Wire Resistance – R = ρL/A, Voltage Drop and Gauge Sizing
No conductor is perfect. Push current down a length of wire and some of your supply voltage is spent getting there rather than doing work at the far end. How much depends on three things and nothing else, which is what makes wire resistance so tractable: R = ρ · L / A. The metal contributes its resistivity ρ, the run contributes its length L, and the conductor's cross-sectional area A divides it all back down. Longer wire, more resistance. Fatter wire, less. This wire resistance calculator evaluates that relation in all four directions, so it also answers “how long a piece of nichrome makes a 12 Ω element?” and “what gauge keeps my drop under 3 %?”
Resistivity is the material, resistance is the object
The two words get used interchangeably and they are not the same thing. Resistivity is a property of the substance — annealed copper is 1.7241 × 10⁻⁸ Ω·m whether it is a hair-thin bond wire or a service-entrance cable. Resistance is a property of a particular piece of that substance, and it depends entirely on how the material has been shaped. That is why a spool of 14 AWG and a spool of 4/0 made from identical copper behave so differently: same ρ, wildly different A.
Why gauge numbers run backwards
AWG numbers get larger as the wire gets thinner, because the scale counts drawing operations — each pass through a smaller die stretched the wire and thinned it. The modern definition is purely geometric: d(n) = 0.127 mm × 92^((36 − n) / 39). The useful consequence is that three gauges up doubles the cross-section and halves the resistance, and ten gauges up changes it by a factor of ten. Once you know 12 AWG copper is about 1.59 Ω per 1000 ft, you can reconstruct most of the table in your head.
The round-trip mistake
This is the single most common error in a voltage-drop calculation. Current has to reach the load and get back, so a 50 ft two-conductor cable presents 100 ft of conductor. Compute the drop on 50 ft and you will report half the real figure and undersize the cable. Use the round-trip toggle and the doubling is done for you, and shown.
Hot wire is worse wire
Metals conduct less well as they heat, and the effect is not small. Copper's temperature coefficient is 0.00393 /°C, so the linear model R_T = R₂₀ · [1 + α(T − T₀)] puts a conductor at 75 °C about 21.6 % above its 20 °C book value. A cable sized with exactly zero margin at room temperature is therefore already over budget once it warms up under load — and since the wire heats itself by P = I²R, the effect partly feeds on itself.
Aluminium, and what %IACS actually means
%IACScompares a conductor against annealed copper, which is defined as exactly 100 %. Aluminium comes in near 65 %, so it needs roughly 1.5 times the cross-section — one to two AWG sizes larger — for the same resistance. What it gives back is mass: at 2700 kg/m³ against copper's 8960, an aluminium run of equal resistance still weighs under half as much. That trade is why overhead distribution and large feeders are aluminium while branch wiring generally is not.
Working backwards
The same relation rearranges to L = R · A / ρ for heating-element and shunt design, to A = ρ · L / R for sizing a cable to a resistance or drop ceiling, and to ρ = R · A / L for identifying an unknown sample from a measurement. That last one is genuinely useful on the bench: measure a known length of mystery wire, and the resistivity that comes back will name the metal.