Quick answer: Transformer copper & core loss formula (η) #

Instant answer: η = Pout ÷ (Pout + Pcore + Pcu,FL×x²), where x is per-unit kVA/current loading. For a 100 kVA unit with Pcore=250 W and full-load Pcu=1200 W, 60 kW @ 0.9 PF is 66.67 kVA, so x=0.667, copper loss is about 533 W, and η ≈ 98.71%.

Verify mid-load kVA — 60 kW · PF 0.9 →

Decision gate: efficiency vs oversizing #

Decision Prefer Do not
Compare operating points Calculate η from each candidate's OEM no-load and load losses Assume one universal best load band
Mostly light / idle load Compare P_core (no-load) dominance Full-load η brochure alone
Need kVA first Run sizing calculator, then apply η formula η math without a kVA candidate
Boundary OEM loss tables / tender specs Generic η% without P_core / P_cu

This guide is for electrical engineers, facility managers, and designers who need to distinguish core (iron) loss from copper loss, estimate efficiency at a given load, and avoid oversizing that worsens part-load efficiency. For the overall sizing process, see the transformer sizing formula method page.

What Determines Transformer Efficiency #

Transformer efficiency is the ratio of output power to input power (output ÷ input). Losses are the difference: input − output. Core (no-load) loss is approximately constant at a stated voltage and frequency, while load loss varies approximately with the square of load current. For a simplified model, maximum efficiency occurs when scaled load loss equals no-load loss, so the per-unit loading is x = √(P_core/P_cu,FL). The resulting point is transformer-specific, not a universal 50–80% band.

Core Loss vs Copper Loss Explained #

Core loss (no-load loss, P_core): Occurs whenever the transformer is energized. It is due to hysteresis and eddy currents in the core and is approximately constant with load. It depends on voltage, frequency, and core design. Nameplate no-load loss is usually given in watts at rated voltage and frequency. At light load, core loss is a large fraction of total loss, so efficiency is relatively low.

Copper loss (load loss, P_cu): Resistive and eddy losses in the windings due to load current. It varies approximately with the square of load current: P_cu ∝ I², so at 50% load copper loss is about 25% of full-load copper loss. At full load, copper loss dominates total loss in most distribution transformers. Nameplate load loss is typically given in watts at rated current.

Formula (efficiency):

η = P_out ÷ (P_out + P_core + P_cu)

Or in terms of losses:

η = P_out ÷ P_in   where  P_in = P_out + P_core + P_cu

At a given load level, P_cu is scaled from the nameplate load loss by (load current ÷ rated current)². P_core is taken from nameplate (constant with load). Then efficiency at that load can be calculated. This is why efficiency varies with load: at low load, P_core is significant relative to P_out; at high load, P_cu grows.

Transformer Efficiency Formula #

Using the loss components:

Efficiency at a given load:

η = (kVA_out × PF × 1000) ÷ [ (kVA_out × PF × 1000) + P_core + P_cu × (I_load / I_rated)² ]

Where kVA_out is the output kVA at the operating point, PF is power factor (for real power), P_core and P_cu are in watts, and I_load / I_rated is the per-unit load. This shows explicitly that efficiency depends on both the transformer (P_core, P_cu) and the operating point (load level).

Example: Transformer Loss and Efficiency Calculation #

Given: 100 kVA transformer. P_core = 250 W, P_cu (at full load) = 1200 W. Load 60 kW at 0.9 PF (output power 60 kW).

Output: P_out = 60,000 W.
Apparent load: S_out = 60 kW ÷ 0.9 = 66.67 kVA, so x = 66.67/100 = 0.667.
Scaled load loss: P_cu = 1200 × 0.667² ≈ 533 W.
Input: P_in = 60,000 + 250 + 533 = 60,783 W.
Efficiency: η = 60,000 ÷ 60,783 ≈ 98.71%.

For the same 0.9 PF, 25% kVA loading means 25 kVA and 22.5 kW output: P_cu = 75 W and η = 22,500/(22,500+250+75) ≈ 98.58%. At 100% kVA loading, output is 90 kW and η = 90,000/(90,000+250+1200) ≈ 98.41%. The simplified maximum-efficiency point is x = √(250/1200) ≈ 45.6% rated kVA, where copper loss equals the 250 W core loss. A different transformer with different loss data will have a different optimum.

How Efficiency Impacts Transformer Sizing #

Sizing affects the operating load point and therefore loss cost, but efficiency is only one constraint. Compare candidate transformer loss data against the measured or forecast load profile, then separately verify thermal capacity, harmonics, starting duty, contingency, environment and growth. Severe oversizing can make no-load loss dominate annual energy; undersizing can violate thermal and reliability limits.

Oversizing vs Undersizing from Efficiency Perspective #

Oversizing: At light load, no-load loss is a larger fraction of delivered power. Compare annualized losses and the actual operating profile rather than applying a universal “one size up” or 25% rule.

Undersizing: Reduces first cost but risks overload, overheating, and shorter life. Efficiency at overload is not the main issue; reliability and safety are. Size to meet load plus margin; do not undersize to “improve efficiency.”

Common Mistakes in Efficiency and Sizing #

Mistake 1: Oversizing Heavily "For Efficiency" #

Error: Adding 50-100% extra kVA thinking it improves efficiency or safety.

Correct approach: Compare the load profile and OEM loss data for each feasible frame. Set reserve from documented growth, contingency, thermal and starting requirements rather than a universal percentage.

Mistake 2: Ignoring No-Load Loss When Comparing Options #

Error: Comparing transformers using only nameplate or full-load efficiency.

Correct approach: Two units with the same full-load efficiency can have different part-load efficiency if P_core differs. For variable or light load, compare P_core and P_cu and estimate efficiency at your typical load. Use the efficiency formula with your operating point.

Use manufacturer loss data #

Do not substitute a generic loss table for the candidate transformer's test or catalog data. Obtain no-load loss and load loss at the stated voltage, frequency, winding temperature, and tap position, then evaluate each candidate against the expected load-duration profile.

Engineering Recommendation #

Use the Transformer Size Calculator to establish load kVA, then compare actual manufacturer frames and loss data across the forecast load-duration profile. Document growth and contingency separately. For loss-sensitive applications, calculate annual no-load and scaled load losses rather than assuming a universal efficient loading band.

Quick loss screen (planner-style) #

Load (% of rated kVA) Copper loss vs full-load P_cu Efficiency trend
25% ≈ 6% of full-load P_cu Core loss share high
50% ≈ 25% of full-load P_cu Near peak only when P_core ≈ 0.25×P_cu,FL
75% ≈ 56% of full-load P_cu Still strong
100% 100% Copper dominates

Use nameplate P_core and P_cu with η = P_out ÷ (P_out + P_core + P_cu × load²).

Frequently Asked Questions #

What is the difference between core loss and copper loss?

Core (iron / no-load) loss is roughly constant at stated voltage and frequency. Copper/load loss scales approximately with I². In the simplified model, peak η occurs at x = √(P_core/P_cu,FL), so the point depends on the transformer's loss data.

How do I calculate transformer efficiency?

η = P_out ÷ (P_out + P_core + P_cu,FL×x²). Example above: 100 kVA unit, 60 kW @ 0.9 PF means x = 0.667 and η ≈ 98.71%.

Why should I avoid severely oversizing a transformer?

Severe oversizing can make no-load loss dominate annual energy and raises first cost. Choose among thermally adequate candidates using the load profile, documented contingency/growth and OEM loss data rather than a fixed margin.

Is there a free transformer efficiency / losses calculator?

CalcPanel keeps the formula and numeric example on this page (transparent assumptions). For kVA selection first, use the transformer kVA calculator, then apply nameplate P_core / P_cu here.

Next step #

Screen candidate kVA in the Transformer sizing calculator, then re-run η with OEM P_core / P_cu at your load duration. Method companion: transformer sizing formula. Hub: Power calculator hub.

Conclusion #

Transformer efficiency depends on no-load loss, load loss and the operating load profile. Calculate efficiency for each candidate using OEM loss data; the simplified peak occurs when scaled load loss equals no-load loss. Size for the actual thermal, harmonic, starting, growth and contingency requirements, then compare annual losses among suitable catalog frames.

  • Transformer Size Calculator: Establish load kVA and view a reference frame; document reserve and verify the actual manufacturer catalog separately.

Technical source #