The resistivity of copper is an intrinsic material property that quantifies how strongly it opposes the flow of electric current, typically measured at 1.724 × 10-8 Ω·m at 20°C for standard annealed wire.
Makers and electricians frequently confuse resistivity (ρ) with resistance (R). Think of the water-in-a-pipe analogy: resistivity is the inherent friction of the pipe's interior material, while resistance is the total friction experienced by water flowing through a specific length and diameter of that pipe. Resistivity is a constant for the material itself; resistance changes based on the geometry of your specific wire or PCB trace. Knowing the exact resistivity of copper value allows you to calculate that resistance before you ever cut a wire or route a trace.
The Exact Numbers: Copper Resistivity vs. Temperature
The resistivity of copper value is not a single static number; it scales linearly with temperature. As copper heats up, its atomic lattice vibrates more intensely, scattering electrons and increasing resistivity. According to data from the HyperPhysics database, the temperature coefficient of resistivity (α) for copper is approximately 0.00393 per °C at 20°C.
When sizing wire for a panel or calculating PCB trace widths, using the 20°C baseline will result in undersized conductors because real-world operating temperatures are much higher. Here is how the resistivity of copper value shifts across common electrical temperature ratings:
| Temperature (°C) | Resistivity (Ω·m) | Resistivity (nΩ·m) | Typical Application Context |
|---|---|---|---|
| 20°C (68°F) | 1.724 × 10-8 | 17.24 | Lab measurements, baseline datasheet specs |
| 50°C (122°F) | 1.927 × 10-8 | 19.27 | Warm PCB traces, lightly loaded branch circuits |
| 75°C (167°F) | 2.171 × 10-8 | 21.71 | Standard THHN wire at breaker terminal limits |
| 90°C (194°F) | 2.335 × 10-8 | 23.35 | Max rated temp for XHHW-2 / THHN-2 insulation |
Note: The values above assume pure, annealed copper. Hard-drawn building wire (like standard THHN) has a slightly higher baseline resistivity (around 1.77 × 10-8 Ω·m at 20°C) due to mechanical stress introduced during the drawing process, as noted by the NIST Physical Measurement Laboratory.
Worked Example: Calculating Voltage Drop in a 50-Meter Run
Let’s look at what the resistivity of copper value actually changes in a real installation. Suppose you are wiring a 120V, 15A dedicated circuit for a workshop tool using 12 AWG solid copper wire. The one-way distance from the panel to the outlet is 50 meters.
Step 1: Identify the geometry.
12 AWG wire has a cross-sectional area (A) of 3.31 mm², which is 3.31 × 10-6 m². The length (L) is 50 m.
Step 2: Calculate baseline resistance at 20°C.
Using the formula R = ρ × (L / A):
R20 = (1.724 × 10-8 Ω·m × 50 m) / (3.31 × 10-6 m²)
R20 = 0.260 Ω (one-way)
Step 3: Calculate operating resistance at 75°C.
Under a continuous 15A load, the wire inside the conduit will heat up. Let’s assume the copper reaches 75°C. We apply the temperature coefficient formula: RT = R20 × [1 + α(T - 20)]
R75 = 0.260 Ω × [1 + 0.00393 × (75 - 20)]
R75 = 0.260 Ω × [1 + 0.216]
R75 = 0.316 Ω (one-way)
Step 4: Determine the real-world voltage drop.
Voltage drop (Vdrop) = Current × Total Resistance (out and back).
Total Resistance at 75°C = 0.316 Ω × 2 = 0.632 Ω.
Vdrop = 15A × 0.632 Ω = 9.48 Volts.
Where You Meet This In Practice
Understanding the resistivity of copper value moves you from guessing to engineering. Here is where this specific material property dictates your hardware choices:
- PCB Trace Width Sizing: When designing custom PCBs in KiCad or Altium, the IPC-2221 standard relies directly on copper resistivity to determine how wide a trace must be to carry a specific current without melting. A 1 oz/ft² copper layer is roughly 35 µm thick; knowing ρ allows the software to calculate the exact milliohms per square and predict temperature rise.
- Solar DC Array Wiring: In low-voltage DC systems (like a 24V or 48V solar battery bank), current is exceptionally high. Because V = IR, even a tiny increase in resistance due to the baseline resistivity of copper can result in massive percentage voltage drops. This is why 2/0 AWG or 4/0 AWG copper is mandatory for battery interconnects, despite the high cost.
- Copper vs. Aluminum Service Entrances: When pricing a 200A residential service upgrade, you will notice aluminum SER cable is significantly cheaper than copper. Aluminum has a resistivity of roughly 2.82 × 10-8 Ω·m—about 60% higher than copper. To carry the same 200A current with the same voltage drop, you must use a much thicker aluminum conductor (e.g., 4/0 AWG Aluminum vs. 2/0 AWG Copper).
Frequently Asked Questions
What is the exact resistivity of copper value at 20°C?
For 100% International Annealed Copper Standard (IACS) pure copper, the exact value is 1.7241 × 10-8 Ω·m (or 17.241 nΩ·m) at 20°C. However, if you are working with standard hard-drawn building wire like THHN, the mechanical drawing process introduces lattice defects that raise the practical resistivity to approximately 1.77 × 10-8 Ω·m.
How does the resistivity of copper value change when the wire gets hot?
Copper has a positive temperature coefficient of roughly 0.00393 per °C. This means for every 1°C increase in temperature above 20°C, the resistivity increases by about 0.393%. By the time a wire inside a hot attic or a loaded conduit reaches 75°C, its resistivity has increased by over 21% compared to its room-temperature baseline.
Why do we use the resistivity of copper value instead of just measuring resistance?
You can only measure resistance on a physical object that already exists. Resistivity allows engineers and electricians to predict the resistance of a wire, busbar, or PCB trace during the design phase, before the material is manufactured or cut. It decouples the material's inherent properties from the physical dimensions of the component.
Is the resistivity of copper value different for stranded vs. solid wire?
The intrinsic resistivity (ρ) of the copper material is identical whether it is solid or stranded. However, a stranded wire will have a slightly higher overall resistance than a solid wire of the same nominal AWG. This is because the individual strands are twisted in a helix, making the actual path the electrons travel slightly longer than the linear length of the cable, and because the air gaps between strands reduce the effective cross-sectional area of copper.
