Calculator Inputs
Enter RMS current for AC systems. The page remains a single vertical flow, while inputs use a responsive three, two, and one column grid.
Example Data Table
| Scenario | System | Current (A) | Reference Resistance per Path (Ω) | Conductor Temp (°C) | AC Factor | Total Copper Loss (W) |
|---|---|---|---|---|---|---|
| Industrial motor winding | Three-Phase AC | 18 | 0.32 | 75 | 1.03 | 389.6 |
| Power transformer secondary | Single-Phase AC | 12 | 0.48 | 60 | 1.02 | 163.2 |
| DC supply pair | DC | 40 | 0.006 | 50 | 1.00 | 21.5 |
Formula Used
1) Resistance from conductor geometry
Rref = ρ × L ÷ (A × n)
Where ρ is resistivity, L is one-way conductor length, A is cross-sectional area, and n is the number of parallel paths.
2) Temperature-corrected resistance
RT = Rref × [1 + α × (T - Tref)]
Copper resistance increases with temperature, so higher winding temperature raises copper loss.
3) Effective operating resistance
Reff = RT × AC factor
The AC factor lets you account for additional resistance caused by skin effect and proximity effect.
4) Copper loss
Pcu = I² × Rtotal
This calculator multiplies the effective per-path resistance by the number of active electrical paths in the selected system.
5) Average loss and energy loss
Pavg = Pcu × duty cycle
Energy = Pavg × hours ÷ 1000
How to Use This Calculator
- Select the system type: DC, single-phase AC, or three-phase AC.
- Choose whether you want to enter resistance directly or calculate it from conductor geometry.
- Enter operating current and temperature values. For AC, use RMS current.
- Add an AC resistance factor if skin and proximity effects matter.
- Set duty cycle and operating hours to estimate average loss and energy waste.
- Optionally enter voltage, output power, fixed losses, thermal resistance, and energy cost.
- Press the calculate button to show results above the form, export data, and review the graph.
Frequently Asked Questions
1) What is copper loss?
Copper loss is the resistive heating created when current flows through copper conductors or windings. It is usually calculated with I²R and rises quickly as current increases.
2) Why does temperature matter so much?
Copper resistance increases with temperature. When a winding runs hotter, its resistance rises, and the same current produces more loss and more heating.
3) Should I enter peak current or RMS current?
Use RMS current for AC calculations because copper heating depends on the effective current value. For steady DC circuits, the actual current value is used directly.
4) What does the AC resistance factor do?
It scales resistance upward to reflect skin effect and proximity effect. This is especially useful at higher frequency, with large conductors, or tightly packed windings.
5) Why are there two copper loss results?
Instantaneous copper loss shows the loss at the entered operating current. Average copper loss applies the duty cycle, which is better for energy and cost estimates over time.
6) Can I use geometry mode for cables and windings?
Yes. Geometry mode is useful for busbars, feeder cables, and winding paths when you know conductor length, area, and material resistivity at the reference temperature.
7) Is the temperature rise value exact?
No. It is a first-pass estimate based on thermal resistance. Real equipment temperature depends on cooling method, airflow, mounting, insulation, and load variation.
8) Can this calculator estimate efficiency?
Yes. Enter output power and any additional fixed losses. The efficiency result is a simple operating-point estimate, not a full machine performance model.