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Wire Resistance Calculator

Physics

The conductor run

Every panel below reads this one run, so the resistance, the voltage drop, the gauge recommendation and the material table always describe the same piece of wire.

Loads a complete worked example into every field.
The International Annealed Copper Standard value, and by definition 100 % IACS. This is the copper behind every published AWG resistance table and cable datasheet.

R = ρ · L / A The everyday direction: a material, a length and a cross-section give the ohms the run adds, and from there the voltage it drops and the watts it wastes.

How the cross-section is specified.
4/0 through 40, by the geometric definition.
A two-conductor cable carries current out and back, so the conductor is twice the run.

497.1196 mΩ

The answer, from ρL/A.
Parallel strands share the current, dividing the resistance.
Identical wires run side by side.
0 to 10, applied to every figure and every export.

Load and temperature

Leave these blank for a bare resistance figure. Filling them in turns the ohms into volts dropped, watts wasted, and a verdict against your allowed-drop budget.

3 % is the usual branch-circuit guideline, 5 % the total budget.
Resistance of the run · R = ρ · L / A
497.1196 mΩ
Excessive

At 6.2140 % the run is over the 3.0000 % budget — go up a gauge or two, shorten the run, or split the load across parallel conductors.

High current density for a continuous load
7.21 A/mm² is above the 6 A/mm² rule of thumb for continuously loaded insulated conductors. Ampacity depends on insulation, grouping and ambient temperature, so check the cable's own rating and your local wiring rules rather than this figure alone.
This is the 100 % IACS reference itself
Annealed copper at 1.7241 × 10⁻⁸ Ω·m defines 100 % IACS, and it is the copper behind every published AWG resistance table. Switch to the high-purity preset (1.68 × 10⁻⁸ Ω·m) and the same wire reads 102.6 % IACS and about 2.6 % less resistance.

Conductor and material

Cross-section A
2.0809 mm²

4106.7239 cmil

Diameter
1.6277 mm

0.0641 in

Effective length
60.0000 m

Round trip (out and back)

Resistance per length
8.2853 mΩ/m

2.5254 Ω/1000 ft

Resistivity used
1.72410e-8 Ω·m

Copper (annealed, IACS standard)

Conductivity σ
5.8001e+7 S/m

100.0000 % IACS

Conductance G
2.0116 S
Conductor mass
1.1187 kg

Whole run, all conductors

L = 60.00 md = 1.628 mmA = 2.081 mm²

Circuit impact

Exceeds the allowed drop
Voltage drop
7.4568 V
Drop percentage
6.2140 %
Voltage at load
112.5432 V
Power lost in the wire
111.8519 W
Current
15.0000 A
Current density
7.2084 A/mm²
Resistance ceiling
240.0000 mΩ
Smallest gauge that fits
10 AWG

6 mm² metric

Left: delivered to the load. Right: 6.2140 % lost in the wire against a 3.0000 % budget.

Effective conductor length

L_eff = 2 × 30.0000 m = 60.0000 m

Resistance of one conductor

R = ρL/A = (1.72410e-8 Ω·m × 60.0000 m) / 2.0809 mm² = 497.1196 mΩ

Conductor mass

m = A · L · ρ_m = 2.0809 mm² × 60.0000 m × 8960 kg/m³ = 1.1187 kg

Voltage dropped in the wire

V_drop = I·R = 15.0000 A × 497.1196 mΩ = 7.4568 V

Power wasted as heat

P = I²R = 15.0000 A² × 497.1196 mΩ = 111.8519 W

Drop as a percentage of the supply

%drop = 7.4568 V / 120.0000 V × 100 = 6.2140 %

Which copper is this?
Published AWG resistance tables, cable datasheets and wiring codes are all built on the International Annealed Copper Standard value of 1.72410e-8 Ω·m, which is 100 % IACS by definition — so that is what this calculator opens on. The high-purity figure most textbooks quote, 1.68 × 10⁻⁸ Ω·m, is a real but different copper: it reads 102.6 % IACS and gives resistances about 2.6 % lower. Both ship as presets, and the one in force is always named above.

About This Tool

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.

Three percent, five percent
The usual guidance allows about 3 % drop on a branch circuit and 5 % total from the service to the outlet. These are design targets, not ampacity limits — a cable can be perfectly safe and still drop far too much voltage to run a motor or a long LED strip properly. Ampacity is a separate question, governed by insulation temperature rating, grouping and ambient conditions.

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.

What this model leaves out
The formula is exact for a solid round conductor at DC. Real stranded cable typically measures 2–3 % higher, because the individual strands spiral and are longer than the cable itself. Skin effect is ignored — negligible at mains frequency below about 4 AWG, real in large conductors and at RF. Termination and contact resistance is not included at all, and on short low-voltage runs a poor crimp can easily outweigh the wire.

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.

Frequently Asked Questions

Is the Wire Resistance Calculator free?

Yes, Wire Resistance Calculator is totally free :)

Can I use the Wire Resistance Calculator offline?

Yes, you can install the webapp as PWA.

Is it safe to use Wire Resistance Calculator?

Yes, any data related to Wire Resistance Calculator only stored in your browser (if storage required). You can simply clear browser cache to clear all the stored data. We do not store any data on server.

How does this wire resistance calculator work?

Everything you type is normalised to SI before any arithmetic happens, and the whole page is then derived from one unrounded resistance. A gauge, diameter or radius is turned into a cross-sectional area, the length is doubled if you picked a round trip and divided by the number of strands and parallel runs, and R = ρL/A is evaluated once. Voltage drop, power loss, load voltage, conductance and the minimum-gauge recommendation all read that same figure, so nothing is ever rebuilt from a value you can see rounded on screen.

Why are there two copper presets, and which should I use?

Because two different resistivities for copper at 20 °C are both in common use and they disagree by 2.6 %. The International Annealed Copper Standard value, 1.7241 × 10⁻⁸ Ω·m, is 100 % IACS by definition and is the copper behind every published AWG resistance table, cable datasheet and wiring code — the tool defaults to it, which is why 100 ft of 12 AWG comes out at 0.1588 Ω, the familiar 1.59 Ω per 1000 ft. High-purity laboratory copper is 1.68 × 10⁻⁸ Ω·m, the figure most physics textbooks quote; on the IACS scale it reads 102.6 % and gives resistances about 2.6 % under the wire charts. Pick IACS to check a real cable, pure copper to match a textbook answer.

Do I enter the length of the cable or the length of the conductor?

Enter the physical run and let the round-trip toggle handle the rest. Current has to get to the load and back, so a 50 ft two-conductor cable is 100 ft of conductor as far as voltage drop is concerned, and forgetting the return leg halves every drop figure. Switch the run type to round trip and the tool doubles the length for you and shows the effective length it actually used, so the doubling is visible rather than assumed.

How much does temperature change the answer?

More than most people expect. Copper's coefficient is 0.00393 per °C, so a conductor running at 75 °C instead of the 20 °C its resistivity is quoted at carries about 21.6 % more resistance — a 0.242 Ω run becomes 0.294 Ω, and the voltage drop rises with it. The tool applies the linear model R_T = R₂₀·[1 + α(T − T₀)] and shows both figures side by side. That straight-line fit is excellent for metals from roughly −50 °C to 200 °C; outside that band it drifts, and the calculator blocks the result outright if the correction factor would fall to zero or below.

Why does aluminium wiring need a larger gauge than copper?

Aluminium's resistivity is 2.65 × 10⁻⁸ Ω·m against IACS copper's 1.7241 × 10⁻⁸, so it is only about 65 % as conductive and needs roughly 1.5 times the cross-section for the same resistance — in practice one to two AWG sizes larger. What it gives back is weight: at 2700 kg/m³ against copper's 8960 it is under a third of the mass, so per kilogram of metal aluminium wins outright. That is why utility distribution and large service entrances use it while branch wiring generally does not.

How accurate is this against a real cable's datasheet?

For a solid round conductor at DC it is exact — R = ρL/A is not an approximation. Real stranded cable typically reads 2–3 % higher than the geometric figure, because a stranded conductor's individual wires spiral and so are longer than the cable, and because the nominal area is rarely the exact area. At mains frequency skin effect is negligible below about 4 AWG but becomes real in large conductors, and the tool models DC only. Contact and termination resistance is not included at all, and on short low-voltage runs that can rival the wire itself.