Hello,
I agree with JimB that you need to tell us the dimensions of the center leg of the transformer. That tells us the cross sectional area of the core from which we can calculate the minimum number of turns required for the primary.
The formula can be broken down for 50 Hz as:
N=(22.5*E)/A
where
A is the center leg cross sectional area in square centimeters,
N is the number of turns on the primary,
E is the maximum RMS voltage assumed to be sinusoidal.
This assumes you are using regular EI laminations used for 50 or 60Hz transformers.
This formula computes the absolute minimum number of turns however, so a good practice would be to use at least 10 percent more turns:
N=1.1*(22.5*E)/A
The wire thickness (wire gauge) must be able to accommodate the required primary excitation current plus the required secondary current reflected back to the primary. For a step down transformer of 10 to 1 for example, the reflected secondary current would be 1/10 (one tenth) of the secondary current, so with a 10 amp secondary current the primary would see 1 amp. The secondary wire must be able to handle the secondary current.
This last requirement also means that there is a constraint on the maximum power that the core can be used for, because of the size of the window area vs the required wire gauges for primary and secondary.
Also, it is customary to increase the number of primary turns to counter the voltage drop in the coils when the transformer secondary is loaded with the full load current. This is based on the resistance of the two windings.
To use the formula at 60 Hz, multiply the calculated number of primary turns by 50/60. At 400Hz this factor would be 50/400.