ElectroHub

Transformer Efficiency and Regulation Calculator

Iron loss is fixed once the transformer is energised; copper loss rises with the square of the load. Efficiency therefore peaks where the two are equal, which is usually well below full load — the reason distribution transformers are sized for their average duty, not their peak.

Transformer Efficiency & Regulation

Efficiency at a given load, with the load fraction for maximum efficiency (where copper loss equals the constant iron loss). Enter losses in watts.

Output power
Copper loss at this load
Total losses
Efficiency η
Load for max efficiency
  1. 1.Given: S = 10 kVA, cos φ = 0.9, P_iron = 100 W, P_cu(FL) = 200 W, load = 1×
  2. 2.FormulaOutput = x·S·cos φSubstitute= 1 × 10000 × 0.9Result= 9 kW
  3. 3.FormulaCopper loss = x²·P_cu(FL)Substitute= 1² × 200Result= 200 W
  4. 4.Formulaη = output ÷ (output + P_iron + P_cu)Substitute= 9000 ÷ (9000 + 300)Resultη = 96.7742 %
  5. 5.FormulaMax η when P_cu = P_iron, at load x = √(P_iron/P_cu)Substitutex = √(100/200)Resultx = 0.7071×, η_max = 96.9531 %
Common trap: Iron (core) loss is essentially constant — it depends on voltage and frequency, not load — while copper loss rises with the square of the load current. Maximum efficiency is therefore not at full load but at the point where the two losses are equal.

The formula

η = P_out / (P_out + P_iron + P_copper) ; Regulation % = (V_no-load − V_full-load) / V_full-load × 100

η
efficiency (per cent)
P_out
output power = kVA × load fraction × power factor
P_iron
core loss — constant at all loads (watts)
P_copper
winding loss — scales with load fraction squared (watts)

Worked example

A 100 kVA transformer at full load, pf 0.8, with 1 kW iron loss and 1.5 kW full-load copper loss.

  1. Output: P_out = 100 × 0.8 = 80 kW
  2. Total losses: 1 + 1.5 = 2.5 kW
  3. η = 80 / (80 + 2.5) = 80 / 82.5

η = 96.97 %. Maximum efficiency would occur at √(1/1.5) = 81.6 % of full load.

Where you'll use it

Machine design papers and energy audits. The condition for maximum efficiency — copper loss equal to iron loss — is one of the most reliably examined results in the subject.

The laws behind it

Parts this applies to

Inductor / CoilTransformer (power)Current / Potential Transformer (CT/PT)DC MotorSpeaker / MicrophoneRCCB / RCD / GFCICurrent Sensor (Hall / Shunt / CT)LVDT & Displacement Transducers

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