Transformer Turns Ratio Calculator
Calculate turns ratio, voltage, current, and impedance transformation for an ideal transformer. Step-up and step-down applications.
How to Use
- Enter primary and secondary turns, or voltage ratio.
- See transformed voltages, currents, and impedance ratio.
- Transformer is assumed ideal (lossless, fully coupled).
Show Work
Formulas
History of the Turns Ratio
The turns-ratio equation V2/V1 = N2/N1 is a direct consequence of Faraday\'s 1831 law of electromagnetic induction. Each turn of a coil encloses the same changing flux, so the voltage induced per turn is the same for both windings on a common core. Stack up N1 turns on the primary and the total induced voltage is N1 times the per-turn voltage; N2 turns on the secondary gives N2 times the same per-turn voltage. The ratio falls out immediately.
Practical use of the turns ratio for industrial voltage transformation dates to the 1880s. Westinghouse\'s 1886 Great Barrington demonstration used Gaulard-Gibbs transformers with about 10:1 step-down ratios to take distribution-line voltage down to lighting-circuit voltage. Edison\'s direct-current rival system had no equivalent mechanism — transformers only work for alternating current — which is why AC won the "War of the Currents."
Impedance matching through turns ratios appeared in early telephony. The Bell system used audio transformers to match the few-hundred-ohm impedance of carbon microphones and the long-line impedance of twisted-pair copper to the ~1000Ω impedance of moving-iron receivers. The same principle still drives tube-amplifier output transformer design and RF balun construction today — the physics hasn\'t changed, only the scale and operating frequency.
About This Calculator
Enter primary and secondary turn counts, a primary voltage, and a secondary load impedance. The calculator returns the turns ratio, the resulting secondary voltage, the impedance ratio (N1/N2)², and the reflected impedance seen on the primary side — the two most commonly needed transformer quantities for audio, RF, and power work.
The math is ideal. Real transformers have ~1–5% loss, leakage inductance that degrades high-frequency response, winding capacitance that causes resonances, and core saturation that limits flux density. For critical designs, simulate with a measured equivalent-circuit model rather than trusting ideal math alone. Everything runs client-side; no values leave your browser.
Frequently Asked Questions
What does turns ratio do?
Primary and secondary voltage are proportional to turn counts: V2/V1 = N2/N1. Currents invert: I2/I1 = N1/N2. Impedance transforms as the square: Z2/Z1 = (N2/N1)².
Why step-up/step-down?
Power transmission benefits from high voltage / low current (less I²R loss in wires). Consumer devices need lower voltage for safety. Transformers convert between them with >95% efficiency.
Impedance matching?
A transformer with N1:N2 turn ratio makes a load Z2 on the secondary appear as Z1 = Z2·(N1/N2)² on the primary. Used to match audio amps to 4/8Ω speakers, or 50Ω RF to antenna impedance.
Common Use Cases
Wall Adapter
Step-down 120V → 12V uses 10:1 turns ratio (modern ones use switchers, but the principle is the same in isolation transformers).
Audio Output Transformer
Match tube amp's high-impedance plate (~4kΩ) to 8Ω speaker: turn ratio √(4000/8) ≈ 22:1.
Antenna Balun
1:1 transformer converts unbalanced (coax) to balanced (dipole) signal.
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