Ideal Transformer Calculator - Turns and Voltage Ratios

An ideal transformer calculator solves the textbook relationships between the windings of a lossless transformer: the voltage ratio equals the turns ratio, the current ratio is its inverse, and the apparent power on each side is the same. Type V1, V2, N1, and N2 to compute the turns ratio, the voltage and current ratios, the apparent power, and the operating mode. Add I1 or I2 to expose the apparent-power balance; the current outputs fall back to the turns ratio if both currents are blank.

• • Sizing a mains step-down transformer: Pick the secondary turns that turn a 230 V primary into a 12 V secondary for low-voltage lighting or a control circuit.
• • Verifying a 1:1 isolation transformer: Confirm turns and measured voltages agree so you can flag a shorted or open winding.
• • Designing a step-up inverter transformer: Estimate secondary voltage and turns for an inverter that boosts 12 V or 24 V battery DC up to mains level.
• • Doing a homework check: Plug in the values your textbook gives and confirm the resulting ratios before you write them down.

The ideal transformer is a teaching model, not a real device. It assumes a perfectly coupled core, no winding resistance, no leakage inductance, no magnetizing current, and no core loss. Use the calculator as a first pass for sizing, not for thermal design or noise.

A switching converter that uses the same turns ratio to set duty cycle is a natural follow-up, so Boost Converter shows how the ratio reappears in a step-up DC-DC topology.

The calculator applies V1 / V2 = N1 / N2 = I2 / I1 and P1 = V1 * I1 = V2 * I2 to your values, then reports the derived ratios and apparent powers.

• V1: RMS voltage across the primary winding.
• V2: RMS voltage across the secondary winding.
• N1, N2: Number of turns in the primary and secondary windings.
• I1: RMS current drawn by the primary winding (optional).
• I2: RMS current delivered to the secondary load (optional).

If you leave a current empty the calculator falls back to the turns ratio to fill in the apparent power, but it always reports both sides so you can spot a sign or wiring mistake. The voltage ratio V1 / V2 is also reported so you can flag a mislabeled or reversed transformer.

Use the apparent-power output as a sanity check. A textbook problem that gives V1, V2, N1, N2, and I1 should always produce an I2 that makes the two apparent powers agree; a discrepancy usually means a typo.

According to Hyperphysics (Georgia State University), an ideal transformer obeys V1 / V2 = N1 / N2 = I2 / I1, so the apparent power on the primary equals the apparent power on the secondary. According to All About Circuits, the turns ratio N1 / N2 equals the voltage ratio V1 / V2 and the inverse of the current ratio I2 / I1, so the ideal transformer has no power loss.

The same V * I balance carries over to switching power, so Buck Converter uses the same apparent-power idea in continuous conduction mode.

Four ideas describe what the calculator does. None require a derivation; each explains what the model assumes.

When the calculator reports a step-up transformer the mode label and the current numbers both flip direction, which makes the difference between a step-up and a step-down easier to keep straight on a schematic. An isolation transformer has a turns ratio of 1 and identical voltages on each side; the only benefit is galvanic isolation.

None of these relationships depend on load type. Whether the secondary feeds a resistor, a bridge rectifier, or a battery charger, the ideal-transformer equations still apply.

An isolated forward converter depends on the turns ratio of its transformer for reset and output, so Forward Converter reuses the ideal-transformer relations in a switching context.

Six numbered steps cover common ways to run the calculator, from a textbook problem to bench verification.

1. 1 Enter the primary voltage V1: Type the RMS voltage the source applies to the primary. For a mains transformer this is 120 V or 230 V; for a battery-fed inverter it is the DC bus voltage after the switching stage.
2. 2 Enter the secondary voltage V2: Type the RMS voltage across the secondary, or the voltage you are designing for. V2 is required so the calculator can compare the voltage ratio against the turns ratio. If you have not measured it yet, use V2 = V1 * N2 / N1 to predict it from V1 and the turns.
3. 3 Enter the primary turns N1: Count the turns on the bobbin if you are reverse-engineering an unknown transformer; use the design target if you are winding a new one.
4. 4 Enter the secondary turns N2: The calculator divides N1 by N2 to get the turns ratio, which controls every other output.
5. 5 Enter the primary current I1: Optional. With a clamp-meter reading on the primary, the calculator can compute the secondary current and the apparent power balance.
6. 6 Read the turns ratio and apparent power: The calculator returns the turns ratio N1 / N2, the voltage and current ratios, the apparent power on each side, and the operating mode.

For a 230 V to 24 V control transformer with 1150 primary turns and 120 secondary turns, the calculator returns a turns ratio of 9.583, a voltage ratio of 9.583, and 240 VA of apparent power at 1.04 A primary current. The secondary can deliver about 10 A continuously at 24 V.

Once you know the secondary voltage and the load current, Ohm's Law Calculator converts the pair into a load resistance for sizing fuses and resistors.

Five reasons students, hobbyists, and practising engineers reach for an ideal-transformer calculator before a soldering iron.

• • Saves homework time: Confirms the ratio a textbook problem asks for without re-deriving V1 / V2 = N1 / N2.
• • Catches mislabeled transformers: If the printed turns and measured voltages disagree, the voltage-ratio output gives you a number to read off the calculator and compare against the label.
• • Supports sizing decisions: Lets you iterate on the turns ratio and watch the secondary voltage change, so you can pick a target winding before cutting wire.
• • Reveals apparent-power balance: Reports both V1 * I1 and V2 * I2 so you can spot a calculation typo that drops a factor of 10 without re-running the problem.
• • Bridges to the rest of the site: Pairs naturally with switching-converter calculators that use the same turns ratio to set duty cycle, including flyback and forward pages.

The calculator also reinforces the intuition that a step-up transformer trades voltage for current, the opposite of a step-down. Once you internalize that, picking the right topology for a new power supply becomes much faster because the same math applies whether you are feeding a bridge rectifier or a high-voltage probe. Use the operating-mode output as a sanity check before you build; if you intended step-down but the calculator reports step-up, you almost certainly typed the turns in the wrong order.

Switching converters that rely on the transformer as the energy-storage element reuse the same turns ratio, so Flyback Converter extends this calculator into a complete isolated DC-DC design.

Five factors drive what the ideal transformer calculator returns. The first three are inputs the calculator accepts; the last two are real-world caveats the ideal model does not cover.

• • The ideal transformer calculator assumes a 100 percent efficient transformer with perfect coupling. Real transformers are typically 95 to 99 percent efficient depending on size and core material.
• • The model ignores frequency-dependent effects such as skin effect, proximity effect, and core loss, which become significant above a few kilohertz, especially in switch-mode flyback or forward converters.

According to Wikipedia, Transformer, the ideal transformer assumes a perfect magnetic core with no leakage flux, no winding resistance, and no magnetizing current, so its efficiency is 100 percent by construction.

The AC output of the secondary often feeds a rectifier before the load, so Bridge Rectifier covers the diode-bridge stage that follows the ideal transformer.