ProcirelTransformer Losses: Copper, Iron and Efficiency Math
No transformer is perfect. Copper loss grows with the square of load current, iron loss is constant whenever the core is energised. Efficiency peaks where the two balance which explains both best operating points and the energy cost of oversized installations.
> At a glance: 7 minute guide · part 4 of 10 in the electrical engineering complete guide track · includes a worked example and a quick-reference table.
## Copper (load) losses
Winding resistance dissipates I²R doubling the load current quadruples the copper loss. It appears as warmth that scales with usage and dominates at full load. Nameplate impedance also predicts voltage regulation under load.
| L | o | s | s | | t | y | p | e | | | |
| — | — | — | — | — | — | — | — | — | — | — | — |
| V | a | r | i | e | s | | w | i | t | h | |
| P | r | e | s | e | n | t | | w | h | e | n |
| R | e | d | u | c | e | d | | b | y | | |
| Copper (I²R) | Load current squared | Any load | Thicker conductors | | | | | | | | |
| Hysteresis | Core material, flux | Energised | Better steel | | | | | | | | |
| Eddy currents | Laminations, frequency | Energised | Thinner laminations | | | | | | | | |
| Stray/leakage | Construction | Any load | Interleaved windings | | | | | | | | |
## Iron (no-load) losses
Hysteresis and eddy-current losses run 24/7 while energised, regardless of load. Better core steel and laminations reduce them. A lightly-loaded transformer still burns its iron loss continuously the argument against casual oversizing.
## Efficiency and loading
Efficiency = output ÷ (output + losses). Because iron loss is fixed and copper loss scales with load², peak efficiency occurs near copper loss equal to iron loss typically 50–80 % load. Large power transformers exceed 99 %; tiny ones may reach only 80.
## How to apply this in your build
Work through the sequence below each step assumes the previous one passed. For numbers that need calculating, the linked tools at the end of this guide do the arithmetic instantly.
1. Read rated losses from the nameplate or test sheet
2. Compute iron loss at no-load and copper loss at load
3. Calculate efficiency across the expected load range
4. Match transformer rating to genuine demand, not fear
### Worked example
A 100 kVA transformer with 0. 4 kW iron loss and 2 kW full-load copper loss. At 25 kVA load, copper loss is 0. 125 kW. Efficiency ≈ 25 ÷ 25. 525 ≈ 98 % the numbers reward measuring, not guessing. Run the numbers yourself with the Transformer Turns Ratio and the result should agree to within rounding.
> Practical note from the bench. Energy audits we publish include the transformer at its real duty cycle the fixed iron tax changes the maths of “right-sizing”.
## Common mistakes to avoid
– Oversizing “for safety” and paying iron loss forever
– Ignoring regulation (voltage sag) on long cable-fed secondaries
– Assuming efficiency is constant across load
## Key takeaways
– Copper (load) losses the foundation of this guide; revisit it if any measurement here surprises you.
– Iron (no-load) losses the foundation of this guide; revisit it if any measurement here surprises you.
– Efficiency and loading the foundation of this guide; revisit it if any measurement here surprises you.
## Prerequisites and preparation
Before starting: read rated losses from the nameplate or test sheet and compute iron loss at no-load and copper loss at load. Keep the [Transformer Turns Ratio](/tools/transformer-turns-ratio) open every number in the worked example is reproducible. Total time including the bench steps: about 6–7 minutes.
## Who benefits most
Hobbyists meeting this topic for the first time, students who want the version with real numbers instead of abstract symbols. Returning engineers refreshing a corner of the craft. The mistake list alone justifies the visit every entry in it was learned the expensive way.
### Quick reference card
| Aspect | Where to find it in this guide |
| — | — |
| Core theory | Copper (load) losses |
| Application steps | How to apply this in your build |
| Worked numbers | Worked example |
| Failure modes | Common mistakes to avoid |
## How this fits the electrical engineering complete guide track
This guide is one stop in the structured learning path. Start from the [electrical engineering complete guide](/tutorial/electrical-engineering-complete-guide) pillar page for the full map, or continue with [transformer families](/tutorial/transformer-types-applications) and [power factor correction](/tutorial/power-factor-explained). For the arithmetic, open the [Transformer Turns Ratio](/tools/transformer-turns-ratio).
## Frequently asked questions
Where is a transformer most efficient?
Where copper loss equals iron loss typically 50–80 % of rated load.
Do losses matter on small transformers?
Proportionally more: a 10 VA transformer may waste 20 % of its input at light load.
Is there a calculator for this?
Yes the [Transformer Turns Ratio](/tools/transformer-turns-ratio) tool runs the formulas from this guide instantly, client-side, with no signup.
## Your next step in this track
– The complete electrical engineering guide: [Electrical Engineering complete guide](/tutorial/electrical-engineering-complete-guide)
– Read next: [pid controller explained: proportional-integral-derivative in practice](/tutorial/pid-controller-explained)
– Also in this track: [single-phase vs three-phase power: the real differences](/tutorial/single-phase-vs-three-phase)
– Continue with: [power factor explained: why real power is not apparent power](/tutorial/power-factor-explained)
– Calculate as you go: [power calculator](/tools/electrical-power) · [transformer turns ratio tool](/tools/transformer-turns-ratio) · [cable sizing helper](/tools/wire-gauge-awg)
– From here, the natural continuation is the next guide in the track index. It assumes exactly the vocabulary this page built and adds the next layer of practice.
## Practical working notes
Component substitution is a legitimate experiment as long as it is deliberate. Swap one part, predict the effect, measure, and record. That single habit converts a parts bin into a teaching lab and makes every future guide in this track faster to absorb.
The fastest way to internalise this topic is to change one variable deliberately and predict the result before measuring. Wrong predictions are the curriculum, they show exactly which mental model needs revisiting, and the bench grades honestly.
## Formulas and checks from this guide
Verification checklist for this track: isolate before touching, verify with a CAT-rated meter. Re-check protective device ratings after any load change. Mains discipline is a habit, not a step, and every guide here assumes it.
Bookmark this page against your next build in the track. The checklist above is the same one used across 27 guides in this series.
## Experience notes
Inrush from motors or supplies. Curve C breakers tolerate it, and sizing follows the datasheet.
Isolated low-voltage work, yes. Mains and panel work needs a qualified electrician, every time.