Formula and Method for the Ideal Transformer Calculator
An ideal transformer transfers electrical energy between two circuits through electromagnetic induction with perfect magnetic coupling and zero resistive, core, or leakage losses. Its behavior is fully described by the turns ratio between the primary (input) winding and the secondary (output) winding: a = Np/Ns. This ratio sets how voltage steps up or down between the windings, and — because an ideal transformer conserves power — how current changes in the opposite direction.
Voltage and current relationships
For an ideal transformer, the voltage ratio equals the turns ratio: Vp/Vs = Np/Ns. Rearranged, the secondary voltage is Vs = Vp × (Ns/Np). Because the transformer is lossless, input power equals output power (Vp × Ip = Vs × Is), so the current ratio is the inverse of the turns ratio: Is = Ip × (Np/Ns). Whatever the voltage gains across the transformer, the current gives up in equal proportion, and vice versa — total apparent power stays the same on both sides.
Step-up vs. step-down, and real-world limits
When Ns > Np (more secondary turns than primary turns), the transformer steps voltage up and current down — the arrangement used at power plants to send electricity long distances at high voltage and low current, which reduces I²R losses in the transmission lines. When Ns < Np, it steps voltage down and current up — the arrangement used to power low-voltage devices such as doorbells, chargers, and control circuits. Real transformers approximate this ideal model closely at typical operating loads, but they lose a small amount of energy to winding resistance (I²R losses), core hysteresis, and eddy currents, so actual secondary output is always slightly less than the ideal calculation predicts.