Transformer Turns Ratio

Solve turns ratio, voltage ratio, current ratio, and impedance ratio for an ideal transformer.

How to Use

  1. Enter any one ratio pair: Turns (Np & Ns) or Voltage (Vp & Vs) or Current (Ip & Is).
  2. Optionally enter a load impedance on the secondary (Zs) to reflect it to the primary (Zp).
  3. Open Show Work for formulas and steps (ideal transformer model).
  4. Use Share Link to generate a URL that restores your inputs (no URL changes while typing).
Ideal Transformer View
Voltage scales with turns. Current scales inversely with turns.
a = Np/Ns
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Vp/Vs
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Ip/Is
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Zp/Zs
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Model: Ideal
Primary Secondary Np Ns a = Np/Ns = — Ideal model: Vp/Vs = Np/Ns and Ip/Is = Ns/Np
Inputs & Settings
Enter any consistent pair. Tool computes ratios + derived values.
Turns are a count. Use integers when known.
a = Np/Ns. Example: 1000/100 → a=10.
Ideal: Vp/Vs = Np/Ns.
Step-down reduces voltage and increases current (ideal).
Ideal: Ip/Is = Ns/Np.
Power is conserved ideally: Vp·Ip ≈ Vs·Is.
Reflected: Zp = (Np/Ns)² × Zs.
Use Solve For if you want the tool to prefer a specific ratio source.
Show Work (step-by-step)
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Work is shown using base units (V, A, Ω) and ideal transformer relations.

Reference (Ideal Transformer)

  • Turns ratio: a = Np/Ns
  • Voltage ratio: Vp/Vs = Np/Ns = a
  • Current ratio: Ip/Is = Ns/Np = 1/a
  • Impedance reflection: Zp = a² · Zs and Zp/Zs = a²
  • Ideal power: Vp·Ip = Vs·Is (ignores losses)
Real transformers deviate due to copper losses, core losses, leakage inductance, magnetizing current, and regulation.

FAQ

Is turns ratio always equal to voltage ratio?

In an ideal transformer, yes: Vp/Vs = Np/Ns. In real units, load and losses cause regulation (Vs drops under load).

Why does current go up when voltage goes down?

Ideally power is conserved, so stepping down voltage steps up current: Ip/Is = Ns/Np.

What does “reflected impedance” mean?

A load on the secondary appears as a different impedance on the primary: Zp = (Np/Ns)² · Zs.

Can I use this for SMPS transformers?

You can use turns ratio relations, but real designs also depend on topology, duty cycle, magnetizing inductance, core limits, and winding resistance.

Tool Info

Last updated:

Updates may include additional unit support, edge-case handling, and UI consistency improvements.