tool" exactly, I wrote this little script that you can run in the browser:
It calculates a set of rational approximations to your desired turns ratio within a given tolerance and maximum number of turns, and sorts by them top to bottom by smallest absolute error. It uses a Stern-Brocot tree, which was a method used by clockmakers to determine gear ratios - essentially a type of binary search.
Finding rational approximations for a given ratio is also possible via brute-force, but has a time complexity of O(n^2) in the number of turns. The Stern-Brocot algorithm has time complexity O(log(n)), so if you need to design a transformer with a million turns in a hurry it might be your best bet.
The results for your given turns ratio, less than 1e-6 absolute error and 10,000 max turns are:
6777/6193: absolute error: 1.61473e-08, relative error:1.47558e-08
4166/3807: absolute error: 2.62674e-08, relative error:2.40038e-08
2611/2386: absolute error: 8.38223e-08, relative error:7.6599e-08
1555/1421: absolute error: 2.11119e-07, relative error:1.92926e-07
1056/965: absolute error: 5.18135e-07, relative error:4.73485e-07