Electrical resistivity is an intrinsic material property that quantifies how strongly a given substance opposes the flow of electric current, measured in ohm-meters (Ω·m) in the SI system or ohm-circular mils per foot (Ω·cmil/ft) in US wire sizing.
Before we go further, let's clear up the most common point of confusion: people constantly mix up resistivity with resistance. Resistivity is a property of the material itself (like the density of copper), while resistance is a property of a specific object made from that material (like the weight of a specific 50-foot spool of 12 AWG copper wire). What resistivity changes in a real circuit is your voltage drop, your heat generation, and ultimately, the minimum wire gauge you are legally and safely allowed to pull through a conduit.
The Core Concept: Resistivity vs. Resistance
To understand the units, you have to understand the formula that links resistivity ($\rho$) to measurable resistance ($R$):
R = ρ × (L / A)
- R = Resistance in Ohms (Ω)
- ρ = Resistivity of the material
- L = Length of the conductor
- A = Cross-sectional area of the conductor
Think of it like fluid dynamics. Resistivity is akin to the inherent viscosity of a fluid—honey has high resistivity to flow, while water has low resistivity. Resistance, on the other hand, is how hard it is to push that specific fluid through a pipe of a certain length and diameter. Even if you use water (low resistivity), pushing it through a 100-foot capillary tube (high length, tiny area) results in high resistance.
In the SI system, the unit of resistivity is the ohm-meter (Ω·m). This is derived by rearranging the formula above: if Resistance is in ohms, Area is in square meters, and Length is in meters, then $\rho = (R \times A) / L$, yielding $(\Omega \times m^2) / m$, which simplifies to $\Omega\cdot m$.
However, if you are pulling THHN through EMT conduit in the US, you will rarely use ohm-meters. Instead, the US electrical industry relies on ohm-circular mils per foot (Ω·cmil/ft). This unit perfectly aligns with the American Wire Gauge (AWG) system, where wire area is measured in circular mils rather than square millimeters.
Worked Example: Calculating Voltage Drop Using Resistivity
Let's look at a real-world scenario where ignoring resistivity units leads to a failed installation. Suppose you are wiring a 120V branch circuit for a 20A compressor in a detached garage. The one-way distance from the subpanel to the outlet is 150 feet. You decide to use standard 10 AWG copper wire.
Here is the step-by-step calculation using US customary resistivity units:
- Identify the variables:
- Current ($I$) = 20 Amps
- Length ($L$) = 150 feet (one-way)
- Wire Area ($A$) = 10,380 circular mils (standard for 10 AWG)
- Resistivity ($\rho$) = 12.9 Ω·cmil/ft (This is the accepted value for uncoated copper at 75°C, which is the standard operating temperature column for THHN in a termination rated for 75°C).
- Calculate one-way resistance:
$R = 12.9 \times (150 / 10,380) = 0.186 \Omega$ - Calculate total loop resistance:
Because current must travel to the load and return, we double the one-way resistance.
$R_{total} = 0.186 \times 2 = 0.372 \Omega$ - Calculate Voltage Drop:
$V_{drop} = I \times R_{total} = 20A \times 0.372 \Omega = 7.44V$
Where You Meet This in Practice
You might think resistivity is just a textbook concept, but it dictates physical choices on the bench and the jobsite every day.
- Wire Sizing and Ampacity: The reason aluminum wire (resistivity ~17.0 Ω·cmil/ft) must be sized larger than copper wire (~10.4 Ω·cmil/ft at 20°C) for the same breaker size is purely due to resistivity. Aluminum has roughly 61% of the conductivity of copper, meaning higher resistivity and more heat generated at the same gauge.
- PCB Trace Routing: When designing a custom PCB for an ESP32 or high-current motor driver, you are calculating the resistivity of 1 oz copper foil (about 35 µm thick). If a trace is too narrow, its high resistance will act as a bottleneck, causing a brownout on your microcontroller's 3.3V rail.
- Grounding Electrode Systems: When installing a ground rod, you are battling soil resistivity, measured in Ω·m. Dry, rocky soil can have a resistivity of 10,000 Ω·m, rendering a standard 8-foot copper-clad rod useless. This is why NEC Article 250 sometimes requires driving two rods or using a concrete-encased electrode (Ufer ground) to achieve the required <25 ohms to ground.
- Heating Elements: We intentionally select materials with high resistivity for toasters and soldering irons. Nichrome (an alloy of nickel and chromium) has a resistivity of about 1.10 × 10⁻⁶ Ω·m—roughly 65 times higher than copper. This high resistivity forces the material to convert electrical energy into heat rather than passing it along.
Reference Table: Resistivity of Common Electrical Materials
Below is a reference chart comparing standard conductors and resistive alloys. Note that the SI values are measured at 20°C. For precise voltage drop calculations on loaded wires, always apply a temperature correction factor.
| Material | SI Resistivity (Ω·m × 10⁻⁸ at 20°C) | US Resistivity (Ω·cmil/ft at 20°C) | Primary Application |
|---|---|---|---|
| Silver | 1.59 | 9.54 | High-end audio contacts, specialized RF shielding |
| Copper (Annealed) | 1.68 | 10.09 | Standard branch wiring (THHN, NM-B), busbars |
| Gold | 2.44 | 14.64 | Corrosion-resistant edge connectors, low-voltage signal pins |
| Aluminum (1350 Alloy) | 2.82 | 16.92 | Service entrance feeders, utility transmission lines |
| Tungsten | 5.60 | 33.60 | Incandescent filaments, TIG welding electrodes |
| Nichrome (80/20) | 110.0 | 660.0 | Toaster elements, industrial furnace coils, vape wire |
Source data derived from standard material properties documented by Georgia State University HyperPhysics and Electronics Tutorials.
Frequently Asked Questions
What are the standard SI units of electrical resistivity?
The standard SI unit is the ohm-meter (Ω·m). Dimensionally, this can be broken down. Since Resistance ($R$) is measured in ohms ($\Omega$), Area ($A$) in square meters ($m^2$), and Length ($L$) in meters ($m$), the formula $\rho = (R \times A) / L$ results in $(\Omega \times m^2) / m$. The meters cancel out partially, leaving $\Omega\cdot m$. In semiconductor physics, you will often see this scaled down to ohm-centimeters (Ω·cm) because silicon wafers are measured in much smaller dimensions.
How do you convert units of electrical resistivity to conductivity?
Conductivity ($\sigma$) is simply the mathematical reciprocal of resistivity ($\rho$). The formula is $\sigma = 1 / \rho$. Therefore, if resistivity is measured in ohm-meters (Ω·m), conductivity is measured in Siemens per meter (S/m). Historically, the unit of conductivity was the "mho per meter" (mho being ohm spelled backward, with an upside-down omega symbol $\mho$), but the Siemens (S) is the modern accepted SI unit. A copper wire with a low resistivity yields a very high conductivity value.
Why do wire tables use circular mil-ohms per foot instead of standard SI units?
The use of Ω·cmil/ft is a legacy of the American Wire Gauge (AWG) system, which was standardized in 1857. A "circular mil" is the area of a circle with a diameter of one mil (0.001 inches). The beauty of the circular mil is that it allows you to calculate the cross-sectional area of a wire simply by squaring its diameter in mils ($Area = d^2$), entirely eliminating the need to use $\pi$ in your calculations. Because US electricians and engineers use AWG and feet, using Ω·cmil/ft allows for rapid, mental-math-friendly voltage drop calculations on the jobsite without converting to square millimeters and meters first.
Does temperature change the units of electrical resistivity for copper wire?
Temperature does not change the units (they remain Ω·m or Ω·cmil/ft), but it drastically changes the numeric value. Copper has a positive temperature coefficient of roughly 0.0039 per degree Celsius. This means for every 1°C increase in temperature, copper's resistivity increases by about 0.39%. This is why a wire that has a safe voltage drop at 20°C in an empty conduit might exceed safe limits at 75°C when fully loaded and bundled with other current-carrying conductors. Always use the resistivity value that matches your expected operating temperature, not just the baseline 20°C laboratory value.
