Calculating the Resistance of Copper Wire: AWG, Temperature, and Voltage Drop

The resistance of copper is the inherent opposition the metal presents to the flow of electrical current, measured in ohms per unit length, which dictates how much voltage is lost and heat is generated in a circuit. When you size a wire for a 240V dryer or a 5V Arduino data line, this single property determines whether your load gets the voltage it needs or if the wire melts inside the wall. While copper is the standard for electrical conductivity, it is not a perfect conductor, and ignoring its resistance leads to undersized feeders, tripped breakers, and damaged electronics.

The Physics and the Numbers: Resistivity vs. Resistance

To understand wire sizing, you must separate resistivity (a material property) from resistance (a physical object's property). Resistivity ($\rho$) is a constant for a given material at a specific temperature. For annealed copper at 20°C, the resistivity is $1.724 \times 10^{-8} \, \Omega\cdot\text{m}$. In the US wire sizing system, we use the circular mil-foot measurement, where the resistivity constant ($K$) for copper is:

Resistance ($R$), on the other hand, changes based on the physical dimensions of the wire you cut from the spool. The formula is:

$R = \frac{K \times L}{A}$

Where $L$ is the length in feet and $A$ is the cross-sectional area in circular mils (cmil). Think of electrons moving through a copper lattice like commuters walking down a crowded hallway; as the hallway gets hotter (temperature rises), the commuters bounce off the walls more erratically, slowing the overall flow and increasing resistance. This is why a wire's resistance is never a static number on a jobsite—it scales with ambient temperature and the heat generated by the current itself.

Worked Example: 12 AWG Copper on a 50-Foot Run

Let's calculate the exact resistance and voltage drop for a standard branch circuit: a 12 AWG solid copper THHN wire running 50 feet from a 20A breaker to a 120V receptacle powering a 15A load.

1. Identify the Area: According to NEC Chapter 9, Table 8, 12 AWG wire has a cross-sectional area of 6,530 cmil.
2. Calculate Total Length: A 50-foot run requires 50 feet of hot wire and 50 feet of neutral wire, making the total electrical length ($L$) 100 feet.
3. Calculate Resistance at 20°C: $R = \frac{10.37 \times 100}{6530} = 0.1588 \, \Omega$
4. Calculate Voltage Drop: Using Ohm's Law ($V = I \times R$), the drop at 15A is: $V_{drop} = 15A \times 0.1588 \, \Omega = 2.38V$
5. Calculate Percentage Drop: $\frac{2.38V}{120V} \times 100 = 1.98\%$

Quick Reference: Copper Resistance by AWG (at 20°C)

Source: Adapted from standard Southwire / NEC Table 8 DC resistance values.

Where You Meet This In Practice

You will rarely measure copper resistance with a multimeter on a finished wall circuit—the values are too low for standard handheld meters to read accurately without a 4-wire Kelvin connection. Instead, you encounter the effects of copper resistance in three specific scenarios:

• Long Feeder Runs: When wiring a 200-foot underground feeder to a barn subpanel, the resistance of the copper causes significant $I^2R$ heating and voltage drop. This is why utility companies use high voltages for transmission; pushing the same wattage at a higher voltage requires less current, minimizing the penalty of the wire's resistance.
• Low-Voltage DC Systems: In a 12V LiFePO4 solar battery bank, a 30A load pulling through just 0.05 ohms of undersized copper wiring wastes 45 watts of power as heat ($30^2 \times 0.05 = 45W$). This is why 12V and 24V DC systems demand massive, short copper cables (like 2/0 AWG) compared to 120V AC systems.
• Current Shunt Measurement: If you are building an Arduino-based ammeter using a shunt resistor, you must avoid using bare copper wire as the shunt. Copper's resistance changes drastically with temperature, meaning your calibration will drift as the wire heats up. Use manganin or constantan instead.

Common Confusions: Resistance vs. Ampacity vs. Impedance

The most frequent mistake DIYers make is conflating the resistance of copper with its ampacity or impedance. These are distinct concepts that dictate different safety limits.

Resistance (Ohms) vs. Ampacity (Amps): Resistance is an electrical property dictating voltage drop. Ampacity is a thermal limit dictated by the wire's insulation, not the copper itself. A 12 AWG copper wire has the exact same electrical resistance whether it is insulated with 60°C TW or 90°C THHN. However, the 90°C THHN insulation can safely dissipate more heat, giving it a higher ampacity rating in the NEC 310.16 tables. The copper doesn't change; the jacket does.

DC Resistance vs. AC Impedance: The values in the table above are for Direct Current (DC). In Alternating Current (AC) circuits, the skin effect forces current to travel primarily along the outer edge of the copper wire. This effectively reduces the cross-sectional area being used, increasing the effective resistance (now called AC impedance) slightly above the DC baseline. For standard 60Hz residential wiring under 1/0 AWG, this difference is negligible, but it becomes a major factor in high-frequency RF engineering or massive 500 kcmil industrial feeders.