Wire Gauge Calculator

About Wire Gauge Calculator

AWG: lower number = thicker wire. AWG 12 is common for 20A circuits. Resistance depends on length and cross-section.

How to use this calculator

1. Enter the wire gauge, or the wire diameter if the calculator asks for it.
2. Choose the material, since copper and aluminum have different resistivities.
3. Enter the wire length so the calculator can find total resistance.
4. Read the resistance and current capacity results, then compare them to your project needs.

The formula explained

The formula \(R = \\frac{\\rho L}{A}\) computes wire resistance, where longer wire means more resistance and larger cross-sectional area means less resistance. Here \(\\rho\) is the material resistivity, \(L\) is the wire length, and \(A\) is the cross-sectional area.

• R = wire resistance in ohms, \(\\Omega\)
• \(\\rho\) = resistivity of the wire material
• L = length of the wire
• A = cross-sectional area of the wire

Step by step method

1. Find the wire area from its gauge or diameter.
2. Use the material resistivity for \(\\rho\).
3. Multiply \(\\rho\) by \(L\), then divide by \(A\) to get \(R\).

Worked example

Problem. Find the resistance of a \(10\\,\\text{m}\) copper wire with cross-sectional area \(A = 2.0 \\times 10^{-6}\\,\\text{m}^2\), using \(\\rho = 1.68 \\times 10^{-8}\\,\\Omega\\cdot\\text{m}\).

1. Substitute into the formula, \(R = \\frac{\\rho L}{A} = \\frac{(1.68 \\times 10^{-8})(10)}{2.0 \\times 10^{-6}}\).
2. Compute the numerator, \(1.68 \\times 10^{-7}\), then divide by \(2.0 \\times 10^{-6}\).
3. The resistance is \(R = 0.084\\,\\Omega\).

Tips and common mistakes

• A longer wire always has more resistance, even if the gauge stays the same.
• Do not confuse wire gauge number with wire size, a smaller AWG number means a thicker wire.

Frequently asked questions