Wire Resistance Calculator
Pure wire-resistance physics: R = ρ·L/A for AWG 8–40 copper and aluminium wire — with temperature correction, loop (round-trip) resistance, conductance, a skin-effect note, and a reverse maximum-length solver. Everything runs in your browser; nothing is uploaded.
Resistance calculator
One-way length of conductor. Loop = out + back (2× one-way).
One-way R
0 Ω
Loop R (2×)
0 Ω
Loop conductance
0 S
R per km
0 Ω/km
R per 1000 ft
0 Ω/kft
Temp factor
0 ×
Reverse solver: max length for a target resistance
How long can the run be before resistance exceeds your budget?
Max one-way length
0 m
Conductor total
0 m
R per metre
0 Ω/m
AWG 8–40 resistance table (@ 20 °C)
Diameters from the AWG definition d = 0.127×92(36−n)/39 mm; resistance from R = ρ/A per unit length.
| AWG | Ø mm | mm² | Cu Ω/km | Al Ω/km | Cu Ω/kft |
|---|---|---|---|---|---|
| 8 | 3.2636 | 8.3656 | 2.008 | 3.371 | 0.612 |
| 9 | 2.9064 | 6.6342 | 2.532 | 4.251 | 0.772 |
| 10 | 2.5882 | 5.2612 | 3.193 | 5.360 | 0.973 |
| 11 | 2.3048 | 4.1723 | 4.027 | 6.759 | 1.227 |
| 12 | 2.0525 | 3.3088 | 5.077 | 8.523 | 1.548 |
| 13 | 1.8278 | 2.6240 | 6.402 | 10.747 | 1.951 |
| 14 | 1.6277 | 2.0809 | 8.073 | 13.552 | 2.461 |
| 15 | 1.4495 | 1.6502 | 10.180 | 17.088 | 3.103 |
| 16 | 1.2908 | 1.3087 | 12.837 | 21.548 | 3.913 |
| 17 | 1.1495 | 1.0378 | 16.187 | 27.172 | 4.934 |
| 18 | 1.0237 | 0.8230 | 20.412 | 34.263 | 6.222 |
| 19 | 0.9116 | 0.6527 | 25.739 | 43.205 | 7.845 |
| 20 | 0.8118 | 0.5176 | 32.456 | 54.480 | 9.893 |
| 21 | 0.7229 | 0.4105 | 40.927 | 68.698 | 12.474 |
| 22 | 0.6438 | 0.3255 | 51.608 | 86.627 | 15.730 |
| 23 | 0.5733 | 0.2582 | 65.076 | 109.235 | 19.835 |
| 24 | 0.5106 | 0.2047 | 82.059 | 137.742 | 25.012 |
| 25 | 0.4547 | 0.1624 | 103.475 | 173.690 | 31.539 |
| 26 | 0.4049 | 0.1288 | 130.479 | 219.019 | 39.770 |
| 27 | 0.3606 | 0.1021 | 164.531 | 276.177 | 50.149 |
| 28 | 0.3211 | 0.0810 | 207.470 | 348.253 | 63.237 |
| 29 | 0.2859 | 0.0642 | 261.615 | 439.139 | 79.740 |
| 30 | 0.2546 | 0.0509 | 329.890 | 553.744 | 100.551 |
| 31 | 0.2268 | 0.0404 | 415.984 | 698.259 | 126.792 |
| 32 | 0.2019 | 0.0320 | 524.546 | 880.488 | 159.882 |
| 33 | 0.1798 | 0.0254 | 661.440 | 1110.275 | 201.607 |
| 34 | 0.1601 | 0.0201 | 834.061 | 1400.031 | 254.222 |
| 35 | 0.1426 | 0.0160 | 1051.732 | 1765.406 | 320.568 |
| 36 | 0.1270 | 0.0127 | 1326.209 | 2226.136 | 404.228 |
| 37 | 0.1131 | 0.0100 | 1672.319 | 2807.106 | 509.723 |
| 38 | 0.1007 | 0.0080 | 2108.755 | 3539.696 | 642.748 |
| 39 | 0.0897 | 0.0063 | 2659.091 | 4463.474 | 810.491 |
| 40 | 0.0799 | 0.0050 | 3353.052 | 5628.337 | 1022.010 |
Skin effect note
For AWG 8–40 at mains frequency, skin effect is negligible.
Skin depth in copper is 9.23 mm at 50 Hz and 8.42 mm at 60 Hz, while even 8 AWG (the thickest gauge here)
is only 3.26 mm across — the AC resistance correction stays well under 1 %. At 400 Hz it is 3.26 mm and at
10 kHz 0.652 mm, where the effect starts to matter for thicker conductors. This calculator reports DC resistance.
Worked examples
1 — 100 m of 14 AWG copper at 20 °C
R = 1.68×10⁻⁸ × 100 / 2.081×10⁻⁶ = 0.8073 Ω one-way; loop = 1.6147 Ω; loop conductance = 0.6193 S.
2 — Same run at 75 °C
Temperature factor 1 + 0.00393×55 = 1.21615, so R = 0.8073 × 1.21615 = 0.9818 Ω one-way — a 21.6 % increase.
3 — Reverse: 2 Ω loop budget, 12 AWG aluminium at 30 °C
Max one-way length = 112.8 m (225.6 m of conductor).
Methodology
R = ρ · L / A R(T) = R20[1 + α(T−20)] G = 1/R
Constants used: copper ρ = 1.68×10⁻⁸ Ω·m, α = 0.00393/°C; aluminium ρ = 2.82×10⁻⁸ Ω·m, α = 0.00403/°C (all at 20 °C reference). AWG diameters follow the standard definition d(mm) = 0.127 × 92(36−n)/39. Honest note on the copper constant: pure-copper 1.68×10⁻⁸ gives 14 AWG = 8.07 Ω/km, while the IACS annealed-copper value 1.7241×10⁻⁸ gives 8.29 Ω/km (≈2.6 % higher) — some of our sibling tools use the latter, so small differences between pages are expected and documented, not errors.
Scope boundary: what this tool is (and isn't)
- This tool = wire RESISTANCE physics. It answers “how many ohms is this wire?” from R=ρL/A, with temperature correction, loop resistance, conductance, and reverse length solving.
- NOT a voltage-drop / wire-sizing tool. For NEC-style voltage-drop percentages, 1-phase/3-phase circuits, and pass/fail verdicts, use the voltage drop calculator (#477) — it uses the NEC Chapter 9 K-method at 75 °C, a different (installation-oriented) methodology.
- NOT a gauge converter. For AWG ↔ mm ↔ mm² conversion and ampacity ratings, use awg-to-mm (#377).
- NOT a circuit drop shortcut. The resistor voltage drop tool (#459) covers quick resistor drops plus a compact 12 V/24 V wire-drop mode — this page goes deeper on resistance itself.
Related tools
Voltage Drop CalculatorNEC K-method wire sizing with % drop verdicts — the installation companion to this physics page.
Resistor Voltage DropQuick resistor drops plus compact 12 V/24 V wire-drop mode.
AWG to mmGauge ↔ metric conversion and ampacity reference.
12V Wire SizeAutomotive/low-voltage gauge picker with ampacity checks.
Frequently asked questions
What is the formula for wire resistance?
Wire resistance is R = ρ × L / A, where ρ (rho) is the material's resistivity in ohm·metres, L is the conductor length in metres, and A is the cross-sectional area in square metres. For example, 100 m of 14 AWG copper wire (2.081 mm²) gives R = 1.68×10⁻⁸ × 100 / 2.081×10⁻⁶ ≈ 0.8073 Ω one-way.
Why does this tool use 1.68×10⁻⁸ Ω·m for copper?
1.68×10⁻⁸ Ω·m is the resistivity of pure copper at 20 °C. The IACS annealed-copper standard is 1.7241×10⁻⁸ Ω·m, which gives results about 2.6 % higher (for example 14 AWG: 8.29 Ω/km instead of 8.07 Ω/km). The assumption is stated here explicitly so you can compare honestly with tables built on the IACS value.
How does temperature change wire resistance?
Resistance rises with temperature: R(T) = R₂₀ × [1 + α(T − 20)], with α = 0.00393 /°C for copper and 0.00403 /°C for aluminium. A 100 m run of 14 AWG copper measures 0.8073 Ω at 20 °C but 0.9818 Ω at 75 °C, a 21.6 % increase. Enter the expected operating temperature above to get the corrected value.
What is loop resistance, and why is it double?
A real circuit needs two conductors — current travels out along one wire and returns along the other — so the total conductor length is twice the one-way run. Loop resistance is therefore 2 × the one-way resistance: 1.6147 Ω for a 100 m run of 14 AWG copper at 20 °C. Use the loop value when the whole round trip matters, for example in long 12 V or speaker runs.
How much higher is aluminium wire resistance than copper?
Aluminium's resistivity (2.82×10⁻⁸ Ω·m) is about 68 % higher than copper's, so the same gauge and length has 68 % more resistance: 100 m of 14 AWG aluminium is 1.3552 Ω versus 0.8073 Ω for copper at 20 °C. Aluminium is lighter and cheaper, which is why utilities use it, but you need a larger gauge for equal resistance.
What is wire conductance?
Conductance G = 1/R, measured in siemens (S), is the reciprocal of resistance — how easily current flows. The 100 m loop above (1.6147 Ω) has a conductance of 0.6193 S. Conductance is handy when combining parallel paths, because conductances add directly while resistances do not.
Why does a bigger AWG number mean thinner wire?
The American Wire Gauge scale is inverted: 40 AWG (0.0799 mm diameter) is far thinner than 8 AWG (3.264 mm). Each 3-gauge step roughly doubles or halves the cross-sectional area, and each 10-gauge step changes it by a factor of ten — so 11 AWG has about twice the area, hence half the resistance per metre, of 14 AWG.
Does skin effect matter for 8–40 AWG wire?
Skin effect pushes AC current toward the conductor surface, but it only matters when the wire is thick compared to the skin depth. At 50/60 Hz the skin depth in copper is about 9.23/8.42 mm, while 8 AWG — the thickest gauge covered here — is only 3.26 mm across, so the AC correction stays well under 1 %. Skin effect becomes significant at kilohertz frequencies and above, which is why this calculator reports DC resistance.
How do I find the maximum wire length for a target resistance?
Use the reverse solver below: it divides your target resistance by the ohms-per-metre of the chosen gauge, material, and temperature. For example, to stay under 1 Ω one-way with 14 AWG copper at 20 °C you may run up to 123.9 m; for a 2 Ω loop budget with 12 AWG aluminium at 30 °C the limit is 112.8 m one-way (225.6 m of conductor).
How is this different from the voltage drop calculator?
This tool computes pure wire resistance from first principles (R = ρL/A) at your chosen temperature. The voltage drop calculator uses the NEC Chapter 9 K-method at 75 °C, computes voltage-drop percentage for DC, single-phase, and three-phase circuits, and gives pass/fail verdicts against the 3 %/5 % NEC guidance. Use this page for resistance physics; use the voltage drop calculator when sizing conductors for a real installation.
How is this different from awg-to-mm?
The awg-to-mm tool is a gauge conversion reference: it converts between AWG, millimetres, mm², and circular mils, and lists ampacity ratings. This page does not convert gauges or rate ampacity — it calculates resistance, temperature correction, loop resistance, and reverse length from the resistivity formula.
Why does the calculator cover AWG 8 to 40?
AWG 8–40 spans common hookup, building, automotive, and electronics wire — from 8.37 mm² down to 0.005 mm². The underlying diameter formula is valid across the whole AWG system, but gauges outside this range (like 4/0 service cable or 44 AWG magnet wire) serve niches with their own dedicated tools.
Is the result valid for AC circuits?
The resistance value is the DC resistance, which equals the AC resistance for 8–40 AWG at 50/60 Hz because skin effect is negligible (see above). Inductance and proximity effect are not modelled, so for long parallel runs or frequencies above a few kilohertz, treat the result as the resistive component only.
Can I use this to size speaker wire or 12 V runs?
Yes for the resistance part: long speaker or 12 V runs are exactly where wire resistance audibly or visibly matters, and the loop resistance output is the number that counts. For choosing a code-compliant gauge for mains wiring, use the voltage drop calculator; for 12 V automotive sizing, the 12 V wire size tool adds ampacity checks this page intentionally omits.
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