What Is the Voltage Drop Formula? AWG Sizing & Worked Examples

The single-phase voltage drop formula is VD = (2 × K × I × L) / CM. This equation calculates the exact voltage lost as heat across a conductor due to its inherent resistance. For three-phase systems, the multiplier changes from 2 to √3 (1.732). If you are running a 120V branch circuit and your calculated VD exceeds 3.6V (3% of 120V), your wire is too small or your run is too long, and you must step up your AWG size immediately to prevent equipment malfunction and excessive heating.

The Exact Voltage Drop Formula (and What Every Symbol Means)

The standard approximate formula for single-phase AC and DC circuits, derived from NEC Chapter 9, Table 8 resistance data, is:

This formula applies to steady-state loads with a power factor near 1.0 (like resistive heating or incandescent lighting) on systems under 600V. It assumes an operating temperature of 75°C. If you are using NM-B (Romex) cable, which is limited to the 60°C ampacity column by NEC 334.80, the actual resistance is slightly lower, making this 75°C formula a conservative, safe baseline that will never underestimate your voltage drop.

Rearranged Forms: Solving for Wire Size, Distance, and Current

On the bench or jobsite, you rarely just want to find the voltage drop. Usually, you know your maximum acceptable drop (e.g., 3.6V on a 120V circuit) and need to find the required wire size or maximum run length. Here are the algebraically rearranged forms of the core equation:

1. Solving for Wire Size (CM)

Use this to find the minimum Circular Mils required, then look up the corresponding AWG in NEC Chapter 9, Table 8.

2. Solving for Maximum Distance (L)

Use this to find how far you can run a specific wire gauge before exceeding your voltage drop limit.

3. Solving for Maximum Current (I)

Use this to find the maximum load you can safely place on an existing wire run without violating the 3% rule.

Worked Examples with Unit Tracking

Abstract formulas are useless without rigorous unit tracking. Here are two real-world scenarios solved step-by-step.

Problem 1: 120V Branch Circuit (Copper)

Scenario: You are wiring a 120V receptacle for a 15A space heater. The one-way wire run is 80 feet using 14 AWG copper THHN. What is the voltage drop, and does it pass the NEC recommended 3% limit?

1. Identify Variables:
   • K = 12.9 (Copper)
   • I = 15 Amps
   • L = 80 Feet
   • CM = 4,110 (from 14 AWG reference)
2. Plug into Formula:
   VD = (2 × 12.9 × 15 × 80) / 4,110
3. Calculate Numerator:
   2 × 12.9 = 25.8
   25.8 × 15 = 387
   387 × 80 = 30,960
4. Divide by Denominator (CM):
   VD = 30,960 / 4,110 = 7.53 Volts
5. Calculate Percentage:
   %VD = (7.53V / 120V) × 100 = 6.27%

Problem 2: 240V Feeder (Aluminum)

Scenario: You are running a 240V subpanel feeder for a 40A welder load. The one-way distance is 150 feet using 2 AWG aluminum SER cable. Find the voltage drop.

1. Identify Variables:
   • K = 21.2 (Aluminum)
   • I = 40 Amps
   • L = 150 Feet
   • CM = 66,360 (from 2 AWG reference)
2. Plug into Formula:
   VD = (2 × 21.2 × 40 × 150) / 66,360
3. Calculate Numerator:
   2 × 21.2 = 42.4
   42.4 × 40 = 1,696
   1,696 × 150 = 254,400
4. Divide by Denominator (CM):
   VD = 254,400 / 66,360 = 3.83 Volts
5. Calculate Percentage:
   %VD = (3.83V / 240V) × 100 = 1.59%

Result: 1.59% is well under the 3% feeder limit. 2 AWG Aluminum is perfectly sized for this specific 40A load at this distance. (Note: Always verify the 40A load does not exceed the ampacity of the 2 AWG aluminum wire, which is 90A at 75°C, so we are safe on both ampacity and voltage drop).

Common Unit Mistakes That Break the Math

When your calculated voltage drop looks wildly wrong, you almost certainly mixed up your units. Here is how to catch the errors:

• Mistake 1: Using mm² instead of Circular Mils (CM). The formula requires CM. If you are looking at IEC metric wire (e.g., 2.5 mm²), you cannot plug 2.5 into the CM slot. You must convert: 1 mm² ≈ 1,973.5 CM. Therefore, 2.5 mm² = 4,933 CM.
• Mistake 2: Using Meters instead of Feet. The constant K (12.9 for copper) is calibrated specifically for feet. If your tape measure reads 25 meters, you must convert to feet (25 × 3.281 = 82 feet) before plugging it into L.
• Mistake 3: Forgetting the '2' Multiplier. The '2' accounts for the hot wire out and the neutral wire back. If you are calculating a 3-phase system, the multiplier is √3 (1.732). If you just use '1', you are only calculating the drop on half the circuit.
• Mistake 4: Using Breaker Size for 'I'. 'I' is the actual continuous current draw of the load, not the breaker rating. If you have a 20A breaker but the load only draws 12A, use 12A for 'I'. Sizing wire for the breaker capacity rather than the actual load results in massive, unnecessary copper costs.

Sanity Check (Realistic Magnitudes): On a standard 120V residential branch circuit, a realistic voltage drop is between 1V and 5V. If your math spits out a 45V drop on a 50-foot run of 12 AWG, you have a decimal error or a unit mismatch. Stop and re-check your CM value.

Decision Tree: Sizing Your Wire to Beat the 3% Rule

Do not guess your wire size. Run the math, calculate the percentage, and use this decision matrix to make your final material pick. The National Electrical Code (NEC) recommends a maximum 3% drop on branch circuits and a maximum 5% total drop (feeder + branch combined). For exact calculator verification, you can cross-reference your manual math with the Southwire Voltage Drop Calculator.