Transformer Turns Ratio Formula (a = N1/N2 = V1/V2 — Free Guide)
Introduction #
Transformer turns ratio formula: for an ideal transformer,
a = N1/N2 = V1/V2 = I2/I1
Z1/Z2 ≈ a²
When this guide fits: You need the formula, a worked example, step-up vs step-down rules, or how nameplate voltages relate to winding turns before sizing.
When it is not suitable: Field TTR (transformer turns ratio) acceptance testing—that needs a calibrated TTR tester and OEM/procedure documents, not a planning formula page.
Use the free Transformer Turns Ratio Calculator for instant N1/N2 or V1/V2 results, then continue to Transformer Size and kVA to Amps.
What Is Transformer Turns Ratio? #
The turns ratio (a) (sometimes written (K) or (n)) is the ratio of primary winding turns (N1) to secondary turns (N2). For an ideal transformer it also equals the voltage ratio V1/V2 and the inverse current relationship I2/I1.
| Symbol | Meaning |
|---|---|
| N1, N2 | Primary / secondary turns |
| V1, V2 | Primary / secondary voltages (same basis: both L-L or both L-N) |
| I1, I2 | Primary / secondary currents |
| a | Turns ratio N1/N2 |
Google Suggest commonly pairs this topic with transformer turns ratio formula, formula with current, formula example, and calculator voltage.
Transformer Turns Ratio Formula (with Current & Impedance) #
Core relations #
a = N1 / N2
a = V1 / V2
I2 / I1 = a
I1 / I2 = 1/a
Z1 / Z2 ≈ a²
Power factor is not in the ideal ratio formula. PF matters for kW↔kVA and regulation—not for computing a from nameplate voltages or turns.
Solve for secondary voltage #
V2 = V1 / a = V1 × (N2 / N1)
Solve for secondary current (ideal, same VA) #
I2 = I1 × a
Impedance ratio vs nameplate %Z #
- Impedance ratio a² tells how a secondary load impedance reflects to the primary (audio/RF matching and ideal circuit analysis).
- Nameplate %Z is a different quantity used for fault / regulation screening—see Transformer Impedance (%Z) Explained and the SCCR calculator.
Step-Up vs Step-Down #
| Type | Condition | Voltage | Current (ideal) |
|---|---|---|---|
| Step-down | a > 1 | V2 < V1 | I2 > I1 |
| Step-up | a < 1 | V2 > V1 | I2 < I1 |
| Isolation | a ≈ 1 | V2 ≈ V1 | I2 ≈ I1 |
Example searches: step up vs step down transformer formula, step up and step down transformer difference.
Worked Examples #
Example 1 — Voltage mode (240 V → 120 V) #
a = 240 / 120 = 2 → 2:1 step-down
Z ratio ≈ 4
If I1 = 10 A, I2 ≈ 20 A (ideal)
Open in the calculator: 240→120 V.
Example 2 — Turns mode, find V2 #
N1 = 400, N2 = 100, V1 = 480 V:
a = 400 / 100 = 4
V2 = 480 / 4 = 120 V
Open: 400:100 turns.
Example 3 — MV distribution screen #
V1 = 13 800 V, V2 = 480 V:
a = 13800 / 480 ≈ 28.75 → ≈28.8:1
Next planning step: size kVA with Transformer Size Calculator.
3-Phase Transformers #
Suggest queries include transformer turns ratio calculator 3 phase and formula 3 phase.
Rules of thumb:
- Use winding voltages that match the connection (do not mix L-L and L-N without converting).
- On a wye winding, L-N = L-L ÷ √3 when you need phase voltage for the winding ratio.
- Confirm Δ/Y (and dual-voltage nameplates) before trusting a single a.
- For acceptance testing of three-phase units, follow TTR procedures per phase/winding—not this planning formula alone.
TTR Test vs Nameplate Formula #
| Planning formula (this guide / calculator) | TTR field test | |
|---|---|---|
| Purpose | Ideal ratio from nameplate turns or voltages | Measure actual winding ratio / tap integrity |
| Tool | Turns ratio calculator | Calibrated TTR tester |
| Output | a, voltage/current/impedance ratios | Measured ratio + deviation vs nameplate |
Treat Suggest intents like transformer turns ratio test procedure and TTR test results as maintenance / commissioning workflows. Do not use the web calculator as a test instrument.
How to Calculate Turns Ratio (Checklist) #
- Collect N1/N2 or nameplate V1/V2 (same voltage basis).
- Compute a = N1/N2 or a = V1/V2.
- Classify step-up / step-down / 1:1.
- Optionally compute a² for impedance reflection.
- Continue: Transformer Size → kVA to Amps → tap / regulation guides as needed.
FAQ #
What is the transformer turns ratio formula? #
a = N1/N2 = V1/V2 = I2/I1, and Z1/Z2 ≈ a² for an ideal transformer.
How do I calculate turns ratio from voltage? #
Divide primary by secondary: a = V1/V2. Example: 480/120 = 4:1.
How do I calculate secondary voltage from turns ratio? #
V2 = V1 / a. If a = 4 and V1 = 480 V, V2 = 120 V.
Does the formula need power factor? #
No for ideal turns/voltage ratio. Use PF in kW↔kVA sizing afterward.
What is impedance ratio vs %Z? #
a² is the ideal impedance transformation. %Z is nameplate short-circuit impedance for fault/regulation screening.
Is a TTR test the same as this formula? #
No. TTR is a measured field test; this formula is for planning from nameplate data.
Next Step #
- Run the Transformer Turns Ratio Calculator with your V1/V2 or N1/N2.
- Size kVA with Transformer Size.
- Convert to line current with kVA to Amps.
- Browse the Power Calculator hub — transformer section for related guides (regulation, tap changer, %Z).