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

Background.

A transformer trades voltage for current at constant power, and the exchange rate is the turns ratio. Wind five thousand turns on the primary and a hundred on the secondary, feed the primary 12 kV, and the secondary produces 240 V — fifty times less voltage, and if the primary draws 2 A the secondary delivers 100 A, fifty times more current. This calculator solves that proportion in whichever direction you need it: secondary voltage from the turns, primary voltage from the secondary, the turns ratio from two voltages, or the secondary winding count from a target voltage.

Three quantities come free with the answer and they are the ones people forget. The secondary current, because a step-down transformer multiplies current by the same factor it divides voltage, which is why the low-voltage side of a distribution transformer is wired in conductors thick enough to be alarming. The apparent power, in volt-amps rather than watts, because nothing here knows the load's power factor. And the reflected impedance — the load as the source sees it — which scales with the SQUARE of the turns ratio, not with the ratio itself. A 2.4 Ω load behind a 50:1 transformer looks like 6000 Ω to the primary. That squaring is the whole basis of impedance matching, and it is the relation most often got wrong by a factor of the ratio.

The turns ratio has two conventions in circulation and this page reports both. It states the ratio as N_P:N_S, so a value above one means step-down; the source equations behind it are written the other way round, as N_S/N_P. A nameplate quoting 1:50 and a textbook quoting 50 can be describing the same transformer, so the verdict beside the result prints the number both ways before you compare anything.

Everything here is the ideal model, and the difference from a real transformer is stated beside the number rather than buried. Ideal means no winding resistance, no leakage flux, no core loss and no magnetising current, so efficiency is exactly 100 % and the secondary voltage does not move at all between no load and full load. Neither is true of hardware. By the source's own figure, a good transformer still loses about 1 % of the power passing through it, and a real secondary sags under load — the amount it sags is voltage regulation, which is a separate calculation. Treat the numbers here as the design centre and the starting point for a real design, not as what a meter will read.

What is ideal transformer calculator?

An ideal transformer is two windings sharing a magnetic core with perfect coupling and no losses. Because the same changing flux links both windings, the voltage induced per turn is identical in each, which gives the voltage relation V_S/V_P = N_S/N_P directly. Because an ideal transformer neither stores nor dissipates energy, the instantaneous power going in must equal the power coming out, V_P·I_P = V_S·I_S, and that forces the current relation I_S/I_P = N_P/N_S. Those two relations are the entire model. Everything else follows from them: dividing the voltage relation by the current relation gives the impedance relation, so a load Z on the secondary appears at the primary as (N_P/N_S)²·Z. A transformer with more secondary turns than primary turns raises voltage and lowers current and is called step-up; the reverse is step-down; equal turns give an isolation transformer, which changes nothing electrically but separates the two circuits galvanically, and that separation is its whole purpose. Note what the model does not contain — resistance, leakage inductance, core loss, saturation, frequency. A real transformer has all of them, which is why it has an efficiency below 100 %, a voltage regulation above 0 %, and a frequency range outside which it does not work at all.

How to use this calculator.

1. 01Pick the quantity you are missing. The same proportion is solved in all four directions and the unused fields are ignored.
2. 02Enter the winding turns. Only their ratio affects the voltages, but the primary count is needed to report a secondary turn count.
3. 03Enter the voltage or voltages you know, as RMS magnitudes. There is no sign or phase convention on this page.
4. 04Enter the primary current. It sets the secondary current, the apparent power and both impedance figures.
5. 05Read the secondary voltage, then check the turns ratio beside it — above 1 is step-down, below 1 is step-up.
6. 06Check the secondary current before choosing conductor sizes on the low-voltage side. It is the number that surprises people.
7. 07If you are matching impedances, use the reflected-impedance output: it scales with the square of the turns ratio, not the ratio.

The formula.

The whole model rests on one fact: perfect coupling means the same changing flux threads both windings, so every turn on either side sees the same induced volts. Divide the primary voltage by its turn count and you get the volts per turn; multiply by the secondary turn count and you have the secondary voltage. That is V_S = V_P × N_S/N_P.

Take the worked example. 5000 primary turns and 100 secondary turns give a ratio of 50 primary turns per secondary turn. With 12000 V on the primary, the secondary sees 12000 ÷ 50 = 240 V. That is the published example from OpenStax University Physics, which states the ratio as N_S/N_P = 1/50 — the same transformer written the other way round.

Current follows from energy conservation rather than from geometry. An ideal transformer stores nothing and dissipates nothing, so V_P·I_P must equal V_S·I_S. With 2.0 A drawn on the primary the apparent power is 12000 × 2 = 24000 VA, and that same 24000 VA leaving at 240 V requires 24000 ÷ 240 = 100 A. The source states 100 A for this example. The general form is I_S = I_P × N_P/N_S — current is multiplied by exactly the factor that voltage is divided by.

Impedance is where the squaring appears. The load on the secondary is V_S/I_S = 240 ÷ 100 = 2.4 Ω. What the source at the primary sees is V_P/I_P = 12000 ÷ 2 = 6000 Ω. The ratio between them is 6000 ÷ 2.4 = 2500, which is 50², not 50. Impedance transforms by the square of the turns ratio because voltage goes up by the ratio while current goes down by it, and impedance is their quotient. Getting this wrong by a factor of the ratio is the single most common error in transformer impedance matching.

Rounding happens once, at the return boundary, to ten decimal places, and the step-up/step-down/isolation band is decided on the unrounded turns ratio, so a ratio of 1.0000000001 is called step-down even though it displays as 1.

What the model omits, and why it matters here rather than in a footnote. Winding resistance and leakage inductance mean a real secondary voltage falls as the load draws current — the 240 V computed above is the no-load figure, and at full load the terminal voltage will be lower by the transformer's voltage regulation, typically a few percent. Core loss and magnetising current mean the primary draws something even with the secondary open. The source states that a good transformer loses about 1 % of the transmitted power, so the 24000 VA in and 24000 VA out on this page is an idealisation by roughly that margin. Nothing here models frequency, saturation or inrush.

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.