The standard single-phase voltage drop calculation formula is VD = (2 × K × I × L) / CM. For a 120V, 20A circuit running 100 feet using 12 AWG copper wire, the voltage drop is approximately 7.9V (6.58%), which exceeds the 3% NEC recommendation. To fix this, you must solve for Circular Mils (CM) and upgrade to 8 AWG copper. This guide breaks down every variable, provides rearranged formulas to solve for wire size, and walks through exact unit-tracked calculations so you can confidently size your next branch circuit or subpanel feeder without guessing.

The Core Voltage Drop Calculation Formula (and Symbols)

Before pulling wire, you need to know exactly how much voltage will be lost as heat across the conductor's resistance. The formula below applies to steady-state DC and single-phase AC circuits (assuming a power factor near 1.0, which is standard for residential resistive loads like lighting and heating).

Single-Phase Formula: VD = (2 × K × I × L) / CM
Three-Phase Formula: VD = (√3 × K × I × L) / CM

Table 1: Voltage Drop Symbol Definitions
Symbol Definition Units / Standard Values
VD Voltage Drop (the actual volts lost) Volts (V)
2 Multiplier for out-and-back single-phase path Dimensionless (Use √3 or 1.732 for 3-phase)
K Conductor resistivity constant 12.9 (Copper) or 21.2 (Aluminum) at 75°C
I Load current Amperes (A)
L One-way distance from source to load Feet (ft)
CM Circular Mils (cross-sectional area of wire) CM (Found in NEC Chapter 9, Table 8)
Assumptions & Scope: This formula assumes standard operating temperatures. The K values of 12.9 (Cu) and 21.2 (Al) are derived from the 75°C column, which aligns with standard THHN/THWN-2 wire and NEC 110.14(C) termination limits for modern residential equipment. If you are calculating for a highly inductive load (like a large motor) with a low power factor, this basic formula will underestimate the drop; you must factor in reactance (X) per NEC Chapter 9, Table 9.

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

In the field, you rarely just want to find the voltage drop. Usually, you know your maximum allowable drop (e.g., 3% of 120V = 3.6V) and need to find the right wire size or maximum run length. Here are the algebraically rearranged forms of the core equation:

  • Solve for Wire Size (CM): CM = (2 × K × I × L) / VD
    Use this to find the minimum Circular Mils required, then look up the corresponding AWG in NEC Table 8.
  • Solve for Maximum Distance (L): L = (VD × CM) / (2 × K × I)
    Use this to find how far you can run a specific wire gauge before exceeding your voltage drop limit.
  • Solve for Maximum Current (I): I = (VD × CM) / (2 × K × L)
    Use this to see how much load an existing long run can safely handle without excessive voltage sag.
NEC Chapter 9, Table 8 Quick Reference: 14 AWG = 4,110 CM | 12 AWG = 6,530 CM | 10 AWG = 10,380 CM | 8 AWG = 16,510 CM | 6 AWG = 26,240 CM | 4 AWG = 41,740 CM.

Worked Example 1: 120V Branch Circuit (12 AWG Copper)

Scenario: You are wiring a 120V, 20A dedicated outlet for a high-draw appliance in a detached workshop. The one-way distance from the main panel is 100 feet. You plan to use 12 AWG copper THHN. Is this acceptable, or do you need to upsize?

Step 1: Establish the target voltage drop.
The NEC recommends a maximum 3% voltage drop for branch circuits.
Target VD = 120V × 0.03 = 3.6V.

Step 2: Calculate the actual drop with 12 AWG.

  1. Identify variables: K = 12.9, I = 20A, L = 100 ft, CM = 6,530 (for 12 AWG).
  2. Plug into formula: VD = (2 × 12.9 × 20 × 100) / 6,530
  3. Multiply numerator: 2 × 12.9 × 20 × 100 = 51,600
  4. Divide by CM: 51,600 / 6,530 = 7.90V
  5. Calculate percentage: (7.90V / 120V) × 100 = 6.58%

Verdict: 6.58% is more than double the 3% recommendation. The 12 AWG wire will cause noticeable dimming and poor motor performance. We must upsize.

Step 3: Solve for required CM.

  1. Use rearranged formula: CM = (2 × K × I × L) / Target VD
  2. Plug in: CM = 51,600 / 3.6V = 14,333 CM
  3. Check NEC Table 8: 10 AWG is only 10,380 CM (too small). 8 AWG is 16,510 CM.

Final Pick: Upgrade to 8 AWG Copper. (Recalculating with 8 AWG yields a 3.12V drop, or 2.6%, which passes).

Worked Example 2: 240V Subpanel Feeder (4 AWG Copper)

Scenario: You are feeding a 60A subpanel in a garage for EV charging and shop tools. The voltage is 240V single-phase, the one-way run is 150 feet, and you are using 4 AWG copper SER cable. Does this meet the 3% feeder recommendation?

Step 1: Establish the target voltage drop.
Target VD = 240V × 0.03 = 7.2V.

Step 2: Calculate the actual drop.

  1. Identify variables: K = 12.9, I = 60A, L = 150 ft, CM = 41,740 (for 4 AWG).
  2. Plug into formula: VD = (2 × 12.9 × 60 × 150) / 41,740
  3. Multiply numerator: 2 × 12.9 × 60 × 150 = 232,200
  4. Divide by CM: 232,200 / 41,740 = 5.56V
  5. Calculate percentage: (5.56V / 240V) × 100 = 2.31%

Verdict: At 2.31%, the voltage drop is well under the 3% threshold. The 4 AWG copper feeder is correctly sized for this distance and load.

Common Unit Mistakes That Break the Math

When your calculated voltage drop looks wildly unrealistic (e.g., 400V drop on a 120V circuit), you have likely triggered one of these common unit errors:

  • Forgetting the '2' Multiplier: In single-phase AC and DC, current must travel to the load and return to the source. If you use '1' instead of '2', you are only calculating the drop on the hot wire and ignoring the neutral/return path, cutting your result in half.
  • Using Millimeters Squared (mm²) Instead of CM: The formula strictly requires Circular Mils. If you are using metric wire (e.g., 2.5 mm²), you must convert it first. The conversion factor is 1 mm² = 1,973.5 CM. Plugging '2.5' directly into the CM slot will result in a mathematically catastrophic overestimation of voltage drop.
  • Mixing Up One-Way Distance vs. Total Wire Length: The variable L represents the physical, one-way distance between the breaker and the receptacle. If you measure out 100 feet of wire and pull it through conduit, your total wire length is 200 feet (hot + neutral), but your L value for the formula is still just 100 feet because the '2' multiplier already accounts for the return path.
  • Using the Wrong 'K' Temperature Coefficient: Resistivity changes with heat. If you use the 20°C value for copper (K = 10.4) on a wire that will operate at 75°C inside a bundled conduit, your calculation will under-predict the voltage drop by roughly 20%. Always use 12.9 for copper and 21.2 for aluminum to match standard 75°C termination ratings.

Decision Tree: Picking the Right AWG for Your Run

Voltage drop calculations optimize performance, but they do not override thermal safety limits. You must always verify that your chosen wire meets the NFPA 70 (NEC) 310.16 ampacity requirements first. Once thermal ampacity is satisfied, use this decision matrix to finalize your wire size for a standard 120V, 20A single-phase branch circuit targeting a 3% maximum drop.

Table 2: Wire Sizing Decision Matrix (120V, 20A, Copper, 75°C)
One-Way Distance (L) Calculated VD with 12 AWG Required CM to meet 3% (3.6V) Concrete Wire Pick (AWG)
Under 50 ft 3.95V (3.2%) 6,388 CM 12 AWG (6,530 CM) - Passes
50 ft to 110 ft 7.90V to 17.3V (Fails) 7,166 to 15,766 CM 10 AWG (10,380 CM) up to 80ft
8 AWG (16,510 CM) up to 110ft
110 ft to 180 ft 17.3V to 28.4V (Fails) 15,766 to 25,796 CM 8 AWG (16,510 CM) up to 115ft
6 AWG (26,240 CM) up to 180ft

Default Recommendation: For any 120V, 20A residential branch circuit where the one-way run exceeds 50 feet, immediately skip 12 AWG and pull 10 AWG copper THHN. For runs exceeding 80 feet, pull 8 AWG copper. This default heuristic prevents you from failing an inspector's voltage drop inquiry and ensures sensitive electronics and motors receive clean, stable voltage. For exact custom distances outside this chart, rely on a trusted tool like the Southwire Voltage Drop Calculator to verify your manual math.