Transformer Efficiency Calculator
Calculate transformer efficiency, total loss and the load at maximum efficiency from kVA rating, iron loss, copper loss, load and power factor.
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Estimate only. Not engineering or safety advice. Check the result against the applicable standard and the equipment data, and have a competent engineer review it before it is relied on. Terms of use.
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About this calculator
Use this to see how efficient a transformer is at a given load and where it peaks. The no-load (iron) loss is present whenever the transformer is energised, while the copper loss grows with the square of the load, so efficiency is highest at a part load rather than at full load.
Limits of this calculator
Iron loss is taken as constant and copper loss as proportional to load squared. Stray, harmonic and cooling-equipment losses are ignored, and losses are taken at the temperature the data sheet quotes them for. Use the guaranteed loss figures from the transformer data sheet.
Cross-check: 6 reference cases, calculated from textbook formulas coded separately from the engine by the same author, agree with this calculator. This is not an independent review.
Verification status: Engineering reference
Engineering reference. Formula and method documented and tested against separately coded reference calculations. Not yet Verified: the evidence listed on this page is still needed.
What this calculator checks
- The arithmetic of the published formula for the values you entered, in the units shown.
What remains unverified
- That the inputs suit your application. Take ratings, resistances and constants from the manufacturer data sheet or project specification.
Verification register entry
| Calculation author | Rahul Sharma (author) |
|---|---|
| Technical review | No independent technical review has been carried out |
| Individual professional approval | Not recorded |
| Formula reference | not recorded |
| Standard and edition | Not applicable: Textbook machine relation (slip, torque, shaft power, transformer efficiency); inputs come from the data sheet |
| Standard review state | Not applicable |
| Scope-screening note | not recorded |
| Cross-check test cases | 6 reference vectors (tests/reference_vectors.json) |
| Review date | not recorded |
| Next review date | not recorded |
| Status | Engineering reference |
Needed before this calculator can be marked Verified: reviewer name, qualification and review date; exact formula reference; formula source (textbook or standard); next review date.
Formula
Worked example
| Input | Value |
|---|---|
| Rating | 1,000 kVA |
| No-load (iron) loss | 1.7 kW |
| Full-load copper loss | 10.5 kW |
| Load (fraction of rating) | 1 |
| Power factor | 0.9 |
- Output = x × S × pf = 900 kW
- Loss = Pfe + x² × Pcu = 12.2 kW
- η = 900 / (900 + 12.2) = 98.6626 %
- Maximum efficiency at 0.402 of rating
Assumptions
- Iron loss constant with load
- Copper loss scales with load squared
- Stray and harmonic losses ignored
Distribution transformers peak at 40% to 60% load, so lightly loaded units can be more efficient than fully loaded ones.
Inputs and results
| Input | Unit | Allowed or shown | Note |
|---|---|---|---|
| Rating | kVA | greater than 0 kVA | |
| No-load (iron) loss | kW | greater than 0 kW | |
| Full-load copper loss | kW | greater than 0 kW | |
| Load (fraction of rating) | (number) | greater than 0, up to 1.5 | |
| Power factor | (number) | greater than 0, up to 1 | Rough starting point only. Resistive heating and incandescent loads are 1.0; a fully loaded induction motor is typically 0.8 to 0.88 and falls sharply when lightly loaded; discharge lighting depends on its ballast or driver. For real work use the nameplate or a measured value. |
| Result | Unit | Allowed or shown | Note |
|---|---|---|---|
| Efficiency (%) | (number) | Shown to 3 decimal places | |
| Total loss | kW | Shown to 2 decimal places | |
| Load at maximum efficiency | (number) | Shown to 3 decimal places |
How it is calculated
Each input is converted to the base unit of its quantity, the formula above is applied in the order shown in the worked example, and each result is shown in the unit you choose. Results are held at full precision and rounded only for display, except where a step selects a standard size, as the worked example shows. A value outside its allowed range is refused with a message instead of giving a result.
Typical values
| Load (fraction of rating) | Efficiency | Total loss (kW) | Load at maximum efficiency |
|---|---|---|---|
| 0.25 | 98.964 | 2.36 | 0.402 |
| 0.5 | 99.048 | 4.33 | 0.402 |
| 0.75 | 98.886 | 7.61 | 0.402 |
| 1 | 98.663 | 12.2 | 0.402 |
| 1.1 | 98.566 | 14.41 | 0.402 |
Other inputs are the same as in the worked example above.
Standards and further reading
- IEC 60076 series (power transformers)
Impedance, losses and cooling class are manufacturer values; enter the figures from the transformer data sheet. These are named as background reading. Elecmetric does not embed clause text or rating tables, and the reviewer record for this calculator is separate from this list.
Frequently asked questions
What do I need to enter?
Enter rating, no-load (iron) loss, full-load copper loss, load (fraction of rating) and power factor. Change the unit of a value with its selector and the result stays the same.
Why is efficiency not highest at full load?
Iron loss stays the same at every load and copper loss rises with the square of the load. Efficiency peaks where the two are equal, which for most distribution transformers is well below full load.
Where do I find the iron and copper loss figures?
On the transformer data sheet or test certificate, usually as no-load loss and load loss at rated current. Use the guaranteed values, not typical ones, when you are comparing offers.
Does power factor change the efficiency?
Yes. The output power is the apparent power times the power factor while the losses stay the same, so a lower power factor gives a lower efficiency for the same kVA load.
How accurate are the results?
Every figure comes from the same tested engine as the Elecmetric calculators and is meant for estimating. 6 reference cases, calculated from textbook formulas coded separately from the engine by the same author, agree with this calculator. This is not an independent review. Check design values against the standard and the equipment data you work to.
Formula guides and reference
Longer explanations with worked examples and tables, written for the same topic.
- Transformer Efficiency and Regulation Formulas: Transformer efficiency formulas: efficiency from iron and copper loss, load at maximum efficiency, voltage regulation
- Transformer Loss of Life Formulas: Transformer ageing formulas: the hot-spot temperature
- Transformer Cooling Class Rating Formulas: Transformer cooling formulas: the ONAN and ONAF ratings
More Transformer Engineering calculatorsAll engineering calculatorsTransformer Efficiency and Losses in Elecmetric