Wire Resistance Calculator by Gauge, Length and Material

Wire Resistance Formula: R = ρL / A

A wire is a resistor. Usually a very small one, which is why schematics draw it as a line with no value — but on a long run, at a high current, or in a measurement circuit, that small resistance is the thing that breaks the design. Its value comes from three numbers and nothing else.

Resistivity, length and area

Current is pushed through the whole cross-section of the conductor, so a thicker wire offers more parallel paths and less resistance, while a longer wire offers more of the same obstruction in series. Both relationships are exactly proportional:

Resistivity is the material’s own contribution, independent of shape. Copper is 1.724 × 10⁻⁸ Ω·m at 20 °C, and every wire table you have ever seen is this one equation evaluated for standard sizes.

From an AWG number to a cross-section

American Wire Gauge is not a diameter, it is a position in a geometric sequence — which is why the numbers run backwards and why the steps feel uneven. The scale is defined so that AWG 36 is exactly 0.005 inch and 4/0 is exactly 0.46 inch, with 39 steps between them:

Two consequences fall straight out of that exponent, and both are worth memorising because they let you check a gauge choice in your head:

• Three gauges thicker doubles the cross-section, and so halves the resistance.
• Ten gauges thicker is very close to ten times the cross-section — and a tenth of the resistance.
• Six gauges thicker doubles the diameter, because area goes with the square.

The area is then the ordinary area of a circle:

Temperature changes the answer more than people expect

Metals conduct worse when hot: the lattice vibrates more and gets in the way of the electrons. The correction is linear over any range wiring sees, referenced to the 20 °C the tables are quoted at:

That is not a rounding detail. A conductor at 70 °C in a hot conduit is 20 % more resistive than the same wire in a room-temperature table, and since the current warming it is the current you are calculating for, a drop worked out from the 20 °C figure is optimistic exactly when it matters.

Material

Resistivity at 20 °C, in units of 10⁻⁸ Ω·m: silver 1.59, copper 1.724, gold 2.44, aluminium 2.826 for the alloy used in building wire. Silver is the best conductor there is and beats copper by only about 8 %, which is why nobody wires a house with it. Aluminium is about 1.64 times as resistive as copper, so it needs roughly 1.6 times the cross-section — two AWG sizes thicker — for the same resistance.

Worked example

About 5.21 mΩ per metre, which agrees with the published figure of 5.211 mΩ/m for AWG 12 copper. A hundred milliohms sounds negligible until a current is put through it: at 10 A this wire drops over a volt and dissipates more than 10 W as heat.

Why Wire Resistance Matters More Than It Looks

Four situations where a few tens of milliohms decides whether something works.

Voltage drop on a long run

The wire is in series with the load, so it takes its share of the supply. At low voltages this is severe: the same absolute drop that is 0.9 % of 230 V is 17 % of 12 V. Long low-voltage runs are where cable sizing stops being a formality.

Heat in the cable

Whatever voltage the wire drops, it dissipates as I² × R inside the insulation, where there is nowhere for it to go. This is why cable has a current rating at all, and why bundling cables together lowers it.

Measurement circuits

Put a current through the same wires you are measuring a voltage with, and the wire’s drop is added to your reading. This is the entire reason four-wire (Kelvin) sensing exists: separate conductors carry the current and sense the voltage, so the current-carrying drop never appears in the measurement.

Ground as a shared resistance

A ground return is a resistor shared between everything that uses it. A high current through it lifts the ground reference of every other circuit connected to the same conductor, which is the mechanism behind most ground-loop noise.

AWG, mm² and the Numbers Worth Knowing

Rules of thumb that follow from the geometry above, and are quicker than a table:

• AWG 10 is about 5.3 mm² and 3.3 mΩ/m — a useful anchor to count from.
• Every 3 gauges: double or halve the area and the resistance.
• Every 6 gauges: double or halve the diameter.
• Every 10 gauges: a factor of about 10 in area and resistance.
• AWG 18 ≈ 1 mm², AWG 12 ≈ 3.3 mm², AWG 6 ≈ 13 mm². Roughly a factor of 3.3 per six sizes.
• A lower gauge number is always a thicker wire. This is the single most common source of confusion with AWG.

AWG against metric cable

Most of the world sells cable by cross-section in mm², which is the more direct description — 2.5 mm² tells you what you are buying without a lookup. AWG sizes do not land on metric values, so a conversion is always approximate: AWG 14 is 2.08 mm² and the nearest metric size is 2.5 mm², which is 20 % more copper.

Stranded, Solid, and What the Table Assumes

The formula treats the conductor as one solid round wire. Real cable often is not, and there are two differences that matter.

Stranded wire has less metal in it

A bundle of strands cannot fill a circle completely — there are gaps between them. A stranded conductor of a given AWG therefore has slightly less copper than the solid figure, typically 2 to 5 % more resistance depending on how finely it is stranded. Treat the calculated value as the optimistic end.

Strands are longer than the cable

Strands are twisted, so each one travels slightly further than the cable’s straight-line length. The effect is small — around 1 to 2 % — and it adds to the packing loss rather than cancelling it.

Stranded wire is used anyway, because it survives flexing and solid wire work-hardens and breaks. The few percent is a fair price. For a critical calculation, take the resistance per metre from the specific cable’s datasheet rather than from a gauge.

When R = ρL / A Stops Being Enough

The formula is DC. At high frequencies the current stops using the whole cross-section: a changing current induces fields that push it towards the surface, so it flows in a thin outer layer whose depth falls as frequency rises.

The practical consequence: at mains frequency skin effect is irrelevant for anything thinner than roughly AWG 4/0, so the DC figure is the right one for ordinary wiring. At radio frequencies the effective resistance is far higher than this calculator gives, the interior of a thick conductor carries almost nothing, and a hollow tube performs nearly as well as a solid rod — which is why RF work uses braid, litz wire and silver plating on the outside.

Common mistakes

• Thinking a higher AWG number means a thicker wire. It is the reverse: AWG 10 is far thicker than AWG 20, and about ten times lower in resistance.
• Using the one-way distance when the current has to come back. For a two-wire circuit the resistance in the path is twice the cable length.
• Taking the 20 °C table figure for a cable that will be hot. Copper gains about 0.4 % per degree, so a loaded cable at 70 °C is 20 % worse than the table says.
• Substituting mm² into R = ρL/A without converting. Resistivity is in ohm-metres, so the area has to be in square metres — 3.309 mm² is 3.309 × 10⁻⁶ m².
• Assuming aluminium can substitute for copper at the same gauge. It needs about 1.6 times the cross-section, roughly two AWG sizes thicker.
• Applying the DC formula at radio frequencies, where skin effect confines the current to the outside of the conductor and the real resistance is much higher.

Frequently asked questions

How do you calculate the resistance of a wire?

Multiply the material’s resistivity by the length and divide by the cross-sectional area: R = ρL/A. For copper ρ is 1.724 × 10⁻⁸ Ω·m at 20 °C. Keep the area in square metres — a 3.31 mm² conductor is 3.31 × 10⁻⁶ m².

What is the resistance of AWG 12 copper wire?

About 5.21 mΩ per metre, or 1.588 mΩ per foot, at 20 °C. A 20 m length is therefore roughly 104 mΩ, and a two-wire circuit 20 m away has twice that in the current path.

Why does a lower AWG number mean thicker wire?

The gauge counts how many drawing operations the wire went through, and each one makes it thinner. So the number is a count of reductions rather than a size, which is why it runs the opposite way to the diameter.

How much thicker is three AWG sizes?

Three sizes doubles the cross-sectional area and halves the resistance. Six sizes doubles the diameter. Ten sizes is about a factor of ten in area. All three follow from the gauge being a geometric scale with a ratio of 92 over 39 steps.

Does wire resistance change with temperature?

Yes, and significantly. Copper rises about 0.393 % per °C, so a conductor at 70 °C is about 20 % more resistive than the 20 °C figure in a wire table. Since the load current is what heats it, a drop calculated cold understates the drop in service.

Is aluminium wire as good as copper?

It is about 1.64 times as resistive, so it needs roughly 1.6 times the cross-section — two AWG sizes thicker — for the same resistance. It is lighter and cheaper per amp, which is why overhead lines and large feeders use it, but it needs terminations rated for it.

How do I convert AWG to mm²?

Work out the diameter from d = 0.005 in × 92^((36−n)/39), convert to millimetres, and take πd²/4. AWG 14 is 2.08 mm², AWG 12 is 3.31 mm², AWG 10 is 5.26 mm². Metric cable is sold in preferred sizes that do not coincide with these, so pick the next one up.