Voltage Drop Formula Explained

The formula

For a single-phase or DC circuit:

VD = (2 × K × I × L) ÷ CM

For a three-phase circuit:

VD = (1.732 × K × I × L) ÷ CM

VD is the voltage drop in volts, K is a constant for the conductor material, I is the load current in amps, L is the one-way length of the run in feet, and CM is the conductor's cross-sectional area in circular mils. Every term is explained below.

Where the '2' and the '1.732' come from

In a single-phase or DC circuit, current has to travel out to the load through one conductor and back through another (the neutral, or the second hot leg on a 240V circuit). Both conductors have resistance, so the voltage drop happens twice, once on the way out and once on the way back, that is why the formula multiplies by 2 rather than treating it as a single one-way run.

In a balanced three-phase circuit, the relationship between the three phase conductors is different, the vector (phasor) math for a balanced three-phase load works out to a factor of the square root of 3, approximately 1.732, instead of 2. This is a standard result from three-phase circuit theory, not specific to voltage drop, the same square-root-of-3 factor shows up in three-phase power calculations generally.

The K constant (resistivity)

K represents how much a specific conductor material resists the flow of current, in units of ohm-circular-mils per foot. It comes from the same NEC Chapter 9, Table 8 data as the circular-mil values. The two values used almost universally in practice:

• Copper: K = 12.9 (at roughly 75 degrees Celsius)
• Aluminum: K = 21.2 (at roughly 75 degrees Celsius)

Circular mils (CM) and wire size

Circular mils measure a conductor's cross-sectional area, a larger circular-mil number means a physically thicker conductor with less resistance per foot. Wire sizes below 4/0 AWG use the American Wire Gauge system (a smaller AWG number is a thicker wire), sizes above 4/0 are specified directly in thousands of circular mils, written as kcmil (for example, 250 kcmil is 250,000 circular mils). See the full AWG-to-circular-mils reference table for every standard size from 14 AWG to 1000 kcmil.

Solving for wire size or maximum distance instead of voltage drop

The same formula rearranges algebraically to answer two other common questions:

1. To find the minimum circular mils (and therefore the minimum wire size) for a target voltage drop: CM = (2 x K x I x L) / VD (or 1.732 in place of 2 for three-phase). Plug in your target VD (for example, 3% of your supply voltage) and solve for CM, then pick the smallest standard wire size with a circular-mil value at or above that result.
2. To find the maximum one-way distance for a target voltage drop: L = (VD x CM) / (2 x K x I) (or 1.732 for three-phase). This is exactly how the maximum-distance columns on the voltage drop chart page were generated.
3. In both cases it is usually faster to try a few wire sizes or distances in the calculator directly and read off the percentage, rather than solving the algebra by hand, the calculator uses the identical formula and the exact NEC Chapter 9, Table 8 circular-mil values.

A worked example, start to finish

Suppose a 120V single-phase branch circuit carries a 20A load over a 100 ft one-way run of 12 AWG copper wire. From the reference table, 12 AWG copper has a circular-mil area of 6,530. Applying the formula:

VD = (2 × 12.9 × 20 × 100) ÷ 6,530 = 51,600 ÷ 6,530 ≈ 7.90V

As a percentage of the 120V supply: 7.90 ÷ 120 × 100 ≈ 6.58%, which is above the NEC-recommended 3% branch-circuit guideline. Moving up to 10 AWG copper (10,380 circular mils) instead: VD = (2 × 12.9 × 20 × 100) ÷ 10,380 ≈ 4.97V, or about 4.14%, still above 3% but now inside the 5% combined guideline. Moving up again to 8 AWG (16,510 circular mils) brings the drop down to about 3.13V, or roughly 2.60%, comfortably under the 3% target. This step-by-step trial is exactly what the voltage drop calculator lets you do instantly by changing the wire size dropdown and reading the new percentage, entirely in your browser, see the privacy policy for details.