Core vs Copper Loss Formula (Transformer Efficiency)
Introduction #
Instant answer: η = Pout ÷ (Pout + Pcore + Pcu×(I/Ir)²). Screen: 100 kVA, Pcore=250 W, Pcu=1200 W, 60 kW @ 0.9 PF → η ≈ 98.9%. Size kVA so typical load sits ~50–80% of nameplate.
Open Transformer Size — 60 kW · 0.9 PF (mid-load screen) →
Decision gate: efficiency vs oversizing #
| Decision | Prefer | Do not |
|---|---|---|
| Typical load 50–80% of nameplate | Size for that band (good η) | Buy “two sizes up for safety” |
| 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 Guide.
What Determines Transformer Efficiency #
Transformer efficiency is the ratio of output power to input power (output ÷ input). Losses are the difference: input − output. Efficiency is determined by two main loss components: core (no-load) loss and copper (load) loss. Core loss is roughly constant with load; copper loss varies with the square of load current. At light load, core loss dominates and efficiency is lower. At high load, copper loss grows and efficiency can drop again. Peak efficiency typically occurs between about 50% and 80% of rated load, where the two loss components are in a favorable balance. Design choices (core material, winding design, flux density) and operating point (load level) together set efficiency. For sizing, the goal is to choose a transformer whose normal operating load falls in the high-efficiency range and to avoid severe oversizing, which pushes the operating point toward light load and worse efficiency.
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.
Input: P_in = 60,000 + 250 + 1200 × (60/100)² = 60,000 + 250 + 432 = 60,682 W (assuming 60 kVA load ≈ 60% of 100 kVA, so I_load/I_rated ≈ 0.6).
Efficiency: η = 60,000 ÷ 60,682 ≈ 98.87%.
At 25% load (25 kW): P_cu ∝ 0.25² = 0.0625 × 1200 = 75 W. η = 25,000 ÷ (25,000 + 250 + 75) ≈ 98.7%. At 100% load: η = 100,000 ÷ (100,000 + 250 + 1200) ≈ 98.57%. So in this example efficiency is high across the range but slightly better in the mid-load region. Heavy oversizing (e.g. 100 kVA for 25 kW) would put operation at 25% load where core loss is a larger share of total loss; a smaller transformer (e.g. 30 kVA) would have lower P_core and could be more efficient at that load level.
How Efficiency Impacts Transformer Sizing #
Sizing affects the operating load point and thus efficiency. If the transformer is sized so that normal load is 50–80% of nameplate, the unit usually operates near peak efficiency. If it is severely oversized (e.g. normal load <30% of nameplate), the no-load loss dominates and efficiency at that load is worse than a smaller, properly sized unit. Undersizing pushes operation toward or above full load, with higher copper loss and temperature; it is not an efficiency optimization, it is a reliability risk. So efficiency considerations support sizing in the “normal load in the 50–80% range” guideline from the Transformer Sizing Guide, rather than adding extra margin “for efficiency.”
Oversizing vs Undersizing from Efficiency Perspective #
Oversizing: Improves thermal margin and can extend life, but at light load no-load loss is a larger fraction of total loss. Severe oversizing (e.g. 2× or more than required kVA for the actual load) is not recommended from an efficiency standpoint: you pay more for the unit and often run at lower efficiency. One size up from calculated kVA with normal safety margin (e.g. 25%) is sufficient; do not oversize by 50–100% “to be safe.”
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: Oversizing moves the operating point to light load where no-load loss dominates and efficiency is often worse. Size for load plus normal margin (e.g. 25%); choose the next standard size. Do not go two sizes up to be safe.
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.
Typical Loss Ranges (Reference) #
| Transformer size (kVA) | No-load loss (W) typical range | Load loss at full load (W) typical range |
|---|---|---|
| 30 | 100–200 | 400–700 |
| 100 | 200–400 | 1000–1800 |
| 300 | 500–900 | 2500–4500 |
| 500 | 700–1200 | 4000–7000 |
Actual values depend on design (efficiency class, material). Use nameplate or manufacturer data for calculation. This table is for order-of-magnitude reference only.
Engineering Recommendation #
Size the transformer so that typical load is 50-80% of nameplate. Use the Transformer Size Calculator to get the required kVA (with margin), then choose the next standard size. Avoid going two sizes up; if in doubt, document the load assumption and margin so that future changes can be reviewed. For loss-sensitive applications, compare P_core and P_cu at your operating load and consider lifecycle cost, not just first cost.
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 | Often near peak η |
| 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 whenever the unit is energized. Copper (load) loss scales ≈ with I². At light load core dominates; at full load copper dominates. Peak η is often near 50–80% load.
How do I calculate transformer efficiency?
η = P_out ÷ (P_out + P_core + P_cu×(I/I_rated)²). Example above: 100 kVA unit, 60 kW @ 0.9 PF → ≈ 98.9%. See the worked example section.
Why should I avoid severely oversizing a transformer?
Severe oversizing parks the unit at light load where no-load loss hurts η and first cost rises. Prefer load + ~25% margin, then one catalog step—not two sizes “just in case.”
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 #
Use Transformer size calculator and kVA to amps calculator to apply the numbers from this guide, then browse the Power calculator hub for related calculators.
Conclusion #
Transformer efficiency depends on core loss and copper loss; use the efficiency formula at your operating load. Size so that typical load is 50-80% of nameplate to stay near peak efficiency. Avoid severe oversizing; compare P_core and P_cu when choosing between options. Use the calculator to get required kVA, then select the next standard size.
Related Tools #
- Transformer Size Calculator: Get required kVA with margin; then choose next standard size.
Related Articles #
- Transformer Sizing Guide: Sizing formulas, margins, and standard sizes.
- Transformer Derating Factors: Temperature, altitude, and harmonic derating when conditions exceed standard.
About the Author: Michael Rodriguez, P.E. is a senior power systems engineer with 12+ years of experience in factory electrical design and facility expansion projects. Specializes in load analysis, transformer sizing, and electrical distribution system optimization. Has designed distribution systems for manufacturing facilities, data centers, and commercial buildings. All content in this guide has been reviewed and validated by licensed engineers.