How the wire resistance calculator works
The engine behind this is one short equation. The resistance of a uniform conductor is its resistivity times length over area, so the resistance and length of a wire are tied together by the cross-sectional area and the metal it is made from. Enter a gauge, an area or a measured diameter and the conductor resistance falls straight out — and because the relationship is simple algebra, the same tool runs it backward to give the length from a target resistance, or the gauge from a length and a resistance.
R = ρ × L / A · ρCu = 0.017241 Ω·mm²/m · ρAl = 0.0265 Ω·mm²/m (at 20 °C)
Resistivity here is the standard annealed-copper value (about 100% IACS) and the standard aluminium value (about 61% IACS); they are public-domain physical constants, not figures lifted from any proprietary table. The wire resistance formula assumes a solid, round conductor, which is the right basis even for stranded cable as long as you feed it the conductor area rather than a measured outside diameter.
Wire cross-sectional area and circular mils
Resistance is driven by the area of a wire, so the calculator exposes that geometry as a live output. For any gauge it reports the cross-sectional area three ways — in mm² (you may see it written mm2), in kcmil, and in plain circular mils — which doubles as a circular mil calculator without needing a separate tool. The AWG geometry comes from the public gauge formula: in millimetres the diameter is d = 0.127 × 92(36−n)/39, and the area is π(d/2)². One circular mil is the area of a 0.001-inch-diameter circle, about 5.067×10−4 mm², and a kcmil is a thousand of them (0.5067 mm²).
Resistance per foot, per metre and per km
Specs and suppliers quote conductor resistance in whatever unit suits them, so every result is shown as ohms per foot, per metre and per km at once. The relationship is linear in length: the resistance of a 1 km copper wire is simply 1000 times its per-metre value, and a 100 ft run is 100 times the per-foot value. As a sanity check, 12 AWG copper at 20 °C works out to about 1.588 Ω per 1000 ft (5.21 Ω/km), so 100 ft of it is roughly 0.159 Ω.
| Conductor | Area (mm²) | Ω / 1000 ft | Ω / km |
|---|
Resistance of copper vs aluminum wire
Material sets the resistivity, and aluminium has roughly 1.6× the resistance of copper for the same size, which is why an aluminum conductor usually needs to be a size or two larger to match a copper one. Switch the material selector to compare them on the same gauge, or pick tinned copper, or type a custom ρ for an alloy the list doesn't cover. The aluminum (also spelled aluminium) figure uses 0.0265 Ω·mm²/m as its room-temperature reference.
Temperature correction
The fixed 20 °C value most charts give is wrong for anything that runs hot — motor leads, an engine bay, a heating element. Metal resistance rises with temperature by RT = R20 × [1 + α(T − 20 °C)], with α ≈ 0.00393 /°C for copper and 0.00403 /°C for aluminum (standard reference coefficients). Set the temperature box to your real operating temperature and the resistance and every per-length figure update with it. At 75 °C a copper conductor reads about 21% higher than its 20 °C value.
Stranded vs solid: enter area, not measured diameter
This is the trap that throws off the most readings. Resistance depends on the conductor's metal area, but a stranded cable's overall diameter is bigger than the equivalent solid wire because of the air gaps between strands — roughly 14% more outside diameter for the same copper. If you put a caliper across stranded wire and enter that as the diameter, you overstate the area and understate the resistance. Enter the gauge or the rated cross-sectional area instead; that is the number that determines the ohms.
Solving for length or gauge from a resistance
The inverse modes are what set this apart from a one-way calculator. Switch to Find length to get how far a chosen wire can run before it reaches a target resistance — rearranged as L = R×A/ρ. Switch to Find gauge / area to get the smallest conductor that keeps a fixed-length run under a target resistance, returned as an area in mm²/kcmil/circular mils plus the nearest standard AWG and the nearest common metric size. If what you ultimately want is the voltage lost across that resistance, carry the run length over to the voltage drop calculator; for resistance derived from a measured voltage and current instead of geometry, the Ohm's Law Calculator handles V = I×R.
One-way vs round-trip length
A circuit needs a conductor out to the load and another back, so the resistance the current actually sees is over the round-trip length, while a run is usually described one way. Tick the round-trip box if your length already counts both legs, or leave it for a one-way distance — the result note says which it used. Voltage-drop sizing then doubles the one-way run for the same reason, which is handled for you in the dedicated drop tool.