Transformer Turns Ratio Calculator

Calculate secondary voltage, current, or turns ratio for any transformer.

Primary turns N₁

Secondary turns N₂

Primary voltage V₁ (V) (V)

Primary current I₁ (A) (A)

Optional

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How a Transformer Trades Voltage for Current

An ideal transformer changes AC voltage according to the ratio of turns on its two windings. The primary winding creates a changing magnetic flux in the core, and that same changing flux links the secondary winding. Faraday's law says the induced voltage per turn is the same for both windings, so a winding with more turns develops proportionally more voltage.

This is why the turns ratio appears directly in the voltage equation. If the secondary has one-tenth as many turns as the primary, its ideal voltage is one-tenth as large. Current changes in the opposite ratio because an ideal transformer conserves power: V₁I₁ = V₂I₂. A tenfold voltage increase therefore corresponds to a tenfold current decrease for the same ideal apparent power. Real transformers also have copper loss, core loss, leakage flux, and voltage regulation, so measured output values differ from the ideal equations under load.

V₂/V₁ = N₂/N₁ I₂/I₁ = N₁/N₂ V₁I₁ = V₂I₂ (ideal)

Symbol	Meaning	Interpretation / units
N₁	Primary turns	Number of turns on the input winding
N₂	Secondary turns	Number of turns on the output winding
V₁, V₂	Primary and secondary voltage	Usually RMS AC voltage, in volts
I₁, I₂	Primary and secondary current	Ideal current relation, in amperes
N₂/N₁	Turns ratio	Greater than 1 steps voltage up; less than 1 steps it down

A 1:1 transformer is an important special case: it ideally keeps the same voltage while providing magnetic coupling and electrical isolation between windings. A transformer requires changing magnetic flux, so these steady-state ratio equations apply to AC or changing waveforms rather than constant DC.

Worked Examples

Example 1: Step-down: 230V mains to 12V

N1=1000, N2=52, V1=230

Result: V2 = 12 V

Turns ratio 1:0.052

Example 2: Step-up ignition coil: 12V to 30kV

N1=200, N2=500000, V1=12

Result: V2 = 30,000 V

High voltage for spark plug ignition

Example 3: One-to-one isolation transformer

N₁ = 500, N₂ = 500, V₁ = 120 V, I₁ = 2 A

Result: V₂ = 120 V and I₂ = 2 A ideal

Equal turns do not step the voltage up or down. The useful feature is isolation, while real output voltage will sag somewhat under load because of losses and winding impedance.

Example 4: Ten-to-one step-up transformer

N₁ = 100, N₂ = 1000, V₁ = 24 V, I₁ = 5 A

Result: V₂ = 240 V, I₂ = 0.5 A ideal

The voltage rises by a factor of 10 while current falls by the same factor. Ideal apparent power remains 120 VA on both sides.

Common Mistakes

⚠️

Reversing the turns ratio

Match secondary quantities with secondary turns: V₂/V₁ = N₂/N₁. If the secondary has fewer turns, its voltage must be lower in the ideal model.

⚠️

Making current change in the same direction as voltage

For an ideal transformer, power is conserved. A step-up transformer raises voltage but lowers available current by the inverse turns ratio.

⚠️

Applying the ideal transformer equation to steady DC

A transformer needs changing magnetic flux. After the brief switching transient, steady DC does not continuously induce a secondary voltage and can cause excessive primary current if applied to a winding not designed for it.

⚠️

Assuming rated voltage guarantees any desired current

The turns ratio sets ideal voltage, but the transformer's core, wire size, temperature rise, and VA rating limit usable current. A load cannot draw unlimited power merely because the voltage ratio is correct.

Frequently Asked Questions

Why does current go opposite to voltage?

Conservation of energy in ideal transformer: V₁I₁ = V₂I₂. Step-up in voltage means step-down in current by the same ratio.

What are real transformer losses?

Core losses (hysteresis, eddy currents) and copper losses (I²R in windings). Real efficiency: 95–99% for large power transformers, 70–90% for small adapters.

How do I know whether a transformer is step-up or step-down?

Compare N₂ with N₁. If N₂ is larger, the ideal secondary voltage is higher and the transformer is step-up. If N₂ is smaller, the secondary voltage is lower and it is step-down.

Does transformer frequency change from primary to secondary?

No. A transformer changes voltage and current magnitude but does not change the supply frequency. A 60 Hz primary produces a 60 Hz secondary waveform in normal operation, apart from waveform distortion caused by nonideal effects.

Why is a transformer's secondary voltage lower under load?

Real windings have resistance and leakage reactance. Load current produces internal voltage drops, so the terminal voltage can fall below the ideal turns-ratio value. The difference between no-load and loaded voltage is part of transformer voltage regulation.

What does a transformer's VA rating mean?

VA is apparent power, approximately RMS voltage multiplied by RMS current. It limits the combination of secondary voltage and current the transformer can supply without exceeding its thermal and magnetic design limits.

Formula Explorer connections

Interpretation: This formula links charge, voltage, current, resistance, capacitance, power or circuit time response. Assumption: Confirm DC versus AC conditions, RMS versus peak values, component topology and steady-state versus transient behavior. Ideal components may be assumed.

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