Transformer Power Conservation Calculator
For an ideal transformer the power going in equals the power coming out: V₁ · I₁ = V₂ · I₂. Enter any three values and solve for the fourth, and read the turns ratio and apparent power.
Inputs
Choose what to solve for, then fill in the other three. Subscript 1 is the primary (input) side and subscript 2 is the secondary (output) side. Voltages and currents are RMS values.
Results
Enter values and press Calculate.
Transformer diagram
The primary winding (N₁ turns) is driven by the source at V₁ and draws current I₁. The secondary winding (N₂ turns) delivers V₂ and I₂ to the load. A higher voltage on one side always means a lower current on that side, so the product V·I stays the same.
Reference tables
Common examples (illustrative values, computed by the same engine)
| Case | V₁ | I₁ | V₂ | I₂ | S = V·I |
|---|
Turns ratio and what it does
| Type | Ratio a = V₁/V₂ = N₁/N₂ | Secondary voltage | Secondary current |
|---|---|---|---|
| Step-down | a > 1 | lower than primary | higher than primary |
| Isolation (1:1) | a = 1 | same as primary | same as primary |
| Step-up | a < 1 | higher than primary | lower than primary |
Typical voltage levels (approximate and varies by country)
| Use | Typical voltage |
|---|---|
| Doorbell and low-voltage control circuits | 8 – 24 V |
| Phone and laptop adapters (output side) | 5 – 20 V |
| Household mains | 100 – 127 V or 220 – 240 V |
| Local distribution | about 11 kV – 33 kV |
| High-voltage transmission | about 110 kV – 765 kV |
Key relations and units
| Quantity | Relation |
|---|---|
| Power conservation (ideal) | V₁ · I₁ = V₂ · I₂ |
| Voltage ratio | V₁ / V₂ = N₁ / N₂ = a |
| Current ratio | I₁ / I₂ = N₂ / N₁ = 1 / a |
| Apparent power | S = V · I (VA) |
| Real power | P = V · I · cos θ (W) |
| Real transformer efficiency | η = Pout / Pin |
| Units | 1 kV = 1000 V · 1 kA = 1000 A · 1 A = 1000 mA · 1 MVA = 1000 kVA = 10⁶ VA |
Formula and notes
- V₁, I₁: primary voltage and current
- V₂, I₂: secondary voltage and current
- Rearranged: V₁ = V₂·I₂/I₁, I₁ = V₂·I₂/V₁, V₂ = V₁·I₁/I₂, I₂ = V₁·I₁/V₂
Example. A 230 V to 12 V transformer supplies 5 A to a load. The output power is 12 × 5 = 60 VA, so the primary current is I₁ = 60 / 230 = 0.261 A. The turns ratio is 230 / 12 ≈ 19.2, a step-down transformer.
This calculator assumes an ideal transformer: no winding resistance, no core losses and no magnetising current. Real transformers lose a few percent as heat, so the input power is slightly larger than the output power. They are rated in kVA, not by the numbers on this page, and their rating is limited by heating. The power factor of the load appears unchanged on the primary side in the ideal case, so the same conservation holds for apparent power and for real power.
Disclaimer. For estimation and education. Selecting or wiring a real transformer needs the manufacturer's rating and local electrical rules, and should be done by a qualified person.
References
- Wikipedia, Transformer: ideal transformer and turns ratio
- Wikipedia, Ideal transformer
- Wikipedia, Volt-ampere: apparent power
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| V₁ | Primary winding RMS voltage | V |
| I₁ | Primary winding RMS current | A |
| V₂ | Secondary winding RMS voltage | V |
| I₂ | Secondary winding RMS current | A |
| S | Apparent power (VA) — identical on both sides for ideal transformer | VA |
What it means
For an ideal transformer, the input power equals the output power. This is expressed as V₁·I₁ = V₂·I₂, assuming no losses. This relationship follows from energy conservation. In a real transformer, there are losses due to winding resistance, core losses (hysteresis and eddy currents), and leakage flux, so the efficiency is less than 100%. However, the ideal power conservation equation is used for basic calculations and design. It shows that if the voltage is stepped down, the current is stepped up, and vice versa. This is the reason transformers are so important in power transmission: high voltage reduces current and thus reduces I²R losses. Example: With V₁=230V, I₁=1A, and V₂=46V (from previous example), the output current would be I₂ = (230*1)/46 = 5A, assuming an ideal transformer.
Worked example
Transformer Power Conservation – Practical Example
Real‑World| Parameter | Value |
|---|---|
| V₂ | 48 V |
| Apparent power S | 100 VA |
| Formula | V₁·I₁ = V₂·I₂ = S |
Common mistakes
- Ideal: Assumes no losses – V₁I₁ = V₂I₂.
- Efficiency: Real transformers have efficiency <100% – include losses.
- Power units: VA (apparent power) – not watts unless power factor =1.
- Sign: The formula holds for both directions (step‑up or step‑down).
- DC: Transformers do not work on DC – only AC.
Applications
Transformer power conservation (ideal) states that input volt‑amps equal output volt‑amps: V₁·I₁ = V₂·I₂. This relation holds for ideal transformers, neglecting losses. Engineers use it to calculate the secondary current from the primary current and voltage levels, and vice versa. It ensures that the transformer is properly rated for the load. In real transformers, losses reduce the efficiency, so a small correction is needed. This formula is the basis for the apparent power rating of transformers in kVA. By applying power conservation, professionals can design transformer‑based power supplies and distribution systems.
- Calculation of primary and secondary currents for given load
- Transformer sizing for power and voltage requirements
- Design of current transformers for measurement
- Understanding of transformer efficiency and losses
- Educational insight into transformer operation
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