Transformer Efficiency
η = Pout / (Pout + Piron + Pcopper)
Quick answer
This calculator solves η = Pout / (Pout + P_iron + P_copper) for η. With Output Power 10 W, Core (Iron) Loss 22 W, Copper Loss 47 W, the result is 0.1266.
Calculator
Formula
Description
Transformer efficiency is the ratio of output power to input power, where the input power equals the output power plus all losses. The two main loss mechanisms are core (iron) losses and copper (winding) losses. Core losses include hysteresis loss (proportional to frequency and B²) and eddy current loss (proportional to f² and B²); these are approximately constant regardless of load. Copper losses are I²R losses in the windings and increase with the square of the load current. Maximum efficiency occurs when core losses equal copper losses.
Variables
- Pout — Output (load) power (W)
- P_iron — Core loss from hysteresis and eddy currents (W)
- P_copper — Winding I²R loss (W)
Practical Notes
Typical efficiencies: small (<10 VA) transformers 80-90%, medium (10-1000 VA) 90-95%, large power transformers (>1 MVA) 97-99.5%. The result is a ratio (0 to 1); multiply by 100 for percentage. Core losses can be found from manufacturer data at the operating flux density and frequency. Copper losses can be measured or calculated from winding resistance and load current.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| Pout | Output Power | W | µW, mW, W, kW |
| Piron | Core (Iron) Loss | W | µW, mW, W, kW |
| Pcopper | Copper Loss | W | µW, mW, W, kW |
Step by step
- 1. What you know: Output Power 10 W, Core (Iron) Loss 22 W, Copper Loss 47 W
- 2. The relation: η = Pout / (Pout + P_iron + P_copper)
- 3. Substitute: Pout = 10 W, Piron = 22 W, Pcopper = 47 W
- 4. Result: η = 0.1266
Worked examples
Minimum range
Given: Output Power 10 mW, Core (Iron) Loss 22 mW, Copper Loss 47 mW
Result: η = 0.1266
Low range
Given: Output Power 100 mW, Core (Iron) Loss 0.22 W, Copper Loss 0.47 W
Result: η = 0.1266
Typical
Given: Output Power 10 W, Core (Iron) Loss 22 W, Copper Loss 47 W
Result: η = 0.1266
High range
Given: Output Power 1 kW, Core (Iron) Loss 2.2 kW, Copper Loss 4.7 kW
Result: η = 0.1266
Maximum range
Given: Output Power 10 kW, Core (Iron) Loss 22 kW, Copper Loss 47 kW
Result: η = 0.1266
How η changes with Output Power
| Output Power (input) | η (result) |
|---|---|
| 1 W | 0.01429 |
| 2.5 W | 0.03497 |
| 5 W | 0.06757 |
| 7.5 W | 0.09804 |
| 10 W | 0.1266 |
| 15 W | 0.1786 |
| 20 W | 0.2247 |
| 40 W | 0.367 |
| 70 W | 0.5036 |
| 100 W | 0.5917 |
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<p><a href="https://vbatpower.com/formulas/transformer-efficiency-ac/">Transformer Efficiency</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Transformer Efficiency?
Use η = Pout / (Pout + P_iron + P_copper). With Output Power 10 W, Core (Iron) Loss 22 W, Copper Loss 47 W, η works out to 0.1266.
How do you calculate mv transformer efficiency 10mva 99.x? what is typical for x? .2 .3?
Rearrange for η: with Output Power 100 mW, Core (Iron) Loss 0.22 W, Copper Loss 0.47 W, η is 0.1266.
What is the formula for Transformer Efficiency?
The formula is η = Pout / (Pout + P_iron + P_copper). Transformer efficiency is the ratio of output power to input power, where the input power equals the output power plus all losses.
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