Load,
The Farady's law is used to calculate AC-line transformer:
B=E*10^8/(4.44*Ac*F*N)
B is operating flux density, depends the core material, you may arbitary choose the value, for example, 0.8*Bmax of core is a good start for high power ones, and 1.2*Bmax of core is used for small power. However, it should be trimmed to meet your requirement.
E is your AC-line voltage, RMS.
Ac is core's cross section area, cm^2
F is your line frequency.
N is primary turns, if the E above is AC-line input.
You now have 3 parameters, ie: B, Ac, N to play around.
In practical, I will suggest to fix the B value, and adjust the Ac to find N.
And then, check core loss, wire loss, temperature rise, regulation, efficiency etc, until they all meet your requirement.
Use B to final/fine tune your design until core lose is prety close to wire lose.
It realy bothersome, and there are lot of software may help you to design such transformer.