Induction law:

The voltage induced across the secondary coil may be calculated from Faraday's law of induction, which states that:
where VS is the instantaneous voltage, NS is the number of turns in the secondary coil and F equals the magnetic flux through one turn of the coil.

If the turns of the coil are oriented perpendicular to the magnetic field lines, the flux is the product of the magnetic field strength B and the area A through which it cuts. The area is constant, being equal to the cross-sectional area of the transformer core, whereas the magnetic field varies with time according to the excitation of the primary. Since the same magnetic flux passes through both the primary and secondary coils in an ideal transformer,[20] the instantaneous voltage across the primary winding equals

Taking the ratio of the two equations for VS and VP gives the basic equation[21] for stepping up or stepping down the voltage