Transformer Turns Ratio Calculator
Your Transformer
Two windings share one iron core. The number of coil loops is drawn in proportion to the turns, so you can see at a glance whether the transformer steps voltage up or down. Labels update with your inputs.
Quick Output: Real-World Examples
Typical single-phase transformers, calculated live. The last column shows the secondary turns you would need if the primary has 1,000 turns (illustrative). Press Use to load a row.
| Application | V₁ (V) | V₂ (V) | Turns ratio N₁:N₂ | Type | N₂ if N₁ = 1,000 |
|---|
How to Use
1. Pick the unknown
Solve for the primary or secondary voltage, or for the primary or secondary number of turns.
2. Enter the other three
Voltages can be in V, kV or mV. Turns are plain numbers. Load a real transformer from the presets if you like.
3. Calculate
The page jumps to the result, with the turns ratio, step-up or step-down type, working and a scaled drawing.
4. Go Advanced
Handle three-phase connections, find currents and losses for a load, size the core, and see the effect of tap changes.
Frequently Asked Questions
The same changing magnetic flux links both windings, and each turn picks up the same voltage. So the winding with more turns develops proportionally more voltage: V₁/V₂ = N₁/N₂.
For an ideal transformer power in equals power out, so current changes the opposite way: I₁/I₂ = N₂/N₁. A step-down transformer gives a larger current on the secondary.
The turns ratio applies to the windings. Line voltages also depend on how they are connected. A delta-wye transformer has line-voltage ratio N₁ / (√3 · N₂), and a wye-delta one has √3 · N₁ / N₂. Advanced mode handles this.
The EMF equation gives V = 4.44 f N Φmax for a sine wave. The peak flux is Φmax = V / (4.44 f N), and the core area is that flux divided by the allowed flux density. The result is a minimum, since real cores have stacking and insulation factors.
Calculating...
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| V₁ | Primary winding RMS voltage | V |
| V₂ | Secondary winding RMS voltage | V |
| N₁ | Number of turns in primary winding | dimensionless |
| N₂ | Number of turns in secondary winding | dimensionless |
| a | Turns ratio (a = N₁/N₂ = V₁/V₂) | dimensionless |
What it means
The turns ratio of a transformer is defined as the ratio of the number of turns in the primary winding to the number of turns in the secondary winding. For an ideal transformer, the voltage ratio equals the turns ratio: V₁/V₂ = N₁/N₂. This relationship is derived from Faraday’s law of induction. The turns ratio determines whether the transformer steps up (N₂ > N₁) or steps down (N₂ < N₁) the voltage. It also determines the current ratio: I₁/I₂ = N₂/N₁ (inverse). The turns ratio is a critical parameter for selecting a transformer for a specific application, such as power supplies, audio amplifiers, or impedance matching. Example: A transformer with N₁=1000 turns and N₂=200 turns, with V₁=230V, gives V₂ = 230 * (200/1000) = 46V. This is a step‑down transformer with a turns ratio of 5:1.
Worked example
Transformer Turns Ratio – Practical Example
Real‑World| Parameter | Value |
|---|---|
| N₁ | 500 |
| N₂ | 100 |
| V₁ | 240 V |
| Formula | V₁/V₂ = N₁/N₂ |
Common mistakes
- Voltage ratio: V₁/V₂ = N₁/N₂ – for an ideal transformer.
- Current ratio: I₁/I₂ = N₂/N₁ – inversely proportional.
- Polarity: Dot convention must be observed for phase relations.
- Step‑up: If N₂ > N₁, the voltage is stepped up (V₂ > V₁).
- Leakage: Real transformers have leakage inductance and losses – the ratio holds approximately.
Applications
The transformer turns ratio V₁/V₂ = N₁/N₂ relates the primary and secondary voltages to their respective turns. This determines whether a transformer steps up or steps down voltage. Engineers use this ratio to design power transformers for transmission and distribution, to adapt voltages for electronic equipment, and to design isolation transformers. The ratio is also used to calculate the current ratio (I₁/I₂ = N₂/N₁). By selecting the appropriate turns ratio, professionals can match the voltage requirements of the load with the available supply. This formula is fundamental to transformer design and application.
- Power transformer design for grid and industrial use
- Voltage conversion for electronic devices (wall adapters)
- Isolation transformers for safety and noise reduction
- Impedance matching with audio transformers
- Educational foundation of transformer operation
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