Volume Resistivity (ρᵥ) – Definition & Calculation

What is Volume Resistivity? 
Volume resistivity represents the electrical resistance of a uniform material considering its geometry — both its length and cross-sectional area. It's a material property that quantifies how strongly a material opposes the flow of electric current.

Formula:
ρᵥ = (A / L) × R

Where: 
ρᵥ = volume resistivity 
A = cross-sectional area (cmil or mm²) 
L = length of the sample (ft or m) 
R = measured resistance (Ω)

Units:
- In imperial units: Ω·cmil/ft 
- In metric units: Ω·mm²/m

These units normalize resistance to a standard size and are often used to compare material performance independently of geometry.

Typical Values:
- Copper: ~10.37 Ω·cmil/ft or ~0.017241 Ω·mm²/m 
- Aluminum: ~16.78 Ω·cmil/ft or ~0.028264 Ω·mm²/m 

These values are at 20°C and serve as industry reference standards.

Example Calculation (Metric):
You measure a copper wire: 
- Cross-sectional area = 2.5 mm² 
- Length = 1 m 
- Measured resistance = 0.0069 Ω

ρᵥ = (2.5 / 1) × 0.0069 = 0.01725 Ω·mm²/m

Interpretation: 
This matches copper's typical resistivity, confirming that the material and measurement are within expected tolerance.

When to Use Volume Resistivity:
- Material comparison in R&D 
- Quality control in conductor production 
- Electrical modeling (e.g., FEA simulations) 
- Verifying supplier material specs

Note: 
Always ensure unit consistency when calculating. If you use cmil and feet, your result will be in Ω·cmil/ft. If you use mm² and meters, it will be in Ω·mm²/m.