Transformer Winding Resistance Calculator
Estimate one transformer winding at a time from turns, mean length per turn, conductor size, and material. The calculator reports DC winding resistance, optional temperature-corrected resistance, voltage drop, and DC-resistance-based winding copper loss without turning it into a full efficiency, regulation, or thermal model.
Engineering tool
Transformer Winding Resistance Calculator
Estimate transformer winding wire length, DC resistance, IR drop, and winding I²R copper loss from turns, MLT, conductor size, and material.
Electrical resistance uses bare conductive cross-sectional area, not insulated outside diameter.
Positive finite turns are accepted for engineering what-if analysis; physical windings normally use integer turns.
Average conductor length per turn. Do not enter core magnetic path length.
Optional first-order resistance correction from the material reference temperature, not a thermal-rise model.
Result console
- Estimated Total Wire Length
- 20m
- DC Winding Resistance
- 0.3448Ω
- Conductor Area
- 1mm²
- Temperature-Corrected Resistance
- 0.3448Ω
This is a DC winding resistance / low-frequency resistance estimate based on conductor geometry.
Mean length per turn is user-entered winding conductor length per turn; it is not magnetic path length.
Copper loss is an I²R winding copper-loss estimate based on true RMS or DC-equivalent winding current.
IR winding drop is not a complete transformer voltage-regulation model.
This calculator does not model window fill, winding temperature rise, skin effect, proximity effect, litz construction, or total transformer efficiency.
Temperature correction adjusts resistance only; it is not a thermal-rise or safe-operating-temperature calculation.
Formula reference
Transformer winding resistance formulas
The resistance formula reuses the shared ECParts wire resistance model. Use conductive metal area for A; window fill and insulated wire diameter belong to a separate transformer winding-fit workflow.
Lwire = N × MLTR = ρL / AR = ρN × MLT / AVdrop = I × RPcu = I² × RR(T) = Rref[1 + α(T - Tref)]Variable definitions
- N
- number of winding turns
- MLT
- mean length per turn
- Lwire
- total conductor length for one winding
- ρ
- conductor resistivity in ohm meters
- A
- conductor cross-sectional area in square meters
- I
- DC or true RMS winding current
- Pcu
- estimated winding copper loss
TRF-008 Formula Audit
| Wire Length Formula | Lwire = N x MLT. |
|---|---|
| Resistance Formula | R = rho L / A = rho N MLT / A. |
| Voltage Drop Formula | Vdrop = I R. |
| Copper Loss Formula | Pcu = I²R. |
| Resistance Convention | DC winding resistance / low-frequency resistance estimate. |
| Reference Temperature | Copper and aluminum presets use the shared AWG material convention at approximately 20 C. |
| Temperature Correction Included | Yes, first-order R(T) = Rref[1 + alpha(T - Tref)] when preset material data is used. |
| AWG Dataset Reused | Yes, `data/reference/awg.ts`. |
| Material Dataset Reused | Yes, shared AWG copper and aluminum material properties. |
| Mean Length per Turn Convention | User-entered average conductor length per winding turn, not magnetic path length. |
| Current Convention | DC or true RMS winding current for I²R loss. |
| AC Resistance Included | No. |
| Skin Effect Included | No explicit skin-effect model. |
| Proximity Effect Included | No explicit proximity-effect model. |
| Copper Loss Called Total Transformer Loss | No; it is winding copper loss only. |
| IR Drop Called Full Voltage Regulation | No; I x R drop is not complete transformer voltage regulation. |
| WIR-001 Consistency | Resistance calculation is delegated to the shared Wire Resistance utility. |
| TRF-007 Scope Separation | TRF-007 accounts for known losses and efficiency; TRF-008 estimates one winding's resistance-derived copper loss. |
| TRF-009 Scope Separation | No window fill, packing factor, insulation occupancy, or bobbin fit calculation. |
Worked Examples
| Case | Calculation | Result |
|---|---|---|
| 100 turns, 0.2 m MLT | 100 x 0.2 m | 20 m wire length |
| 20 m copper, 1 mm² | 1.724e-8 x 20 / 1e-6 | 0.3448 Ω |
| 0.3448 Ω at 2 A | V = IR; P = I²R | 0.6896 V; 1.3792 W |
| 500 turns, 100 mm MLT | 500 x 0.1 m | 50 m wire length |
| 50 m copper, 0.5 mm² | 1.724e-8 x 50 / 0.5e-6 | 1.724 Ω |
| 1.724 Ω at 0.5 A | V = IR; P = I²R | 0.862 V; 0.431 W |
| Turns doubled | N x2 with same MLT and area | Length x2; resistance x2 |
| Area doubled | A x2 with same length | Resistance divided by 2 |
| Current doubled | I x2 with same resistance | Voltage drop x2; copper loss x4 |
| 1000 turns, 0.1 m MLT | 1000 x 0.1 m | 100 m wire length |
Engineering Notes
- Transformer winding resistance depends on total conductor length, material resistivity, and conductive cross-sectional area.
- MLT is normally measured or estimated from the actual winding build; V1 does not infer it from core geometry.
- Physical windings normally use integer turns, but positive finite turn values are useful for design exploration.
- AWG mode uses the raw shared AWG conductor area for calculations and only rounds for display.
- Area mode uses conductive metal area. Do not use insulated outside diameter as conductor area.
- Copper and aluminum resistivity values come from the shared ECParts AWG material data.
- The reference material convention is approximately 20 C for the shared copper and aluminum presets.
- The optional temperature correction changes resistance, but it does not predict winding temperature rise.
- Primary, secondary, and auxiliary windings can be analyzed by running the calculator once per winding.
- Estimated winding copper loss is Pcu = I²R based on DC resistance or temperature-corrected resistance.
- Use true RMS current for AC waveforms, especially for rectifier, pulse, or non-sinusoidal winding currents.
- DC winding resistance is not always equal to AC winding resistance at switching or RF frequencies.
- Skin effect, proximity effect, winding layering, and litz-wire construction can increase real AC copper loss.
- Inductor Q, leakage, capacitance, insulation, and mechanical construction are outside this resistance model.
- IR drop is not the full transformer voltage-regulation model.
- Winding copper loss is not total transformer loss; core and stray losses must be handled separately.
Common Mistakes
- Confusing MLT with magnetic path length.
- Entering one turn length and forgetting the turns multiplier.
- Using mm² as if it were mm or m².
- Using 1 mm² = 0.001 m² instead of 1e-6 m².
- Rounding AWG area before doing the resistance calculation.
- Mixing material resistivity datasets with different reference conventions.
- Ignoring the resistivity reference temperature.
- Using peak current instead of RMS current for I²R loss.
- Calling DC winding resistance AC winding resistance.
- Ignoring skin and proximity effects at high frequency.
- Calling winding copper loss total transformer loss.
- Treating I x R winding drop as full voltage regulation.
- Using conductor diameter instead of conductor area.
- Using bare conductor area for window-fill geometry.
Support reference
FAQ
What is transformer winding resistance?
Transformer winding resistance is the electrical resistance of one primary, secondary, or auxiliary winding conductor path.
How do I calculate transformer winding resistance?
Estimate the conductor length from turns times mean length per turn, then use R = rho L / A with material resistivity and conductor area.
What is mean length per turn?
Mean length per turn, or MLT, is the average conductor length used by one turn of the winding.
How do I calculate transformer wire length from turns?
Use Lwire = N x MLT, where N is winding turns and MLT is the mean length per turn.
What is the formula R = rho L / A?
It means resistance equals material resistivity times conductor length divided by conductive cross-sectional area.
What resistivity does the calculator use for copper?
Copper uses the shared ECParts AWG material reference value of 1.724e-8 ohm meter.
At what temperature is copper resistivity specified?
The shared copper material reference is documented at approximately 20 C.
How does winding temperature affect resistance?
For copper and aluminum presets, the optional temperature correction applies R(T) = Rref[1 + alpha(T - Tref)].
Can I use AWG wire?
Yes. AWG mode resolves conductor area from the shared ECParts AWG dataset rather than a transformer-specific copy.
Can I use wire area in mm²?
Yes. Area mode supports mm² and converts internally to square meters for R = rho L / A.
How do I convert mm² to m²?
Multiply by 1e-6. For example, 1 mm² equals 1e-6 m².
How does wire size affect winding resistance?
For the same material and length, doubling conductor area halves the winding resistance.
How does the number of turns affect resistance?
For the same MLT, material, and area, doubling turns doubles wire length and resistance.
How does mean length per turn affect resistance?
For the same turns, material, and area, doubling MLT doubles total wire length and resistance.
How do I calculate transformer copper loss?
Use Pcu = I²R with DC current or true RMS winding current and the winding resistance.
Why is copper loss I squared R?
Resistive heating power in the winding conductor follows the same Joule heating relationship as any resistance.
Should I use RMS or peak winding current?
Use true RMS current for AC copper-loss estimates. Peak current should not be used unless converted to the correct RMS-equivalent value.
Can I use this calculator for non-sinusoidal current?
Yes, if the current input is the true RMS value for the waveform.
Is DC winding resistance the same as AC winding resistance?
No. At higher frequency, skin effect, proximity effect, strand arrangement, and winding geometry can raise AC resistance.
What is skin effect?
Skin effect is the tendency for AC current to crowd toward the conductor surface as frequency increases.
What is proximity effect?
Proximity effect is current redistribution caused by nearby magnetic fields from adjacent winding conductors.
Can actual AC copper loss be higher than this estimate?
Yes. This calculator reports a DC-resistance-based winding I²R estimate, so high-frequency AC loss can be higher.
Does this calculator calculate transformer efficiency?
No. Use the Transformer Efficiency & Loss Calculator when you need input power, output power, and total loss accounting.
Is winding copper loss the same as total transformer loss?
No. Total transformer loss can include core loss, stray loss, auxiliary loss, and other mechanisms.
Does winding voltage drop equal transformer voltage regulation?
No. I x R winding drop is only one part of regulation; leakage reactance, load power factor, and temperature also matter.
Can I use this for primary and secondary windings?
Yes. Run the calculation separately for each primary, secondary, or auxiliary winding.
Does this calculator determine winding temperature rise?
No. Temperature correction adjusts resistance only; it does not compute self-heating or thermal safety.
What is the difference between TRF-008 and the Wire Resistance Calculator?
TRF-008 uses transformer-specific turns, MLT, winding current, and copper-loss context. The Wire Resistance Calculator is a generic conductor resistance tool.
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Open calculatorDocumentation
Related Engineering Resources
Guides and lookup references linked to this tool.
Engineering Guide
Transformer Winding Design: Current Density, Window Fill, Insulation, and Thermal Limits
Design transformer windings using RMS current, conductor area, physical window fill, insulation constraints, hot resistance, copper loss, and prototype verification.
20 min · Intermediate
Engineering Guide
Transformer Load, Voltage Regulation, Efficiency, and Winding Loss
Connect RMS VA loading, hot winding resistance, copper loss, voltage regulation, and real-power efficiency.
20 min · Intermediate
Engineering Guide
Transformer Core Loss: Waveform, Frequency, Flux Density, and Thermal Design
Estimate material-based core loss, combine it with winding and stray losses, iterate temperature, and verify the completed transformer.
19 min · Advanced
View all 4 Guides ↓Show fewer Guides ↑
Engineering References
Engineering Reference
Transformer Parameters and Equivalent-Circuit Terms Reference
Lookup tables for transformer turns, voltage, current, impedance, VA, regulation, efficiency, magnetizing, leakage, winding, and reflected-load terms.
15 min · Reference
Engineering Reference
Transformer Winding, Wire and Window-Fill Reference
Lookup reference for transformer winding terms, wire area, mean length per turn, window fill, insulation allowances, center taps, series connections, parallel windings, and build boundaries.
14 min · Reference