Wire Resistance vs Temperature Calculator
Calculate copper, aluminum, or custom-TCR wire resistance at temperature, resistance change, percent change, and estimated temperature from measured conductor resistance. It is a wire-specific first-order TCR tool, not a self-heating, ampacity, RTD, NTC, or generic coefficient page.
Engineering tool
Wire Resistance vs Temperature Calculator
Calculate first-order conductor resistance change from reference resistance, wire temperature, and temperature coefficient of resistance.
Preset copper and aluminum TCR values are nominal room-temperature engineering references.
Enter conductor temperature directly. This calculator does not solve wire temperature from current.
Result console
- Resistance at Target Temperature
- 1.3144Ω
- Resistance Change
- 0.3144Ω
- Resistance Change
- 31.44%
- Resistance Ratio
- 1.3144RT/Rref
- Temperature Factor
- 1.3144
- Temperature Difference
- 80°C / K
- Temperature Coefficient
- 0.003931/°C
- Temperature Coefficient
- 3,930ppm/°C
- Reference Resistance
- 1Ω
- Material
- Copper
Engineering summary
- Mode
- Resistance at Temperature
- Material / Custom
- Copper
- Reference Resistance
- 1 Ω
- Reference Temperature
- 20 °C
- Target / Estimated Temperature
- 100 °C
- Temperature Difference
- 80 °C
- Temperature Coefficient
- 0.00393 1/°C
- Resistance Ratio
- 1.3144
- Target Resistance
- 1.3144 Ω
- Resistance Change
- 0.3144 Ω
This is a first-order wire resistance temperature correction. It is not a self-heating, ampacity, RTD, NTC, or nonlinear material model.
The model assumes conductor geometry change from thermal expansion is negligible.
Temperature coefficient values are nominal engineering references and can vary with alloy, purity, processing, and temperature range.
Electrical resistivity, mass density, and temperature coefficient are separate material properties with different units.
Large predicted resistance change; verify that a constant linear TCR is suitable over this temperature range.
Formula reference
Wire resistance temperature formulas
The same factor applies to resistance and resistivity when conductor geometry is treated as unchanged.
ΔT = T - TrefRT = Rref[1 + αΔT]ΔR = Rref αΔT%ΔR = αΔT × 100%RT/Rref = 1 + αΔTT = Tref + (RT/Rref - 1)/αρT = ρref[1 + αΔT]Variable definitions
- RT
- resistance at target temperature, Ω
- Rref
- reference resistance, Ω
- α
- temperature coefficient of resistance, 1/°C
- T
- target wire temperature
- Tref
- reference temperature
- ρT
- temperature-adjusted electrical resistivity, Ω·m
WIR-011 Formula Audit
| Core Linear Formula | RT = Rref[1 + alpha(T - Tref)]. |
|---|---|
| Delta Temperature Formula | Delta T = T - Tref. |
| Resistance Change Formula | Delta R = Rref alpha Delta T. |
| Percentage Change Formula | %Delta R = alpha Delta T x 100%. |
| Resistance Ratio Formula | RT/Rref = 1 + alpha Delta T. |
| Inverse Temperature Formula | T = Tref + (RT/Rref - 1)/alpha. |
| Resistivity Temperature Formula | rhoT = rhoref[1 + alpha Delta T] when geometry is unchanged. |
| Temperature Factor Validation | 1 + alpha Delta T must be greater than zero. |
| Reference Temperature Policy | Preset material TCR values are nominal room-temperature engineering references. |
| Temperature Coefficient Unit | Internal alpha is 1/°C; 1/K is equivalent for temperature intervals. |
| ppm Conversion | 1 ppm/°C = 1e-6 /°C. |
| Percent Conversion | 0.393%/°C = 0.00393 /°C. |
| Fahrenheit Coefficient Conversion | alpha per °F = alpha per °C / 1.8. |
| °C/K Delta Policy | 1 °C difference equals 1 K difference. |
| Absolute Zero Validation | Absolute temperatures below 0 K are rejected. |
| Material Alpha Dataset Source | data/reference/awg.ts shared material records. |
| Duplicate Alpha Table Created | No. |
| Electrical Resistivity Boundary | WIR-011 may adjust reference resistivity but does not own WIR-009 conductivity intent. |
| Mass Density Boundary | Mass density in kg/m³ belongs to WIR-010 and is not used here. |
| Geometry Expansion Included | No. |
| Self-Heating Included | No. |
| Current Input Required | No. |
| Ampacity Included | No. |
| RTD Boundary | PT100/PT1000 IEC sensor behavior remains THM-006. |
| NTC Boundary | Beta and Steinhart-Hart thermistor behavior remains THM-005. |
| THM-012 Boundary | THM-012 is generic coefficient drift; WIR-011 is wire resistance specific. |
| WIR-001 Boundary | WIR-001 computes R from rhoL/A; WIR-011 adjusts known R with temperature. |
| WIR-009 Boundary | WIR-009 owns resistivity/conductivity measurement and conversion. |
| WIR-010 Boundary | WIR-010 owns mass density and conductor mass. |
Worked Examples
| Case | Calculation | Result |
|---|---|---|
| Copper 1 Ω, 20°C to 100°C | 1[1 + 0.00393(80)] | 1.3144 Ω |
| Resistance change | 1.3144 - 1 | 0.3144 Ω |
| Percent change | 0.00393 × 80 × 100 | 31.44% |
| Resistance ratio | 1.3144 / 1 | 1.3144 |
| Inverse temperature | 20 + (1.3144/1 - 1)/0.00393 | 100°C |
| Copper resistivity at 100°C | 1.724e-8 × 1.3144 | 2.2660256e-8 Ω·m |
| Zero ΔT | T = Tref | RT = Rref |
| Positive TCR, colder wire | 20°C to 0°C | Resistance decreases |
| Rref scaling | 2 Ω with same factor | 2.6288 Ω |
| Coefficient scaling | alpha doubled | fractional change doubles |
| Delta-T scaling | Delta T doubled | fractional change doubles |
| 1 ppm/°C | 1 × 1e-6 | 0.000001 /°C |
| 3930 ppm/°C | 3930 × 1e-6 | 0.00393 /°C |
| 0.393%/°C | 0.393 / 100 | 0.00393 /°C |
| Per K | 0.00393 /K | same as 0.00393 /°C for intervals |
| 20°C | 20 × 9/5 + 32 | 68°F |
| 100°C | 100 × 9/5 + 32 | 212°F |
| 80°C difference | 80 × 9/5 | 144°F difference |
| Fahrenheit coefficient | 0.00393 / 1.8 | 0.0021833333 /°F |
| 1 Ω | ×1000 | 1000 mΩ |
| 1 mΩ | ×1000 | 1000 µΩ |
| Alpha = 0 forward | RT = Rref | same resistance |
| Alpha = 0 inverse | division by zero | rejected |
| Negative TCR valid factor | alpha < 0, factor > 0 | allowed |
| Factor <= 0 | 1 + alpha Delta T <= 0 | rejected |
| Below absolute zero | T < -273.15°C | rejected |
Engineering Notes
- Temperature coefficient of resistance, or TCR, is a relative change per degree.
- Copper and aluminum usually have positive TCR near room temperature.
- Custom alpha can be positive, zero, or negative in forward mode as long as the resistance factor remains positive.
- A zero alpha cannot be used to infer temperature from resistance.
- Preset TCR values are nominal engineering coefficients, not exact constants for every alloy or temperature range.
- The formula uses the temperature difference T - Tref, not the absolute target temperature by itself.
- Celsius and kelvin temperature intervals are numerically identical.
- Fahrenheit intervals must be scaled by 5/9; do not apply the absolute +32 offset to a temperature difference.
- WIR-011 assumes conductor geometry expansion is negligible.
- This calculator does not estimate wire self-heating, current limit, safe ampacity, insulation temperature, or code compliance.
- PT100/PT1000 RTDs use a different sensor model; NTC thermistors use nonlinear Beta or Steinhart-Hart models.
- WIR-011 is wire-specific. Use THM-012 for generic non-wire temperature coefficient drift.
Common Mistakes
- Using target temperature instead of Delta T.
- Forgetting T - Tref.
- Using a Fahrenheit difference as if it were a Celsius difference.
- Adding 32 to temperature differences.
- Using 3930 instead of 0.00393 for a ppm coefficient.
- Using 0.393 instead of 0.00393 for a percent coefficient.
- Confusing ppm and percent.
- Confusing resistivity with resistance.
- Confusing mass density with resistivity.
- Assuming alpha is exact at every temperature.
- Using linear TCR far outside its useful range.
- Assuming wire temperature equals ambient temperature.
- Assuming the calculator predicts self-heating.
- Using RTD equations for ordinary wire.
- Trying inverse mode with alpha = 0.
- Allowing a zero or negative resistance factor.
Support reference
FAQ
How does temperature affect wire resistance?
Most metal wire resistance increases as conductor temperature rises because electrical resistivity increases with temperature.
What is the wire resistance temperature formula?
The first-order formula is RT = Rref[1 + alpha(T - Tref)], where alpha is the temperature coefficient of resistance.
What is temperature coefficient of resistance?
It is the fractional resistance change per degree temperature change, usually written as alpha or TCR.
What does TCR mean?
TCR means temperature coefficient of resistance. It describes how resistance changes with conductor temperature.
How do I calculate resistance at another temperature?
Convert the coefficient to 1/°C, calculate Delta T = T - Tref, then multiply Rref by 1 + alpha Delta T.
How do I calculate temperature from resistance?
Use T = Tref + (RT/Rref - 1)/alpha. Alpha must be nonzero.
What is reference resistance?
Reference resistance is the known resistance at the reference temperature before applying the temperature correction.
What is reference temperature?
Reference temperature is the temperature where the reference resistance or reference resistivity is known.
Why does copper resistance increase with temperature?
Copper has a positive TCR near room temperature, so electron scattering increases and resistance rises as temperature increases.
What is the temperature coefficient of copper?
This calculator uses the shared nominal copper value 0.00393 /°C, or 3930 ppm/°C.
What is the temperature coefficient of aluminum?
This calculator uses the shared nominal aluminum value 0.00403 /°C, or 4030 ppm/°C.
Does the temperature coefficient depend on alloy?
Yes. TCR varies with material purity, alloy, processing, temperature range, and reference condition.
Is TCR constant at all temperatures?
No. A constant TCR is a first-order approximation over a limited temperature interval.
What does ppm/°C mean?
ppm/°C means parts per million per degree Celsius. One ppm/°C equals 1e-6 /°C.
How do I convert ppm/°C to 1/°C?
Multiply ppm/°C by 1e-6. For example, 3930 ppm/°C equals 0.00393 /°C.
How do I convert percent per °C to 1/°C?
Divide percent per °C by 100. For example, 0.393%/°C equals 0.00393 /°C.
Is 1/°C the same as 1/K?
For temperature differences, yes. A 1 °C interval equals a 1 K interval.
How do Fahrenheit temperature differences affect TCR?
Fahrenheit temperature differences must be converted by 5/9. A coefficient per °F is alpha per °C divided by 1.8.
Does this calculator account for wire self-heating?
No. The calculator requires the wire temperature as an input and does not solve temperature rise from current.
Does this calculator calculate wire temperature from current?
No. Current, I²R heat, ambient temperature, convection, and thermal resistance are outside WIR-011.
Does this calculator calculate ampacity?
No. It does not calculate safe current, maximum current, code compliance, or ampacity.
Does wire geometry change with temperature?
Real geometry changes slightly with thermal expansion, but this first-order model ignores length and area expansion.
Does this calculator account for thermal expansion?
No. It treats resistance change as a resistivity/TCR effect and leaves geometry unchanged.
Can this calculator be used for PT100 or PT1000?
Use the RTD PT100 / PT1000 Calculator for IEC RTD sensor behavior instead of WIR-011.
Can this calculator be used for NTC thermistors?
No. NTC thermistors are nonlinear and should use the NTC Thermistor Calculator.
What is the difference between WIR-011 and a temperature coefficient calculator?
WIR-011 is wire-specific and focuses on conductor resistance. The Thermal temperature coefficient calculator is a generic linear coefficient tool.
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Related Engineering Resources
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