Wire Resistivity Calculator and Formula

This page provides a wire resistivity calculator and explains the formula behind it. The calculator uses wire resistance, length, and cross-sectional area to determine the resistivity of the wire material.

Understanding Resistance

The electrical resistance of a conductor isn’t fixed; it depends on several factors:

• Length of the conductor: Longer wires offer more resistance.
• Cross-sectional area: Thicker wires offer less resistance than thin ones.
• Type of conductor material: Different materials have different inherent resistances.
• Temperature of the material: Resistance often changes with temperature.

The relationship between these factors is expressed in the following formula:

Resistance (R) = ρ * l / a

Where:

• R = Resistance, measured in Ohms (Ω)
• ρ (rho) = Resistivity of the material, measured in Ohm-meters (Ω⋅m)
• l = Length of the wire, measured in meters (m)
• a = Cross-sectional area of the wire, measured in square meters (m²)

Key Points About Resistivity

• Resistivity is a measure of a material’s ability to resist the flow of electric current.
• It’s a material property, meaning it doesn’t change based on the wire’s shape or size.
• Resistivity changes with temperature.
• Good electrical conductors (like copper) have very low resistivity values.
• Good insulators (like glass) have extremely high resistivity values.

Here are some common materials and their approximate resistivity values:

• Copper: 1.7 x 10⁻⁸ Ω⋅m
• Aluminum: 2.6 x 10⁻⁸ Ω⋅m
• Carbon: 10 x 10⁻⁸ Ω⋅m
• Glass: 1 x 10⁸ Ω⋅m
• Mica: 1 x 10¹³ Ω⋅m

Wire Resistivity Calculator

The following calculator helps you determine the resistivity of a wire using its resistance, length, and cross-sectional area.

Inputs:

• Resistance (Ω): (Enter the resistance of the wire)
• Length (meters): (Enter the length of the wire)
• Cross-sectional area (mm²): (Enter the cross-sectional area of the wire. Note this is in square millimeters, the calculator will convert it to meters)

Output:

• Resistivity (ρ) : (The calculated resistivity of the wire material, in Ω⋅m)

Example

Inputs:

• Wire resistance = 0.25 Ω
• Wire length = 40 meters
• Area = 3.2 mm²

Outputs:

• Resistivity = 2 x 10⁻⁸ Ω⋅m

Resistivity Formula

The calculator uses the following formula to determine the resistivity (ρ) from the other inputs.