What is K in the voltage drop formula?

The resistivity constant. Use 12.9 for copper and 21.2 for aluminum at 75 degrees C.

Is voltage drop a code requirement?

Mostly no. The 3 percent branch and 5 percent total figures are informational notes in NEC 210.19(A) and 215.2(A)(2), not enforceable rules, though some sections such as 647.4(D) and 695.7 are mandatory.

Do I use one way or round trip distance?

One way. The 2 in the single phase formula and the 1.732 in the three phase formula already account for the return path.

What is the formula for finding the voltage drop from the breaker to the load?

The two working formulas are short. For single phase, Vd equals 2 times K times I times L divided by CM. For three phase, Vd equals 1.732 times K times I times L divided by CM. Vd is the voltage dropped in the conductors, K is the resistivity constant, I is the load current in amperes, L is the one way length of the run in feet, and CM is the circular mil area of one conductor from Table 8 in Chapter 9 of the NEC.

K is 12.9 for copper and 21.2 for aluminum at 75 degrees C. The 2 in the single phase formula accounts for the current traveling out on the hot and back on the neutral or the second hot, which is why you use the one way distance and let the formula double it. The 1.732 is the square root of 3 and reflects the phase relationship in a balanced three phase system.

Working an example

Say you have a 40 ampere single phase 240 volt load on 8 AWG copper, 150 feet from the breaker. Table 8 gives 8 AWG copper 16,510 circular mils. Vd equals 2 times 12.9 times 40 times 150 divided by 16,510, which is 154,800 divided by 16,510, or 9.4 volts. As a percentage that is 9.4 divided by 240, or 3.9 percent. That exceeds the 3 percent branch circuit recommendation, so step up to 6 AWG at 26,240 circular mils. The new drop is 154,800 divided by 26,240, or 5.9 volts, which is 2.5 percent and acceptable.

Solving for wire size directly

Rearrange for CM when you know the drop you will accept. CM equals 2 times K times I times L divided by Vd for single phase, or 1.732 times K times I times L divided by Vd for three phase. Using the same example with a 3 percent target on 240 volts, Vd allowed is 7.2 volts. CM equals 154,800 divided by 7.2, or 21,500 circular mils. Table 8 shows 6 AWG at 26,240 is the next size up, which confirms the answer above.

What the NEC actually requires

Voltage drop is not a mandatory rule in most of the Code. Informational Note 4 to 210.19(A) recommends branch circuit conductors sized to prevent a voltage drop exceeding 3 percent at the farthest outlet, with the maximum total drop on both feeders and branch circuits not to exceed 5 percent. Informational Note 2 to 215.2(A)(2) gives the matching 3 percent feeder recommendation. Informational notes are advisory, not enforceable, unless your local jurisdiction adopts them as law.

Some sections are mandatory. Section 647.4(D) limits voltage drop on sensitive electronic equipment branch circuits to 1.5 percent and total to 2.5 percent. Section 695.7 sets fire pump voltage drop limits. Article 680 has requirements for pool equipment feeders.

Two things that trip people up

First, if you upsize conductors for voltage drop, Section 250.122(B) requires the equipment grounding conductor to be increased proportionally to the increase in circular mil area of the ungrounded conductors. Second, the formula ignores reactance, which is fine on small conductors but understates drop on large conductors in steel raceway. For runs over 250 kcmil, use Table 9 in Chapter 9, which gives effective Z values by raceway type.

Field takeaway

Single phase: 2 K I L over CM. Three phase: 1.732 K I L over CM. Copper K is 12.9, aluminum is 21.2. Target 3 percent on the branch circuit, 5 percent total, and upsize the equipment grounding conductor to match whenever you upsize the phase conductors.