Reference
Resistivity, length over area, and the factor of two everyone drops
A conductor's resistance is its resistivity times its length over its cross-section. Copper's resistivity is a standardised number. Length is the run there and back. Cross-section is the square millimetres of copper, not the diameter of the jacket, and for stranded cable not quite the number printed on it either. Everything on this page is that one formula, with the corrections that real cable, real temperature and real regulations put on it — and each correction is checked against the table it comes from.
The formula, and what goes into it
R = ρ · L / A
ρ, resistivity: the International Annealed Copper Standard fixes it at 1/58 Ω·mm²/m at 20 °C, which is 1.724 × 10⁻⁸ Ω·m. Cable manufacturers work to it and "100 % IACS" means exactly this figure. Aluminium is about 1.6 times worse and is not covered here.
L, length: the current has to come back. A 25 m extension is 50 m of conductor in the circuit, and forgetting the return is the commonest error in a quick estimate — it halves every answer. Three-phase is the exception and is handled in the calculator.
A, cross-section: the copper, in mm². A stranded conductor's nominal size is the sum of its strands' sections, and its overall diameter is larger and useless for this purpose. Where the user asks about conductor diameter — the AWG world does — the section is π d² / 4 of the equivalent solid, which is how the AWG column below is derived.
And temperature, which is not in the formula but should be: copper's resistance rises 0.39 % per degree. A conductor at 70 °C, which is where a fully loaded PVC cable is designed to run, is 20 % more resistive than the datasheet says at 20 °C.
| Conductor at | Relative to 20 °C |
|---|---|
| 0 °C | × 0.921 |
| 20 °C | × 1.000 |
| 40 °C | × 1.079 |
| 60 °C | × 1.157 |
| 70 °C | × 1.196 |
| 90 °C | × 1.275 |
R(T) = R₂₀ · (1 + 0.00393 · (T − 20)). A loom coiled on its drum in the sun, carrying its full rating, is generating heat it cannot shed and climbing this table while it does.
Conductor sizes: metric, AWG, and what the standard allows
The metric sizes are nominal areas. The AWG sizes are defined as diameters in a geometric series — each gauge is 92^(1/39) smaller than the last, ASTM B258 — and their resistances follow from that and the resistivity alone; the build derives every AWG figure and checks it against the published table. The right-hand columns are IEC 60228's maximum resistance for a flexible (class 5) conductor of each nominal size, and how far above pure copper that maximum sits.
| Nominal | Solid equiv. Ø | Nearest AWG | Pure copper | IEC 60228 class 5 max | Allowance |
|---|---|---|---|---|---|
| 0.75 mm² | 0.98 mm | 18 AWG (0.82 mm²) | 22.99 Ω/km | 26.00 Ω/km | +13 % |
| 1 mm² | 1.13 mm | 17 AWG (1.04 mm²) | 17.24 Ω/km | 19.50 Ω/km | +13 % |
| 1.5 mm² | 1.38 mm | 15 AWG (1.65 mm²) | 11.49 Ω/km | 13.30 Ω/km | +16 % |
| 2.5 mm² | 1.78 mm | 13 AWG (2.62 mm²) | 6.90 Ω/km | 7.98 Ω/km | +16 % |
| 4 mm² | 2.26 mm | 11 AWG (4.17 mm²) | 4.31 Ω/km | 4.95 Ω/km | +15 % |
| 6 mm² | 2.76 mm | 9 AWG (6.63 mm²) | 2.87 Ω/km | 3.30 Ω/km | +15 % |
| 10 mm² | 3.57 mm | 7 AWG (10.55 mm²) | 1.72 Ω/km | 1.91 Ω/km | +11 % |
| 16 mm² | 4.51 mm | 5 AWG (16.77 mm²) | 1.08 Ω/km | 1.21 Ω/km | +12 % |
| 25 mm² | 5.64 mm | 3 AWG (26.67 mm²) | 0.690 Ω/km | 0.780 Ω/km | +13 % |
| 35 mm² | 6.68 mm | 2 AWG (33.63 mm²) | 0.493 Ω/km | 0.554 Ω/km | +12 % |
- Flexible cable is allowed to be 11 to 16 % worse than pure copper of its nominal size. Fine strands pack imperfectly, are drawn to a tolerance, and are laid up helically so each strand is longer than the cable. The standard's maximum absorbs all of that, and a loom bought to a price will be near the maximum. The tables below use the class 5 maximum, not the theory, for exactly that reason.
- "Nearest AWG" is nearest, not equal. 2.5 mm² sits between 14 and 12 AWG and 4 mm² is a hair under 11, which does not exist commercially. Convert by area, and round towards the larger conductor.
- Skin effect is not why. At 50 Hz current penetrates 9.3 mm into copper, deeper than the radius of any cable on this page, so mains volt drop is a DC calculation. At 20 kHz the depth is 0.47 mm, which begins to matter on a loudspeaker line only for conductors thicker than about 0.9 mm, and then only at the very top of the band.
The regulation's numbers, reproduced
BS 7671 Appendix 4 tabulates volt drop in millivolts per ampere per metre for every cable size, and installers use it as a lookup. It is not a lookup value. Take IEC 60228's class 2 resistance — the stranded fixed-wiring conductor — correct it to the 70 °C the cable is rated to run at, and double it for the loop, and the regulation's column comes out to within 3 % at every size the build checks. Two things follow from being able to do that.
The first is that the tabulated figure silently assumes a conductor at 70 °C. A lightly loaded cable is cooler and drops less; the table is conservative for it, which is the right way round.
The second is that it assumes a class 2 conductor, and a flexible loom is class 5. The mV/A/m for a flex is the class 5 figure treated the same way — a few percent higher again — which is what the mains table on this page is built from. BS 7671 gives 3 % of the supply voltage as the volt-drop limit for lighting and 5 % for other uses, measured from the origin of the installation, so a temporary feed's loom is only part of a budget that includes everything upstream of the socket it plugs into.
| Cable | BS 7671 | Derived | Error |
|---|---|---|---|
| 1 mm² | 44 mV/A/m | 43.3 mV/A/m | -1.6 % |
| 1.5 mm² | 29 mV/A/m | 29.0 mV/A/m | -0.2 % |
| 2.5 mm² | 18 mV/A/m | 17.7 mV/A/m | -1.5 % |
| 4 mm² | 11 mV/A/m | 11.0 mV/A/m | +0.3 % |
| 6 mm² | 7.3 mV/A/m | 7.4 mV/A/m | +1.0 % |
| 10 mm² | 4.4 mV/A/m | 4.4 mV/A/m | -0.5 % |
| 16 mm² | 2.8 mV/A/m | 2.8 mV/A/m | -1.7 % |
Mains: a 16 A feed on a flexible loom
| 230 V, 16 A, class 5 at 20 °C — conductor ↓ length → | 10 m | 25 m | 50 m | 100 m |
|---|---|---|---|---|
| 1.5 mm² | 1.9 %4.3 V, 68 W as heat | 4.6 %10.6 V, 170 W as heat | 9.3 %21.3 V, 340 W as heat | 18.5 %42.6 V, 681 W as heat |
| 2.5 mm² | 1.1 %2.6 V, 41 W as heat | 2.8 %6.4 V, 102 W as heat | 5.6 %12.8 V, 204 W as heat | 11.1 %25.5 V, 409 W as heat |
| 4 mm² | 0.7 %1.6 V, 25 W as heat | 1.7 %4.0 V, 63 W as heat | 3.4 %7.9 V, 127 W as heat | 6.9 %15.8 V, 253 W as heat |
| 6 mm² | 0.5 %1.1 V, 17 W as heat | 1.1 %2.6 V, 42 W as heat | 2.3 %5.3 V, 84 W as heat | 4.6 %10.6 V, 169 W as heat |
| 10 mm² | 0.3 %0.6 V, 10 W as heat | 0.7 %1.5 V, 24 W as heat | 1.3 %3.1 V, 49 W as heat | 2.7 %6.1 V, 98 W as heat |
Volt drop as a percentage of 230 V at a full 16 A, flexible cable at the IEC 60228 class 5 maximum, conductor at 20 °C. Amber beyond the 3 % lighting allowance, red beyond 5 %. The wattage is what the loom itself dissipates: a hundred metres of 1.5 mm² at 16 A is a 681 W heater, and a coiled one is a 681 W heater with no ventilation — which is why the drum says to unwind it.
- Length and section trade one for one. Doubling the run or halving the copper does the same thing to the drop. A 50 m run of 2.5 mm² and a 100 m run of 4 mm² are close neighbours in the table, which is the arithmetic a distro plan is made of.
- The percentage is the number that means anything. Six volts off 230 is 2.6 % and unremarkable; six volts off 120 is 5 % and at the limit; six volts off 24 is a quarter of the supply and the thing has stopped working. The same loom, the same current, three different outcomes.
- Signal lines are exempt. A microphone line carries microamps and an AES3 or DMX pair a few milliamps. Their length limits come from capacitance, impedance and attenuation, which are the other pages; volt drop is a problem for conductors carrying real current — mains, DC power, PoE and loudspeakers.
Low voltage DC, where the same ohm hurts ten times as much
The drop in volts depends only on the current and the resistance; the supply voltage sets what fraction it is. At 5 A over 10 m of light flex the volts lost are the same on a 12 V line as on a 48 V one, and they are 22 % of the first and 5 % of the second. It is why LED tape goes dim at the far end, why a 12 V camera on a long run browns out when its lens motor moves, and why the industry moved to 48 V for anything that has to travel — PoE included.
The remedy is the same as for mains, with the numbers ten times harsher: thicker copper, shorter runs, or a higher voltage and a converter at the far end.
| 5 A over 10 m of flex | 0.75 mm² | 1.5 mm² | 2.5 mm² |
|---|---|---|---|
| 12 V | 21.7 % (2.60 V) | 11.1 % (1.33 V) | 6.7 % (0.80 V) |
| 24 V | 10.8 % (2.60 V) | 5.5 % (1.33 V) | 3.3 % (0.80 V) |
| 48 V | 5.4 % (2.60 V) | 2.8 % (1.33 V) | 1.7 % (0.80 V) |
Your run
Length one way, the conductor, the current or the load, the supply, the system and the conductor temperature. The tool gives the loop resistance, the drop in volts and percent, the power the cable dissipates, and the smallest standard size that would keep the run inside a 3 % allowance.
This calculator needs JavaScript. The tables above cover the common sizes and lengths.
Resistive load, so power factor is one and reactance is ignored — correct for conductors up to about 16 mm² and for DC, and a slight underestimate for large cables on AC. Three-phase is the balanced case, drop expressed line-to-line, which is √3 / 2 of the equivalent single-phase loop. The AWG options use the class allowance of the nearest metric size. The size for 3 % is the smallest standard section whose class-5 maximum at the stated temperature keeps the drop within 3 % of the supply.
Sources
- IEC 60028:1925, International standard of resistance for copper — the IACS figure of 1/58 Ω·mm²/m at 20 °C and the temperature coefficient of 0.00393 per °C. The oldest document cited on this site and still the definition manufacturers quote copper against.
- ASTM B258, Standard Specification for Standard Nominal Diameters and Cross-Sectional Areas of AWG Sizes of Solid Round Wires — the gauge as a geometric series with 36 AWG at 0.005 in and 0000 at 0.46 in, from which every AWG figure above is derived and then checked against the conventional table.
- IEC 60228:2004, Conductors of insulated cables, Tables 2 and 3 — maximum resistance at 20 °C for class 2 and class 5 plain copper conductors. Paywalled; the values are reproduced on essentially every cable manufacturer's datasheet, and the build checks each one for plausibility against pure copper.
- BS 7671:2018+A2:2022, Requirements for Electrical Installations, Appendix 4 (mV/A/m volt-drop tables) and Appendix 12 (the 3 % and 5 % limits). Paywalled; the small-cable single-phase figures used here are the widely reproduced ones, and the page's point is that they can be derived.
- Skin depth — √(ρ / π f μ₀), computed.
Assembled 8 September 2026 with AI assistance. The arithmetic is checked at build time against three independent published tables and reproduces all three; the checks catch a transcription error and cannot catch a wrong source. Volt drop is the easy half of cable sizing — current-carrying capacity, grouping, ambient temperature and protective-device coordination are the hard half and are not on this page. Sizing a mains circuit is a job for someone qualified to do it.
Companion pages: multipin looms for the same resistance judged as damping factor on a loudspeaker loom, loudspeaker impedance for why it hurts more at 2 Ω, and Ethernet cabling for the PoE case, where the standard's power budget turns out to be exactly this loss.