Transformer Turns Ratio
N = V1 / V2
Quick answer
This calculator solves N = V_primary / V_secondary = N_primary / N_secondary for Turns Ratio. With Primary Voltage 12 V, Secondary Voltage 26.4 V, the result is 0.4545. It solves in 3 directions, so you can enter the values you have and get the one you need.
Calculator
Formula
Description
The transformer turns ratio relates the primary and secondary voltages (and inversely, the currents) of an ideal transformer. A step-down transformer has N > 1, reducing voltage while proportionally increasing current. A step-up transformer has N < 1, increasing voltage while reducing current. The turns ratio is determined by the number of wire turns on each winding, and power is conserved (minus losses): V1 × I1 = V2 × I2. Real transformers have efficiency of 90-99% depending on size, with losses due to copper resistance, core hysteresis, and eddy currents.
Variables
- N — Turns ratio (primary to secondary, dimensionless)
- V1 — Primary (input) voltage (V)
- V2 — Secondary (output) voltage (V)
Practical Notes
Transformer impedance transformation follows the square of the turns ratio: Z_reflected = N² × Z_load. This principle is used in audio output transformers, RF matching networks, and current sensing transformers. For isolation transformers, N = 1 but the galvanic isolation between windings is the key feature. Multiple secondary windings can provide different voltage outputs from a single transformer.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| N | Turns Ratio | — | — |
| V1 | Primary Voltage | V | pV, nV, µV, mV, V, kV |
| V2 | Secondary Voltage | V | pV, nV, µV, mV, V, kV |
Step by step
- 1. What you know: Primary Voltage 12 V, Secondary Voltage 26.4 V
- 2. The relation: N = V_primary / V_secondary = N_primary / N_secondary
- 3. Substitute: V1 = 12 V, V2 = 26.4 V
- 4. Result: Turns Ratio = 0.4545
Worked examples
Minimum range
Given: Primary Voltage 0.33 V, Secondary Voltage 0.726 V
Result: Turns Ratio = 0.4545
Low range
Given: Primary Voltage 3.3 V, Secondary Voltage 7.26 V
Result: Turns Ratio = 0.4545
Typical
Given: Primary Voltage 12 V, Secondary Voltage 26.4 V
Result: Turns Ratio = 0.4545
High range
Given: Primary Voltage 0.23 kV, Secondary Voltage 0.506 kV
Result: Turns Ratio = 0.4545
Maximum range
Given: Primary Voltage 2.3 kV, Secondary Voltage 5.06 kV
Result: Turns Ratio = 0.4545
Solving for each variable
Solve for Turns Ratio
Primary Voltage 0.33 V, Secondary Voltage 0.726 V → 0.4545
Solve for Primary Voltage
Turns Ratio 0.025, Secondary Voltage 0.726 V → 18.15 mV
Solve for Secondary Voltage
Turns Ratio 0.025, Primary Voltage 0.33 V → 13.2 V
How Turns Ratio changes with Primary Voltage
| Primary Voltage (input) | Turns Ratio (result) |
|---|---|
| 1.2 V | 0.04545 |
| 3 V | 0.1136 |
| 6 V | 0.2273 |
| 9 V | 0.3409 |
| 12 V | 0.4545 |
| 18 V | 0.6818 |
| 24 V | 0.9091 |
| 48 V | 1.818 |
| 84 V | 3.182 |
| 120 V | 4.545 |
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<p><a href="https://vbatpower.com/formulas/transformer-turns-ratio/">Transformer Turns Ratio</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Transformer Turns Ratio?
Use N = V_primary / V_secondary = N_primary / N_secondary. With Primary Voltage 12 V, Secondary Voltage 26.4 V, Turns Ratio works out to 0.4545.
What is the formula for Transformer Turns Ratio?
The formula is N = V_primary / V_secondary = N_primary / N_secondary. The transformer turns ratio relates the primary and secondary voltages (and inversely, the currents) of an ideal transformer.
How do you find Primary Voltage when you know the other values?
Rearrange for Primary Voltage: with Turns Ratio 0.025, Secondary Voltage 0.726 V, Primary Voltage is 18.15 mV.
How do you find Secondary Voltage when you know the other values?
Rearrange for Secondary Voltage: with Turns Ratio 0.025, Primary Voltage 0.33 V, Secondary Voltage is 13.2 V.
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