Transformer calculator

What is the transformer equation?

For an ideal transformer the voltages are in the ratio of the turns: Vs ÷ Vp = Ns ÷ Np. The currents go the other way: Is ÷ Ip = Np ÷ Ns (OpenStax University Physics).

Example

OpenStax steps 12 kV down to 240 V — a turns ratio of 50 : 1. A primary current of 2.0 A becomes 100 A on the secondary side.

Step-up or step-down?

More turns on the secondary than on the primary raise the voltage (step-up); fewer lower it (step-down). Power companies step voltage up for long lines because the lower current wastes less power in the wires.

Is power the same on both sides?

In an ideal transformer, yes — voltage × current is the same on both sides. Real transformers lose a little to heat.

Does it work with DC?

No — a transformer needs a changing current. It works with alternating current (AC).

How do I find the turns ratio from the voltages?

Divide the secondary voltage by the primary voltage: Ns ÷ Np = Vs ÷ Vp. For 12,000 V down to 240 V that is 50 to 1 in turns, or 1 turn on the secondary for every 50 on the primary. The ratio fixes only the proportion, not the actual number of turns.

What resistance does the source see through a transformer?

A load resistance R on the secondary appears to the source as (Np ÷ Ns)² × R. OpenStax gives this relation for the ideal transformer. With a 10 to 1 step-down ratio, a 4 Ω load looks like 400 Ω on the primary side.

What the ideal-transformer equations assume

The equations hold when all the magnetic flux stays in the core, so that the same flux passes through every turn of both windings, and when the losses from hysteresis, winding resistance and eddy currents are ignored. Power in then equals power out, Ip × Vp = Is × Vs, and any change in voltage is paid for by an opposite change in current. OpenStax notes that a good transformer can lose as little as 1% of the power it passes, so the ideal values are close for a well-made unit. The voltages and currents are rms values, and the calculator gives the ideal secondary voltage and current, not the rating of any particular transformer.

Worked example

OpenStax steps 12 kV down to 240 V with a 50:1 turns ratio, so the secondary voltage is 240 V. A primary current of 2.0 A becomes 100 A on the secondary. Suppose the line feeding the load has 200 Ω of resistance. Carrying 2.0 A at 12 kV it loses 2.0² × 200 = 800 W. Delivering the same power at 240 V with no transformer would need 100 A and lose 100² × 200 = 2,000,000 W, which is why power companies send electricity over long lines at high voltage. A smaller case: a 100 W load on a 24 V secondary, a 10:1 step-down from 240 V, draws 4.17 A, and the primary carries 0.42 A.

Common mistakes

Turning the ratio upside down is the frequent slip: voltage follows Ns ÷ Np, current follows Np ÷ Ns, and the winding with more turns has the higher voltage and the lower current. Entering a DC voltage is another, because a steady current produces a constant flux and induces no voltage in the secondary. Reading the calculated current as what the transformer can supply is the third; the nameplate rating limits the current, so check it before connecting a load. For mains-voltage work, have a licensed electrician confirm the circuit.

Sources: OpenStax, University Physics Volume 2, section 15.6, “Transformers,” including Example 15.6 (openstax.org, read October 27, 2026). Related: resonant frequency calculator, three-phase power calculator, voltage drop calculator, watts to amps calculator. How we check our calculators.