Voltage Drop Calculator

American Wire Gauge looks like an arbitrary list of sizes that runs backwards. It is not a list at all. The National Bureau of Standards sets it out as a law:

The gage is formed by the specification of two diameters and the law that a given number of intermediate diameters are formed by geometrical progression. Thus, the diameter of No. 0000 is defined as 0.4600 inch and of No. 36 as 0.0050 inch. There are 38 sizes between these two, hence the ratio of any diameter to the diameter of the next larger gage number = 1.122 932 2.

Two fixed ends, 0.4600 in at No. 0000 and 0.0050 in at No. 36, and everything between them in geometric progression. That ratio, 1.1229322, is 92 to the power of one thirty-ninth, so the diameter of any gauge is:

d (mils) = 5 × 92^{(36 − n)/39}

Run it and every published circular-mil figure falls out. A #10 comes to 101.9 mils, so 10,383 circular mils, against the 10,380 the circular prints. The table below does that check on all thirteen sizes.

Two consequences the circular states outright, and they are exact rather than rules of thumb:

• Three gauge numbers doubles the area. The ratio cubed is 1.4160, and squared that is 2.0050. So a #7 has twice the copper of a #10, and half the resistance.
• Six gauge numbers doubles the diameter. The sixth power of the ratio is 2.0050, which the circular gives as 2.0050. So six sizes up is four times the area and a quarter of the resistance.

Which is worth carrying around. If a #10 is dropping 6 volts and you need 3, you need three gauge numbers, not one.

Every voltage drop calculator uses K = 12.9 for copper and 21.2 for aluminium. Almost none of them say what K is or where it came from, and the usual gesture is at a code book behind a login.

K is simply the resistance of one circular mil of conductor, one foot long. So it is the published resistance per 1,000 ft times the circular mils, divided by 1,000, and you can compute it from the NBS table on any row:

K₂₀ = 0.9988 × 10,380 / 1,000 = 10.37  (that is the #10 row)

Do it on all thirteen rows and it lands on 10.37 every time, because that is what resistivity means: it is a property of the copper, not of the wire size. The last column of the table below is that calculation.

So why does the industry say 12.9? Two adjustments, both physical:

1. Temperature. The NBS figures are at 20 °C. The industry constant is quoted at 75 °C, a conductor working hard. The circular's own temperature coefficient for annealed copper is 0.00393 per degree, so 55 degrees multiplies resistance by 1.216: 10.37 × 1.216 = 12.61.
2. Stranding. A stranded conductor's wires are laid in a helix, so each wire is about 2% longer than the cable it is in, and carries about 2% more resistance. 12.61 × 1.02 = 12.87.

Which is 12.9. And aluminium of the standard grade is defined as 61% the conductivity of copper, so its K is 12.87 / 0.61 = 21.1, which is the 21.2 everybody quotes.

None of that is a secret and none of it needs a code book. It needed a sixty-year-old government pamphlet and a calculator.

The factor of 2 in the single-phase formula is the round trip: current leaves on one conductor and returns on the other, and both of them have resistance.

So the length you enter is the one-way distance, panel to load. Entering the round trip and keeping the factor of 2 reports twice the real drop, and it is the single commonest error on this calculation. It usually shows up as somebody concluding they need 4/0 for a garage circuit.

Three phase uses 1.732, the square root of three, because the return path in a balanced three-phase circuit is shared between the phases rather than doubled.

The gage law makes this predictable. Consecutive gauge numbers differ in area by a factor of about 1.26, so going up one size cuts the drop by about 21%. Three sizes doubles the area and halves the drop.

That means a run failing at 6.6% against a 3% limit is not one size short. It needs the area roughly doubled, so three gauge numbers, or the next size that clears the circular-mil figure the calculator prints.

The other lever is length, and it is linear rather than logarithmic. Halving the run halves the drop exactly. On a long outbuilding feed it is often cheaper to move the subpanel than to upsize the whole run.

Raising the voltage is the third and it is quadratic in effect: the same power at 240 V draws half the current of 120 V, and half the current on twice the voltage is a quarter of the percentage drop.

Copper's resistance rises with temperature, at 0.00393 per degree by the NBS figure. A conductor working near its rating sits far above room temperature, and the industry constant is quoted at 75 °C for that reason: it is the pessimistic case, and voltage drop should be checked at the condition that makes it worst.

The difference is not small. Between 20 and 75 degrees the resistance is up by nearly 22%, which is most of the gap between the 10.37 in the government table and the 12.9 everyone uses.

If your conductor genuinely runs cool, the real drop will be lower than this page reports, and being wrong in that direction is the right way round.

Nearly every voltage drop calculator presents 3% on a branch circuit and 5% overall as a code limit. In the NEC as published they sit in Informational Notes, at 210.19 for branch circuits and 215.2 for feeders, and NEC 90.5 defines informational notes as explanatory material that is not enforceable as a requirement.

This page could not verify that against the primary document, for the same reason the ampacity table is missing: NFPA's reader cannot be read from here. It is stated on the strength of secondary sources and it is flagged as such rather than presented as established. If it matters to your job, read the code itself or ask your inspector.

What is not in dispute is the practical part. Some jurisdictions adopt the 3% and 5% figures as mandatory local amendments, which is exactly the pattern this site keeps finding in the IRC: a model document says one thing and the place you are actually building says another. So the calculator lets you set the limit rather than assuming one, and defaults to 3% because that is the figure people are usually working to.

And whether or not it is enforceable, it is good engineering. A 3% drop on a 120 V circuit is 3.6 V, and equipment is designed for a supply within a band.

This page does not size a conductor for ampacity, and you must not use it that way.

Two different questions get asked of a wire. Will the voltage at the far end be high enough for the equipment to work properly? That is voltage drop, it is the arithmetic on this page, and getting it wrong makes a motor run hot or a light dim.

Will the wire itself get hot enough to be a fire? That is ampacity. It comes from NEC Table 310.16, adjusted for ambient temperature, for the number of current-carrying conductors bundled together, and for the temperature rating of the terminations at both ends. Getting it wrong burns a house down.

That table is not on this page because it could not be obtained from a source worth trusting. NFPA's free-access reader is a JavaScript application behind a login and returns nothing to a fetch; every reproduction found sat on a commercial site or a document-sharing service. This site does not launder a safety table by copying it from a stranger, and a conductor's ampacity is the last figure on earth to guess at.

So: size for ampacity first, from the code, then check voltage drop here and go up if it fails. That is the order the two questions come in anyway. Voltage drop only ever makes a conductor bigger, never smaller.

Read 2026-09-08. Copper Wire Tables, NBS Circular 31, 4th edition, United States Department of Commerce, National Bureau of Standards. Table 5 gives diameter, circular mils and ohms per 1,000 ft at 20 C for standard annealed copper. A US government publication in the public domain, hosted by NIST. Every figure on this page is either from it or derived from it.

It is worth saying why a single source is enough here, when most pages on this site carry several. Everything on this page is either printed in that circular or derived from what is printed in it by arithmetic you can repeat. There is nothing to triangulate: the AWG ratio is a definition, the resistance table is a measurement published by the national metrology institute, and K is the two of them multiplied together.

The claims this page could not source that way are labelled where they appear: the status of the 3% figure, and the ampacity table that is absent altogether.