Ideal Transformer Calculator — Turns Ratio, Voltage, Current and Impedance

Background.

Wind two coils on one iron core, drive one with alternating current, and every turn on both coils picks up the same voltage from the shared magnetic flux. That single fact is the transformer. Put 12,000 V across a primary of 5,000 turns and each turn carries 2.4 V; a secondary of 100 turns collects 100 × 2.4 = 240 V. Change the secondary turn count and the output voltage changes in proportion.

Current moves the other way. A lossless transformer cannot create power, so when the voltage falls fiftyfold the current must rise fiftyfold to keep volts times amps equal on both sides: 2 A drawn from a 12 kV line becomes 100 A at 240 V. That is why the low-voltage cables leaving a distribution transformer are so much thicker than the high-voltage line feeding it.

Solve the proportion for whichever of four values is missing — either voltage, the turns ratio, or the secondary turns for a target voltage — and you also get the secondary current, the volt-amps, and the load impedance seen from each side. Impedance is where intuition fails: it transforms with the square of the turns ratio, so a 2.4 Ω load behind a 50:1 transformer looks like 6,000 Ω from the primary.

These are the ideal relations, with no winding resistance, stray flux or core loss. Good real transformers come close, losing as little as 1% of the power they carry according to OpenStax, but their output voltage drops as load increases, which is what the voltage regulation calculator estimates.

What is ideal transformer calculator?

An ideal transformer is a model of two windings coupled perfectly through a lossless core: all the flux from one winding links the other, nothing is dissipated, and no current is needed just to magnetise the core. Under those assumptions the voltages are in the ratio of the turns and the currents in the inverse ratio. More secondary turns than primary turns makes a step-up transformer; fewer makes step-down; equal turns make a 1:1 isolation transformer. The ratio is reported here as a = N_P ÷ N_S, so a value above 1 means step-down, while OpenStax and many textbooks write the reciprocal N_S ÷ N_P.

How to use this calculator.

1. 01Under "Solve for" choose the unknown: secondary voltage, primary voltage, turns ratio, or secondary turns. Fields that mode does not need are ignored.
2. 02Enter Primary turns N_P, and Secondary turns N_S if the mode asks for it. Only the ratio sets the voltages, so 50 and 1 give the same voltages as 5,000 and 100.
3. 03Enter the voltages as RMS values, the figures a multimeter or nameplate gives, without signs or phase angles.
4. 04Enter Primary current I_P, the current drawn from the supply. It must be above zero because the current, power and impedance results all scale from it.

The formula.

Because the same changing flux links every turn, volts per turn are equal on both windings: V_P ÷ N_P = V_S ÷ N_S, which rearranges to V_S = V_P × N_S ÷ N_P. Solving for the ratio or the turns from two voltages uses the same equation backwards: a = V_P ÷ V_S and N_S = N_P × V_S ÷ V_P.

Current follows from conservation of power rather than from the winding geometry. With no losses, V_P × I_P = V_S × I_S, so I_S = I_P × a: the current is multiplied by exactly the factor the voltage is divided by. The common product is the apparent power S = V_P × I_P, in volt-amps.

Impedance is voltage over current. On the secondary the load is Z_load = V_S ÷ I_S; at the primary the source sees V_P ÷ I_P. Voltage has been multiplied by a while current has been divided by it, so the ratio between the two impedances is a², not a: Z_primary = a² × Z_load.

Everything is a magnitude. The model assumes a passive load and carries no phase angle, so it cannot split volt-amps into real and reactive power, and it says nothing about frequency, core saturation or the inrush current when a transformer is switched on.

A worked example.

Frequently asked questions.

References& sources.

1. [1]OpenStax (Rice University), University Physics Volume 2, §15.6 'Transformers'. Primary source for every relation implemented: the voltage relation 'v_S(t) = (N_S/N_P)v_P(t)' with the abbreviated form V_S/V_P = N_S/N_P; the current relation 'i_S(t) = (N_P/N_S)i_P(t)'; power conservation 'i_P(t)v_P(t) = i_S(t)v_S(t)'; the definitions that a step-up transformer 'increases voltage and decreases current' while a step-down transformer 'decreases voltage and increases current'; and the real-world figure that 'a good transformer can have losses as low as 1% of the transmitted power'. Example 15.6, used as this page's worked example, steps 12 kV down to 240 V with N_S/N_P = 1/50 and an input current of 2.0 A, giving an output current of 100 A. Retrieved 2026-07-29.
2. [2]Tony R. Kuphaldt, 'Electric Circuits II — Alternating Current' (Lessons in Electric Circuits, Volume II), Workforce LibreTexts §10.2 'Step-up and Step-down Transformers'. Independent second authority, consulted to check this page rather than to derive it. States that 'a transformer that increases voltage from primary to secondary (more secondary winding turns than primary winding turns) is called a step-up transformer', that 'a transformer designed to reduce voltage from primary to secondary is called a step-down transformer', and that 'the voltage and current transformation ratio is equal to the ratio of winding turns between primary and secondary'. Its simulated 10:1 example gives a secondary of 0.9962 V and 0.9962 mA from a primary of 10 V and 0.09975 mA — against the exactly 1.0000 V and 0.9975 mA this ideal model returns, a 0.4 % gap that is precisely the winding loss the ideal model omits. Retrieved 2026-07-29.
3. [3]Tony R. Kuphaldt, 'Electric Circuits II — Alternating Current', Workforce LibreTexts §10.6 'Voltage Regulation'. Cited for the boundary of this page's model: an ideal transformer has zero voltage regulation by construction, while a real one does not, and the source's benchmark is that 'a good power transformer should exhibit a regulation percentage of less than 3%' on a resistive load. This is the quantity the secondary-voltage figure on this page does not include, and the reason the two pages cross-link. Retrieved 2026-07-29.