When sizing conductors for alternating current (AC) circuits, relying solely on breaker ampacity is a critical error. Long wire runs introduce resistance that causes voltage drop, leading to overheated motors, dim lighting, and tripped breakers. The direct answer to sizing wire for AC voltage drop relies on the Circular Mil (CM) formula. For a single-phase AC circuit, the required wire size in Circular Mils is calculated as CM = (2 × K × I × L) / VD. Once you calculate the CM value, you simply round up to the next standard American Wire Gauge (AWG) size and verify it against the NEC ampacity tables.
The Core AC Voltage Drop Formula and Symbol Definitions
To calculate the minimum wire cross-section required to keep voltage drop within acceptable limits (typically 3% for branch circuits, 5% total for feeder plus branch), we use the following single-phase formula:
CM = (2 × K × I × L) / VD
| Symbol | Definition | Standard Unit | Typical Value / Notes |
|---|---|---|---|
| CM | Circular Mils | cmil | Cross-sectional area of the wire. 14 AWG = 4,110 CM; 4/0 AWG = 211,600 CM. |
| K | Resistivity Constant | ohms·cmil/ft | 12.9 for Copper at 75°C; 21.2 for Aluminum at 75°C. |
| I | Current | Amperes (A) | The continuous or maximum expected load current, not the breaker rating. |
| L | Length | Feet (ft) | The strict one-way distance from the source (panel) to the load. |
| VD | Voltage Drop | Volts (V) | Maximum allowable drop. For 120V at 3%, VD = 3.6V. For 240V at 3%, VD = 7.2V. |
| 2 | Multiplier | Dimensionless | Accounts for the out-and-back path (Line and Neutral/Line) of a single-phase circuit. |
Rearranged Forms for Any Unknown Variable
While sizing wire (solving for CM) is the most common use case, bench testing and troubleshooting often require solving for a different variable. Here are the algebraically rearranged forms:
- Solve for Voltage Drop (VD):
VD = (2 × K × I × L) / CM
Use this to find the exact voltage lost across an existing wire run. - Solve for Current (I):
I = (VD × CM) / (2 × K × L)
Use this to find the maximum load a specific wire length can carry before exceeding your VD limit. - Solve for Length (L):
L = (VD × CM) / (2 × K × I)
Use this to find the maximum physical distance you can run a specific wire gauge for a given load.
When This Formula Applies (And When It Breaks)
This formula is highly accurate for standard residential and light commercial AC wiring, but it relies on specific assumptions. It assumes a steady-state single-phase AC load with a power factor near 1.0. It also intentionally ignores inductive reactance (the AC resistance caused by alternating magnetic fields). According to Mike Holt Enterprises' NEC voltage drop guidelines, ignoring reactance is perfectly valid for wire sizes 1/0 AWG and smaller installed in non-magnetic conduit (like PVC).
Unit Mistakes That Break the Calculation
The most common reason DIYers and junior electricians get wildly incorrect results is unit misalignment:
- The Length Trap: The formula requires the one-way distance. If you measure the total length of wire pulled from the spool (which includes both the hot and the neutral), you must drop the "2" multiplier from the formula, or your calculated CM will be double what it should be.
- Metric Mixing: This formula strictly uses Imperial units (feet, Circular Mils). If you attempt to plug in meters or square millimeters (mm²), the math collapses. (To convert mm² to CM, multiply by 1,973.5).
- Using Breaker Size for 'I': Plugging in a 20A breaker size when the actual continuous load is only 12A will result in massively oversized, expensive wire. Always use the actual calculated load.
Realistic Answer Magnitudes
If your final CM calculation yields a number like 45 or 300,000,000, you have a unit error. Realistic CM values for residential branch circuits and feeders fall strictly between 4,110 CM (14 AWG)211,600 CM (4/0 AWG).
Worked Example 1: 120V Dedicated Tool Circuit
Scenario: You are wiring a dedicated 120V outlet in a detached garage for a 15A continuous-duty air compressor. The one-way distance from the subpanel to the outlet is 120 feet. You are using 75°C rated copper THHN wire and want to limit voltage drop to 3%.
Step 1: Define the variables with units.
- K = 12.9 (Copper at 75°C)
- I = 15 A
- L = 120 ft
- VD = 120V × 0.03 = 3.6 V
Step 2: Plug into the formula and track units.
CM = (2 × 12.9 ohms·cmil/ft × 15 A × 120 ft) / 3.6 V
Step 3: Solve the numerator (out-and-back resistance factor).
Numerator = 2 × 12.9 × 15 × 120 = 46,440
Step 4: Divide by the denominator.
CM = 46,440 / 3.6 = 12,900 cmil
Result: You need a wire with at least 12,900 Circular Mils. Looking at the AWG chart, 10 AWG is only 10,380 CM, which is too small. You must step up to 8 AWG (16,510 CM).
Worked Example 2: 240V EV Charger Feeder
Scenario: You are installing a hardwired Level 2 EV charger rated for 48A continuous draw. The one-way run from the main panel to the garage is 150 feet. The nominal voltage is 240V, and you are using copper wire with a strict 3% maximum voltage drop limit.
Step 1: Define the variables.
- K = 12.9 (Copper)
- I = 48 A (The actual continuous load, not the 60A breaker it requires)
- L = 150 ft
- VD = 240V × 0.03 = 7.2 V
Step 2: Plug into the formula.
CM = (2 × 12.9 × 48 × 150) / 7.2
Step 3: Solve the numerator.
Numerator = 2 × 12.9 × 48 × 150 = 185,760
Step 4: Divide by the denominator.
CM = 185,760 / 7.2 = 25,800 cmil
Result: You need a minimum of 25,800 CM. Checking the standard wire table, 8 AWG (16,510 CM) and 6 AWG (26,240 CM) are the closest. Since 25,800 exceeds 8 AWG, the mathematical pick is 6 AWG (26,240 CM).
Decision Path: From Calculated CM to Final AWG Pick
Once your calculator spits out a CM value, use this decision-tree-table to lock in your exact wire gauge and verify the physical constraints. This path terminates in a concrete part selection.
| Calculated CM Range | Minimum AWG Required | Standard CM Value | Max Breaker (Copper 75°C) | Concrete Action |
|---|---|---|---|---|
| 0 to 4,110 | 14 AWG | 4,110 | 15A | Buy 14 AWG. Verify load is ≤ 12A continuous. |
| 4,111 to 6,530 | 12 AWG | 6,530 | 20A | Buy 12 AWG. Verify load is ≤ 16A continuous. |
| 6,531 to 10,380 | 10 AWG | 10,380 | 30A | Buy 10 AWG. Standard for 30A dryer/RV outlets. |
| 10,381 to 16,510 | 8 AWG | 16,510 | 40A / 50A* | Buy 8 AWG. *50A only if rated for 75°C terminations. |
| 16,511 to 26,240 | 6 AWG | 26,240 | 55A / 60A | Buy 6 AWG. Ideal for 48A continuous EV chargers. |
| 26,241 to 41,740 | 4 AWG | 41,740 | 70A / 85A | Buy 4 AWG. Common for 100A subpanel feeds (derated). |
Sizing Verification and NEC Ampacity Check
The voltage drop formula dictates the minimum wire size to maintain power quality, but it does not override fire safety codes. Your final step is an absolute verification against manufacturer ampacity charts and NEC Table 310.16.
If your voltage drop calculation demands 10 AWG wire, but your breaker is sized at 40A, the 10 AWG wire will melt before the breaker trips. The rule is rigid: The wire's allowable ampacity must always be greater than or equal to the breaker rating, regardless of what the voltage drop formula suggests. If the voltage drop formula yields a wire size smaller than the breaker's required ampacity, you must discard the voltage drop result and size the wire strictly to the breaker. If the voltage drop formula yields a wire size larger than the breaker requires, you must buy the larger wire. Always pick the larger of the two requirements, terminate it correctly, and torque the lugs to the manufacturer's specified inch-pound rating.
