# Wire Resistance Calculator

Created by Luciano Mino
Last updated: Feb 18, 2023

With the wire resistance calculator, you will be able to easily find the resistance and conductance of different wires based on their length, material, and cross-sectional area.

We have paired this calculator with an explanation of different areas related to this topic, such as:

• How to find the resistance of a wire;
• How to calculate the resistance of a copper wire using the wire resistance formula; and
• How to calculate the length of a wire using resistance.

## Wire resistance and resistivity

Resistance and resistivity are two similar properties of an object. However, they are not precisely the same.

Resistivity ρ describes the opposition to the flow of charged particles through an object, and it's an intrinsic property of the material which doesn't depend on the wire's dimensions.

Similarly, resistance σ refers to how strong a wire of specific dimensions (length and area) resists the flow of electrons.

The wire resistance calculator also has a field for conductance, which is the inverse of resistance.

Don't worry. These concepts will become clear once you understand their formulas. Be also sure to check the intrinsic carrier concentration calculator, where you can find the carrier concentration in the semiconductors.

🙋 With this tool, you can calculate the resistance of a copper wire or any other material. Our wire resistance calculator lets you select different wire materials with their corresponding resistivity. Feel free to experiment with it!

## Wire resistance formula and its relation to conductance

The resistance for a straight wire can be calculated with the following equation:

$R = \frac{\rho L}{A}$

where:

• $\rho$ is the material's resistivity, in ohm-meters $Ω \cdot m$;
• $L$ is the wire's length, in meters;
• $A$ is the cross-section area, in square meters $m^{2}$; and
• $R$ is the resistance, in ohms $Ω$.

Another concept, conductivity, is the inverse of resistivity, and its a measure of how easy it is for current to flow through a material:

$\sigma = \frac{1}{\rho}$

Likewise, conductance is the inverse of resistance:

$G = \frac{1}{R} = \frac{A}{\rho L}$

and their units are siemens per meter and siemens, respectively.

## How to calculate the length of a wire using resistance

Assume we have a copper wire with a $40\ \text{mm}^{2}$ cross-section area, a known resistance value, say $0.05\ \Omega$, and we want to find how long it is.

We can obtain the length of this wire by rearranging the equation of the wire resistance formula:

$L = \frac{RA}{\rho}$

The resistivity of Copper at $10\ \text{°C}$ is $1.68\times10^{-8}\ \Omega \cdot \text{m}$. Now, we can simply replace each parameter with our data in the equation above to get:

$L = 119.05\ \text{m}$

🙋 Remember to be consistent with the area and length units. You can try the area converter or the length converter if you have doubts about these conversions.

Or you can input the information in the wire resistance calculator, and our tool will automatically find any missing parameter!

Luciano Mino
Material at 20°C
Annealed copper
Length
ft
Area
in²
Resistance
Conductance
kS
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