Transformer Calculator

A 100 kVA transformer with 500 W core and 1500 W copper loss runs at 97.8095 % efficiency at 75 % load and 0.8 power factor.

Rating S (kVA):

Primary voltage V₁:

Secondary voltage V₂:

Core (iron) loss Pᵢ (W):

From the open-circuit test; constant at any load.

Full-load copper loss P_cu (W):

From the short-circuit test; varies with the square of the load.

Load as a fraction of full load:

Load power factor:

Efficiency η =

97.809475292919 %

Precision

Full answer, then cut to fewer decimals (not rounded):

97.809475292919 %
97.80947529291 %
97.8094752929 %
97.809475292 %
97.80947529 %
97.8094752 %
97.809475 %
97.80947 %
97.8094 %
97.809 %
97.80 %
97.8 %

Turns ratio N₁ : N₂: 26.5060241
Full-load primary current (single-phase): 9.090909091 A
Full-load secondary current (single-phase): 240.9638554 A
Output power at this load: 60 kW
Total losses at this load: 1343.75 W
Load for maximum efficiency √(Pᵢ/P_cu): 57.73502692 % of full load
Maximum efficiency: 97.88081812 %

Step-by-step solution

Copper loss at x = 0.75: x²P_cu = 843.75 W
η = xS cos φ ÷ (xS cos φ + Pᵢ + x²P_cu) = 60000 ÷ (60000 + 500 + 843.75)
η = 97.80947529 %

Transformer Formula

η = xS cos φ / (xS cos φ + Pᵢ + x²P_cu)

x load fraction, Pᵢ core loss, P_cu full-load copper loss; maximum η at x = √(Pᵢ/P_cu)

Worked Example

A 100 kVA, 11 kV/415 V transformer with 500 W core loss and 1500 W full-load copper loss, at 75 % load and 0.8 power factor:

Copper loss at x = 0.75: x²P_cu = 843.75 W
η = xS cos φ ÷ (xS cos φ + Pᵢ + x²P_cu) = 60000 ÷ (60000 + 500 + 843.75)
η = 97.80947529 %

Full-load primary current (single-phase): 9.090909091 A · Full-load secondary current (single-phase): 240.9638554 A · Output power at this load: 60 kW · Total losses at this load: 1343.75 W · Load for maximum efficiency √(Pᵢ/P_cu): 57.73502692 % of full load · Maximum efficiency: 97.88081812 %

GATE tip

All-day efficiency uses energies, not powers: core loss runs 24 h while copper loss scales with x² for each period. Add up kWh of output and losses over the day.

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rotor frequency sf; rotor copper loss = sP_ag; mechanical power = (1 − s)P_ag

Example: A 4-pole, 50 Hz motor running at 1440 rpm with 10 kW crossing the air gap: Slip s = 4 %.

Open the induction motor slip calculator →
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E = PΦZN / (60A)

A = P for lap, 2 for wave windings; motor: E_b = V − IₐRₐ, T = E_b Iₐ/ω

Example: A 4-pole lap-wound machine with 20 mWb per pole and 500 conductors at 1200 rpm: Generated EMF E = 200 V.

Open the dc machine emf calculator →

Frequently asked questions

When is a transformer most efficient?

When copper loss equals core loss: at x = √(Pᵢ/P_cu) of full load. Distribution transformers are designed to peak around 50–70 % load.

What about three-phase currents?

Use I = S/(√3 V_L). The calculator’s currents are single-phase; divide them by √3 for a three-phase unit with line voltages.

Sources

The International System of Units (SI), 9th edition (SI Brochure), Bureau International des Poids et Mesures .

Last reviewed: 2026-10-15. Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.

Cite this page

APA

Scientific Converters. (2026, October 15). Transformer Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/transformer-calculator/

IEEE

Scientific Converters, "Transformer Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/transformer-calculator/