0.00393
1/°C
55
°C
1.21615
x
1.21615
Ω
0.21615
Ω
21.62
%
0.00393
1/°C
55
°C
1.21615
x
1.21615
Ω
0.21615
Ω
21.62
%
The Conductor Resistance at Temperature Calculator determines how the electrical resistance of a conductor changes as its temperature varies. This is one of the most practically important calculations in electrical engineering, because virtually every conductor — from the copper windings inside a motor to the aluminum transmission lines spanning kilometres of countryside — changes its resistance as it heats or cools. Understanding and predicting this change is essential for cable sizing, motor protection, fault analysis, metering accuracy, and energy efficiency studies.
The fundamental relationship between resistance and temperature is expressed by the linear approximation: R₂ = R₁ × (1 + α × (T₂ − T₁)). Here, R₁ is the known resistance at a reference temperature T₁, R₂ is the resistance at the new operating temperature T₂, and α (alpha) is the material's temperature coefficient of resistance. This coefficient quantifies how much resistance changes per degree Celsius per unit of original resistance.
Copper, the most widely used conductor in electrical installations, has a temperature coefficient of approximately 0.00393 /°C at 20 °C. This means that for every 1 °C rise in temperature, copper's resistance increases by roughly 0.393%. Aluminium has a slightly higher coefficient near 0.00403 /°C. In contrast, resistance alloys like Nichrome (used in heating elements) have coefficients close to 0.0004 /°C, making them far more stable with temperature. Some materials, such as thermistors, have strongly nonlinear or even negative coefficients, but for metallic conductors the linear model is accurate across the practical range of −60 °C to +200 °C.
Why does this matter in practice? Consider a copper cable installed at 20 °C with a measured resistance of 0.5 Ω. Under full load, the conductor may reach 90 °C. Using the formula: R₂ = 0.5 × (1 + 0.00393 × 70) = 0.5 × 1.2751 = 0.638 Ω — a 27.5% increase. This higher resistance means more voltage drop along the cable, greater I²R heating losses, and potentially different protection relay settings.
In motor winding analysis, engineers use the resistance-temperature relationship to estimate winding temperature without embedded sensors. By measuring cold resistance (at known ambient temperature) and hot resistance after a run, the formula can be rearranged to solve for T₂ directly — a technique standardised in IEC 60034 and IEEE 112 motor testing standards.
Power utilities rely on this calculation for transmission line ampacity corrections. Standard resistance tables (such as those in IEEE 738) list conductor resistance at 25 °C; actual operating resistance at 50–75 °C must be derived using the temperature coefficient. This corrected resistance feeds into sag-and-tension models and real-time line rating systems.
Battery and fuel cell engineers apply the same principle to internal resistance monitoring. As lithium-ion cells age and temperature changes, their internal resistance rises — captured by similar linear models, though with additional electrochemical factors. For copper bus bars in switchgear and substations, knowing resistance at rated current and temperature allows precise calculation of I²R losses and thermal budget allocation within the enclosure.
This calculator accepts the reference resistance, reference temperature, target temperature, and the material's temperature coefficient. It returns the resistance at the new temperature, the absolute change in resistance, and the percentage change — giving a complete picture for engineering documentation and verification.
The calculation follows the standard linear temperature-resistance model used in IEC and IEEE standards:
The temperature coefficient α is a material property measured at the reference temperature T₁. Common values: Copper ≈ 0.00393/°C, Aluminium ≈ 0.00403/°C, Silver ≈ 0.0038/°C, Gold ≈ 0.0034/°C, Tungsten ≈ 0.0045/°C, Iron ≈ 0.005/°C, Nichrome ≈ 0.0004/°C.
The model is valid for metallic conductors over the range typically encountered in electrical installations. For very wide temperature ranges or semiconductor materials, higher-order polynomial models may be needed.
A result greater than R₁ indicates the conductor is hotter than the reference — higher resistance means more voltage drop and more heat generation under load. A result less than R₁ means the conductor is cooler. Large percentage changes (>20%) signal that temperature effects must not be ignored in circuit design. For derating or protection relay coordination, always use the resistance at the maximum expected operating temperature.
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A 0.5 Ω copper cable at 20 °C increases to 0.638 Ω at 90 °C — a 27.5% rise. This must be accounted for in voltage drop calculations.
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Results
An aluminium overhead conductor at 25 °C reference resistance 0.12 Ω rises to 0.144 Ω at 75 °C — a 20.15% increase, important for line loss calculations.
The temperature coefficient of resistance (α) is a material constant that describes how much resistance changes per degree Celsius per ohm of original resistance. A value of 0.00393/°C for copper means resistance increases by 0.393% for each 1 °C rise from the reference temperature.
Most conductor resistance data and standards (IEC, IEEE) use 20 °C as the reference temperature. Some older references use 25 °C. Always check which reference temperature corresponds to the resistance value you are starting with.
The linear formula is accurate for pure metals and most metallic alloys over practical temperature ranges (−60 °C to +200 °C). It does not apply to semiconductors, thermistors, or superconductors, which have nonlinear or negative resistance-temperature relationships.
By measuring resistance cold (at known ambient T₁) and hot (after running), the formula is rearranged to T₂ = T₁ + (R₂/R₁ − 1)/α. This is the standard resistance method for measuring motor winding temperature rise per IEEE 112 and IEC 60034-1.
In metallic conductors, charge carriers (electrons) collide with thermally vibrating lattice atoms. At higher temperatures, atoms vibrate more vigorously, increasing the frequency of collisions and impeding electron flow — hence higher resistance.
Using an incorrect temperature coefficient introduces proportional error in the result. For precise work — especially in metering, protection relay settings, or winding temperature measurement — use the manufacturer's specific α value rather than a generic material constant.
The linear model begins to deviate above approximately 200 °C for copper and aluminium. At very high temperatures near the melting point, resistance increases more steeply than the linear model predicts. For temperatures above 200 °C, use higher-order polynomial models or empirical data.
Higher resistance at elevated temperature means greater I²R heat generation for the same current. Cable ampacity tables already account for this by using resistance values at the maximum conductor temperature (e.g., 90 °C for XLPE insulation). When verifying losses at partial load, use the resistance at the actual expected temperature.
Roboculator Team
The Roboculator Team explains calculations, planning tools, and practical formulas in clear language for real-life situations.
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