Voltage Drop and Conductor Sizing

Current goes out, and it has to come back

A conductor is a resistor nobody intended to install. Push current along it and part of the supply is spent reaching the load rather than arriving at it. Voltage drop is nothing more exotic than Ohm's law applied to the wiring instead of to the appliance.

The factor of two is what catches people. A circuit needs a return path, and the return conductor is the same length and the same size as the outgoing one. Both carry the load current, both lose voltage, and the load sits between them — so a run measured at fifteen metres puts thirty metres of copper in series with whatever is plugged in at the end. Every voltage-drop calculator on this site takes the one-way distance and doubles it internally; the ampacity pages take no distance at all, for the reason set out further down. Entering the doubled figure yourself reports an answer twice as bad as the installation.

Balanced three-phase is the exception. The return current is shared among the phases rather than sent back down a dedicated conductor, and the line-to-line multiplier is the square root of three — about 1.732 — not two.

The constant has a temperature buried inside it

K = 12.9 is not a property of the universe. It is copper's resistivity rewritten into the units the trade formula uses, and resistivity climbs with temperature — roughly four tenths of a percent per kelvin for copper. The constant therefore carries a hidden assumption about how hot the conductor is at the moment the answer matters.

The assumption is recoverable. Divide 12.9 by the 6,530 circular mils of 12 AWG and scale to a thousand feet: 1.98 ohms. That is the tabulated resistance of stranded 12 AWG at 75 °C — the figure in Chapter 9, Table 8, whose solid row reads 1.93 — the temperature a fully loaded conductor with 75 °C insulation is presumed to reach. The same wire near room temperature measures closer to 1.6 ohms per thousand feet, and its matching constant is about 10.4.

The two differ by nearly a quarter, which is why two pages on this site can use different figures without either being in error. A branch circuit carrying its rated continuous load is a warm conductor and earns 12.9. A garden lighting run drawing five amps through buried 12 AWG never approaches 75 °C, and the ambient-temperature resistance table describes it better. Choosing between them is a question about duty, not about arithmetic — and where the duty is unknown, the hotter constant is the one that fails safe.

Aluminium's companion constant is 21.2, about 1.64 times copper's, which is simply the ratio of the two resistivities. Two gauge numbers multiply a conductor's area by 1.59, which falls about 3% short of cancelling that penalty, so aluminium of equal resistance sits a little more than two gauge numbers up. Among the sizes building wire comes in, that is two sizes up from 14 to 6 AWG, where each size is two gauge numbers, and usually three from 4 AWG up, where the sizes run one gauge number apart — the arithmetic behind aluminium feeders sitting two or three sizes above the copper they replace.

Twelve volts is punished by the square

Volts lost depend on current and resistance; the supply voltage does not appear in that product at all. But a low-voltage system is hit from both sides at once. A fixed wattage draws current in inverse proportion to voltage, so a lower supply means a proportionally larger current and proportionally more volts burned in the cable. Those volts are then measured against a supply that is itself smaller. The percentage loss consequently rises with the square of the voltage reduction.

The numbers are stark. Sixty watts of lighting fifteen metres away along 12 AWG copper: at 12 volts the load draws five amps and the cable eats 0.8 V, which is 6.6 percent, and the far fixture is visibly duller than the near one. Put those same sixty watts on a 120 V circuit and it draws half an amp — 0.08 V, or 0.066 percent. One hundredth of the problem, through identical wire over an identical distance. Against a 230 V supply the same run is roughly three hundred and seventy times gentler.

This is why low-voltage landscape lighting is a voltage-drop problem before it is anything else, and why ordinary household circuits usually are not. It also explains the looser working limit — around ten percent on a 12 V run, against three on a branch circuit — and why that looser limit is still exceeded routinely.

One caution about how these runs are modelled here. The whole connected wattage is treated as though it sat at the far end of the cable, which is the pessimistic case. Fixtures spaced evenly along a daisy chain lose about half that at the last lamp, because the current feeding the near fixtures only travels part of the distance. A hub layout, where each fixture takes its own leg back to the transformer, abandons the geometry the formula assumes altogether and has to be worked leg by leg.

Ampacity answers a different question, and length is not in it

A conductor faces two independent sizing tests, and they are not two versions of one test. Ampacity asks whether the wire can shed the heat its own resistance produces without degrading its insulation. Voltage drop asks whether enough of the supply survives the journey. Length appears nowhere in the ampacity tables, and insulation temperature ratings appear nowhere in the drop formula.

A conductor can therefore pass one and fail the other. Twelve AWG copper is thermally fit for a 20 A breaker at any distance whatever — a hundred feet of it runs no hotter than ten feet, because the heat is both generated and shed per unit length. Loaded to 20 A on a 120 V circuit, it crosses the three percent recommendation at about forty-five feet one way. Fourteen AWG at 15 A crosses it at about thirty-eight. Past those distances the circuit is thermally sound, correctly protected, and delivering a saw that bogs down and a lamp that reads yellow.

The regulatory weight of that failure varies. Under the NEC the three and five percent figures live in informational notes, which explain rather than require, so exceeding them breaks nothing enforceable on an ordinary branch circuit. A few articles written for particular occupancies do impose a drop limit as a requirement rather than a suggestion — fire pump supplies and the sensitive-electronic-equipment systems of Article 647 among them — but those are exceptions aimed at named installations, not the general rule. BS 7671 frames it as an obligation on the result — the voltage at equipment terminals must be suitable — and offers three percent for lighting and five for everything else as values that satisfy it. Same physics, two different kinds of document.

Ampacity itself is a lookup rather than an equation, tabulated by conductor size and insulation temperature rating, and then reduced twice: once for ambient temperature above the 30 °C the table assumes, and again for the number of current-carrying conductors sharing a raceway, because bundled conductors warm one another. Two further rules cap what the table appears to permit. The final ampacity may not exceed what the lowest-rated termination in the circuit allows — commonly the 60 °C column on equipment rated 100 A or less, even where the cable itself is rated 90 °C, though the 90 °C column may still be used as the starting value for the correction arithmetic. And small conductors carry a flat overcurrent ceiling regardless of ampacity: 15 A on 14 AWG, 20 A on 12 AWG, 30 A on 10 AWG copper. That is why one page here reports all three temperature columns and another quotes only the 60 °C figure; they answer the table and the installation respectively.

Choosing a size, and where the expression runs out

Checking a gauge and selecting one are the same equation read in opposite directions. Fix the drop you will tolerate, and solve for area. The result is a bare number in square millimetres, and conductors are made in discrete sizes, so it has to be taken up to the next standard one. Rounding to the nearest size is a genuine error here — consecutive AWG steps differ in area by about twenty-six percent, so the size below is not close.

The expression is a direct-current one. It uses resistance, and an alternating-current conductor also has reactance, plus an AC resistance above its DC resistance because the current crowds toward the surface. On branch-circuit sizes those terms round away. On conductors around 1/0 and larger they no longer do, and with a poor power factor the reactive term can govern the answer — which is why long feeders are sized against tabulated impedance rather than against this formula.

Heat and resistance also feed each other. A conductor running warm resists more, drops more, and dissipates more heat in doing so. Over the range these circuits occupy the effect is modest, but it points the wrong way, and it is the second argument for the 75 °C constant when the duty is uncertain.

What the sag actually costs depends on what is at the end of it. A heater is close to a fixed resistance: it draws less current as the voltage falls, so the drop partly self-corrects, but its output falls with the square of the voltage — a ten percent sag costs nineteen percent of the heat. A motor or a switch-mode supply behaves more like a constant-power load and answers a sag by pulling more current, which deepens the sag and puts the extra dissipation into its own windings. That is where an undersized run does damage rather than merely disappointing, and it is worth separating from the ampacity failure: overheating insulation is a safety matter, while losing volts along the way is a matter of performance, efficiency and equipment life.