# Wire Resistance Calculator

Created by Dominik Czernia, PhD
Reviewed by Bogna Szyk and Jack Bowater
Last updated: Jun 05, 2023

This wire resistance calculator can quickly compute the electrical properties of a specific wire - its resistance and conductance. Resistance describes how strongly a given cable opposes the flow of an electric current, and conductance measures a wire's ability to conduct it. Two physical quantities are also associated with them - electrical resistivity and electrical conductivity. After reading the text below, you will, for example, learn how to estimate a wire's resistance using the resistance formula (so-called Pouillet's Law).

Nowadays, one of the most frequently used conductors is copper, which can be found almost in every electrical device. Read on if you want to find out the conductivity and resistivity of copper and what resistivity and conductivity units to use. You may also want to calculate the voltage drop on a specific wire - in this case, give our voltage drop calculator a try!

## Resistivity units and conductivity units

Resistivity ρ, unlike resistance, is an intrinsic property of a material. It means that it doesn't matter whether the wire is thick or thin, long or short. The resistivity will always be the same for a specific material, and the resistivity units are "ohm meter" (Ω × m). The higher the resistivity is, the more difficult it is for the current to flow through a wire. You can check our drift velocity calculator to find out how fast electricity is.

On the other hand, we have conductivity σ, which is strictly related to resistivity. Specifically, it is defined as its inverse: σ = 1 /ρ. As well as resistivity, it is an intrinsic property of the material, but the conductivity units are "siemens per meter" (S / m). Electrical current can smoothly flow through a wire if conductivity is high.

In some materials, at very low temperatures, we can observe a phenomenon called superconductivity. Resistivity in a superconductor drops sharply to zero, and thus the conductivity approaches infinity. We can say that it is a perfect conductor.

## Conductance formula and resistance formula

Both conductance and resistance depend on the geometrical dimensions of a wire. Our wire resistance calculator uses the following resistance formula:

R = ρ × L / A

where

• R is the resistance in Ω;
• ρ is the resistivity of material in Ω × m;
• L is the length of the wire; and
• A is the cross-sectional area of the wire.

You can use this wire resistance calculator to estimate conductance too, since:

G = σ × A / L

where

• G is the conductance in siemens (S);
• σ is the conductivity in S / m; and
• L and A keep the same meaning.

In the advanced mode, you can directly change values of resistivity ρ and conductivity σ. Combining the above two equations with the ρ = 1 / σ relation, we obtain a similar connection between resistance and conductance:

R = 1 / G

Have you already computed the resistance of your wire? Try our series resistor calculator and parallel resistor calculator to learn how you can calculate the equivalent resistance of various electrical circuits. You can also check out our wheatstone bridge calculator to learn how to measure unknown resistances.

## Conductivity of copper and resistivity of copper

Materials such as copper and aluminum have low levels of resistivity, making these materials ideal for the production of electrical wires and cables. You should remember that resistivity (and, therefore conductivity) is affected by temperature. In our wire resistance calculator, we have , which you can select to find their resistivity and conductivity at 20°C. For example, the electrical conductivity of copper is σ ≈ 5.95 × 10^7 S / m, and the electrical resistivity of copper is ρ ≈ 1.68 × 10^(-8) Ω × m.

## FAQ

### How do I calculate the resistance of a wire?

To calculate the resistance of a wire:

1. Find out the resistivity of the material the wire is made of at the desired temperature.

2. Determine the wire's length and cross-sectional area.

3. Divide the length of the wire by its cross-sectional area.

4. Multiply the result from Step 3 by the resistivity of the material.

### How does the wire length affect resistance?

The resistance of a wire is directly proportional to its length. Hence the longer the wire, the higher its resistance since the electrons have to travel a longer distance through the wire and suffer more collisions.

### How does the area of a wire affect resistance?

The resistance of a wire is inversely proportional to its cross-sectional area. Therefore, if we decrease the cross-sectional area of the wire, its resistance will increase.

### What are four factors affecting resistance in a wire?

The factors that affect the resistance of a wire are:

• The length of the wire;
• The cross-sectional area of the wire;
• The material the wire is made of; and
• The temperature of the material.
Dominik Czernia, PhD
Material at 20 °C
Annealed copper
Length
ft
Diameter
in
Cross-sectional area
in²
Resistance
Conductance
kS
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