Wire Resistance Calculator

The Wire Resistance Calculator works out the electrical resistance of a conductor from its length, gauge (AWG, area or diameter), material and operating temperature. It applies the temperature coefficient to the resistivity, handles round-trip runs and parallel conductors, and — unlike most resistance calculators — also gives you the AC resistance with skin effect, the resulting voltage drop and I²R power loss, and a side-by-side comparison with the neighbouring wire gauges.

Wire Resistance Formula

The resistance of any uniform conductor comes from three things: how resistive the material is, how long the current path is, and how much cross-section the current has to flow through.

Here \( \rho_{20} \) is the resistivity at 20 °C in Ω·m, \( \alpha \) is the temperature coefficient of resistance per °C, \( T \) is the operating temperature in °C, \( L \) is the total conductor length in metres (double the run length for an out-and-back circuit), \( A \) is the cross-sectional area in m², and \( n \) is the number of conductors in parallel.

Resistivity and Temperature Coefficient of Common Conductors

All values are at 20 °C. Resistivity is given both in Ω·m and in the practical unit Ω·mm²/m, which is simply the resistance of a 1 metre length with a 1 mm² cross-section.

AWG Wire Size Chart — Copper Resistance per 1000 ft and per km

American Wire Gauge is a geometric series: the diameter of gauge n is \( d = 0.127 \times 92^{(36-n)/39} \) mm. Every 3 gauges the area halves and the resistance doubles; every 6 gauges the diameter halves. Resistance figures below are for solid annealed copper at 20 °C.

How Temperature Changes Wire Resistance

In a metal, heat makes the lattice vibrate more, electrons scatter more often, and resistance goes up. The relationship is close to linear over normal working temperatures, which is what the coefficient α captures. Copper's α of 0.00393 per °C means +0.39% resistance for every degree above 20 °C:

Alloys behave very differently. Constantan and manganin were designed to have an almost zero temperature coefficient, which is exactly why they are used for precision shunts and strain gauges — their resistance barely moves as they warm up.

Skin Effect: Why AC Resistance Is Higher

With alternating current, the changing magnetic field inside the conductor induces eddy currents that cancel the flow in the centre and reinforce it at the surface. The current ends up concentrated in a surface layer about one skin depth thick:

where \( f \) is the frequency in Hz, \( \mu_0 = 4\pi \times 10^{-7} \) H/m and \( \mu_r \) is the relative permeability of the conductor. This calculator then solves the exact Bessel-function expression for the AC-to-DC resistance ratio of a solid round wire (switching to the classic asymptotic form at very high frequency), so the figure stays accurate from mains frequency up into the RF range.

Note that ferromagnetic conductors such as steel and nickel have a relative permeability in the hundreds, so their skin depth is roughly \( \sqrt{\mu_r} \) times smaller — a steel wire's AC resistance climbs far faster than copper's.

Voltage Drop and Power Loss

Once you know the resistance of the run, the two numbers an installer actually cares about follow directly from Ohm's law:

The commonly quoted design targets, taken from the informational notes in the National Electrical Code, are 3% maximum drop on a branch circuit and 5% total including the feeder. Remember that the current flows out and back, so for a two-wire circuit you must use the round-trip length — which is why this calculator has a run-type selector rather than leaving you to double the number yourself.

What Affects Wire Resistance?

Worked Example

A 12 AWG copper cable feeds a 15 A load 50 ft away on a 120 V supply. The current runs out and back, so the conductor length is 100 ft (30.48 m). 12 AWG has a diameter of 2.053 mm, giving an area of 3.31 mm². At 20 °C:

\( R = \dfrac{1.724 \times 10^{-8} \times 30.48}{3.31 \times 10^{-6}} \approx 0.159\ \Omega \)

The voltage drop is \( 15 \times 0.159 \approx 2.38 \) V, which is 1.99% of 120 V — comfortably inside the 3% guideline — and the cable dissipates \( 15^{2} \times 0.159 \approx 35.8 \) W as heat. Warm the conductor to 60 °C and the resistance rises to about 0.184 Ω, pushing the drop to 2.30% and the loss to 41 W.

How to Use This Calculator

1. Pick the conductor: Choose the material, then set the size by AWG gauge, by cross-sectional area (mm², kcmil or circular mils) or by diameter.
2. Describe the run: Enter the wire length with its unit, choose one-way or round trip, and set how many conductors run in parallel.
3. Set the temperature: Enter the operating temperature in °C or °F. Leave it at 20 °C for datasheet conditions.
4. Add the load (optional): Enter the current, system voltage and AC frequency to get voltage drop, power loss and skin-effect resistance.
5. Click Calculate Resistance: Read the resistance, the cross-section diagram, the temperature curve, the gauge comparison table and the step-by-step formulas.

Frequently Asked Questions

How do you calculate the resistance of a wire?

Wire resistance is R = ρ × L / A, where ρ is the resistivity of the conductor material in Ω·m, L is the conductor length in metres and A is the cross-sectional area in square metres. For a round wire the area is π × d² / 4. Because resistivity changes with temperature, ρ is first corrected with ρ_T = ρ₂₀ × [1 + α × (T − 20)].

What is the resistance of copper wire per foot?

At 20 °C, annealed copper has a resistivity of 1.724 × 10⁻⁸ Ω·m. That gives about 1.59 Ω per 1000 feet for 12 AWG, 2.53 Ω per 1000 feet for 14 AWG, 4.02 Ω per 1000 feet for 16 AWG and 6.39 Ω per 1000 feet for 18 AWG. Each three-gauge step roughly doubles the resistance.

Does wire resistance increase with temperature?

Yes, for metals. Copper has a temperature coefficient of about 0.00393 per °C, so its resistance rises about 0.39% for every degree above 20 °C. A copper conductor running at 75 °C has roughly 21% more resistance than the same conductor at 20 °C, which is why cable tables are published at a rated temperature.

Should I use one-way or round-trip length?

Use round trip whenever the current has to flow out and back through the same cable, which covers almost all DC, single-phase and low-voltage circuits. The current travels the length of the run twice, so the circuit resistance and the voltage drop are twice the one-way figure. Use one-way only when you want the resistance of a single conductor.

Why is AC resistance higher than DC resistance?

Alternating current pushes itself toward the outside of the conductor, an effect called skin effect. The current is concentrated within roughly one skin depth of the surface, so the effective cross-section shrinks and the resistance rises. At 60 Hz the skin depth in copper is about 8.5 mm, so only large conductors are affected, but at 1 MHz it is about 0.066 mm and even thin wire sees several times its DC resistance.

How much voltage drop is acceptable?

The widely used guideline, based on the informational notes in the National Electrical Code, is a maximum of 3% drop on a branch circuit and 5% total across feeder plus branch circuit. If your run exceeds those figures, use a larger conductor, shorten the run, split the load across parallel conductors or raise the system voltage.

Which wire material has the lowest resistance?

Silver has the lowest resistivity of any metal at 1.59 × 10⁻⁸ Ω·m, followed by copper at 1.724 × 10⁻⁸ and gold at 2.44 × 10⁻⁸. Copper is the practical choice because silver is expensive and gold conducts worse than copper. Aluminium has about 1.6 times the resistivity of copper but is roughly one third the weight, which is why it dominates overhead and large feeder cable.

Additional Resources

• Electrical Resistivity and Conductivity - Wikipedia
• American Wire Gauge - Wikipedia
• Skin Effect - Wikipedia