Introduction #

Transformer turns ratio formula: for an ideal transformer using corresponding winding (phase) quantities,

a = N1/N2 = E1_phase/E2_phase = I2_phase/I1_phase
Z1/Z2 ≈ a²

For a single-phase transformer—or a three-phase transformer with the same connection on both sides—the no-load terminal-voltage ratio is approximately the turns ratio. For Δ–Y or Y–Δ units, the line-to-line nameplate voltage ratio is not N1/N2; apply the connection's √3 factor.

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.

Megger's TTR guidance also distinguishes winding turns ratio, nameplate voltage ratio, and the vector-group correction needed for three-phase field measurements; use the tester/OEM procedure for acceptance work.

Use the free Transformer Turns Ratio Calculator for single-ratio N1/N2 or terminal-voltage division, then continue to Transformer Size and kVA to Amps. The calculator does not currently apply Δ/Y vector-group correction; for mixed connections, calculate winding phase voltages as shown below.

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 equals the ratio of the induced voltages across the corresponding windings and the inverse ratio of their winding currents. Terminal line-voltage and line-current ratios require the connection factors shown below.

Symbol Meaning
N1, N2 Primary / secondary turns
E1_phase, E2_phase Induced voltage across the corresponding primary / secondary winding
V1_LL, V2_LL Primary / secondary line-to-line terminal voltage
I1_phase, I2_phase Current in the corresponding primary / secondary winding
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 = E1_phase / E2_phase
I2_phase / I1_phase = a
I1_phase / I2_phase = 1/a
Z1 / Z2 ≈ a²

In simplified single-phase/no-load calculations, E1/E2 ≈ V1/V2. In a real transformer, applied terminal voltage also includes excitation-current drops, and three-phase line quantities include the vector-group connection factors.

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 #

E2_phase = E1_phase / a = E1_phase × (N2 / N1)

Solve for secondary current (ideal, same VA) #

I2_phase = I1_phase × 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 E2_phase < E1_phase I2_phase > I1_phase
Step-up a < 1 E2_phase > E1_phase I2_phase < I1_phase
Isolation a ≈ 1 E2_phase ≈ E1_phase I2_phase ≈ I1_phase

Example searches: step up vs step down transformer formula, step up and step down transformer difference.

Worked Examples #

Example 1 — Single-phase 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 — Corresponding winding turns, find induced E2 #

N1 = 400, N2 = 100, E1_phase = 480 V:

a = 400 / 100 = 4
E2_phase = 480 / 4 = 120 V

Open: 400:100 turns.

Example 3 — MV nameplate line-voltage ratio #

V1 = 13 800 V, V2 = 480 V:

terminal L-L voltage ratio = 13800 / 480 ≈ 28.75 → ≈28.8:1

This is not enough information to state the winding turns ratio. For the same 13.8 kV/480 V line-voltage ratings:

  • Δ–Y: a = N1/N2 = 28.75 × √3 ≈ 49.8
  • Y–Δ: a = 28.75 ÷ √3 ≈ 16.6
  • Y–Y or Δ–Δ: a = 28.75

Confirm the vector group and which physical windings the TTR procedure compares.

Next planning step: size kVA with Transformer Size Calculator.

3-Phase Transformers #

Turns ratio always compares corresponding winding/phase quantities. Convert line-to-line nameplate voltage to winding voltage before using a = N1/N2:

  • Wye winding: E_phase ≈ V_LL / √3
  • Delta winding: E_phase ≈ V_LL

Assuming side 1 is primary and side 2 is secondary:

Connection Line-voltage ratio V1_LL/V2_LL Turns ratio from nameplate L-L voltages
Y–Y a a = V1_LL/V2_LL
Δ–Δ a a = V1_LL/V2_LL
Δ–Y a/√3 a = √3 × V1_LL/V2_LL
Y–Δ √3a a = V1_LL/(√3 × V2_LL)

The simple inverse current relationship also applies to winding phase currents, not automatically to line currents across unlike connections. On wye, I_line = I_phase; on delta, I_line = √3 × I_phase. Confirm the vector group, tap position, terminal identification and tester method before interpreting a three-phase measurement.

TTR Test vs Nameplate Formula #

Planning formula (this guide / calculator) TTR field test
Purpose Ideal ratio from stated winding turns/phase voltages; terminal-voltage ratio only after connection correction Measure actual voltage ratio/phase displacement and assess winding/tap condition under the selected procedure
Tool Turns ratio calculator Calibrated TTR tester
Output a, voltage/current/impedance ratios Measured ratio + deviation vs nameplate

Treat transformer turns ratio test procedure and TTR test results as maintenance / commissioning workflows. Do not use the web calculator as a test instrument or apply a universal acceptance tolerance; use the applicable standard, transformer nameplate/vector group, OEM criteria and calibrated tester procedure.

How to Calculate Turns Ratio (Checklist) #

  1. Collect N1/N2 or nameplate voltages plus the vector group/connection and tap position.
  2. For single-phase or the same three-phase connection, compute the ideal ratio directly; for Δ–Y or Y–Δ, convert L-L voltage to winding phase voltage first.
  3. Classify step-up / step-down / 1:1.
  4. Optionally compute a² for impedance reflection.
  5. Continue: Transformer Size → kVA to Amps → tap / regulation guides as needed.

FAQ #

What is the transformer turns ratio formula? #

For corresponding winding quantities in an ideal transformer, a = N1/N2 = E1_phase/E2_phase = I2_phase/I1_phase, and a load impedance reflects by a². Terminal line-voltage and line-current ratios require the three-phase connection factors.

How do I calculate turns ratio from voltage? #

For a single-phase transformer or the same connection on both sides, divide the corresponding no-load voltages: a ≈ V1/V2. For Δ–Y or Y–Δ nameplate line voltages, first convert each side to winding phase voltage.

How do I calculate secondary voltage from turns ratio? #

For corresponding winding induced voltages, E2_phase = E1_phase / a. If a = 4 and E1_phase = 480 V, E2_phase = 120 V. Convert back to line voltage according to the secondary connection.

Using the transformer nameplate, what is the line-neutral turns ratio? #

Do not divide one side's L-L voltage by the other side's L-N voltage. Identify each winding connection. For a wye winding, E_phase ≈ V_LL/√3 and equals its L-N voltage when the neutral is available; for a delta winding, E_phase ≈ V_LL. Compare the two winding phase voltages to obtain N1/N2.

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. Field TTR/voltage-ratio testing uses a calibrated instrument and must account for vector group, tap position, phase displacement, test direction and OEM/standard criteria. This planning formula is not an acceptance test or universal pass/fail limit.

Next Step #

  1. Run the Transformer Turns Ratio Calculator with N1/N2 or a single-phase/same-connection voltage ratio; manually apply the connection correction for mixed Δ/Y units.
  2. Size kVA with Transformer Size.
  3. Convert to line current with kVA to Amps.
  4. Browse the Power Calculator hub — transformer section for related guides (regulation, tap changer, %Z).

Technical sources #