If you are sizing conductors for a 240V single-phase circuit, the direct answer to your voltage drop problem relies on the Circular Mil (CM) formula: CM = (2 × K × I × L) / V_d. To keep voltage drop under the NEC-recommended 3% limit for branch circuits (7.2V on a 240V system), you must calculate the required circular mils and map that to the nearest standard AWG size. Relying purely on ampacity tables without running this math is how you end up with dimming lights and stalled compressor motors at the end of a long run.
The Core AC 240V Wire Sizing Formula (And What Every Symbol Means)
The standard formula used in NEC Chapter 9 for single-phase AC voltage drop derives from Ohm's Law, adjusted for the physical geometry of the wire and the fact that current must travel to the load and return to the panel. Here is the master equation:
CM = (2 × K × I × L) / V_d
| Symbol | Definition | Standard Value / Unit |
|---|---|---|
| CM | Circular Mils (cross-sectional area of the wire) | cmil (Look up in NEC Chapter 9, Table 8) |
| 2 | Multiplier for single-phase AC (out and return path) | Dimensionless constant |
| K | DC resistivity constant of the conductor material at a specific temperature | 12.9 for Copper / 21.2 for Aluminum (at 75°C) |
| I | Load current (use 125% of continuous load per NEC 210.20) | Amperes (A) |
| L | One-way length of the circuit from panel to load | Feet (ft) |
| V_d | Allowable voltage drop (typically 3% of 240V = 7.2V) | Volts (V) |
Rearranged Forms: Solving for Any Variable
On the bench or in the field, you rarely just solve for wire size. Often, you already have the wire in your truck and need to know how far you can run it, or you need to verify the maximum load a buried feeder can handle. Here are the rearranged forms:
- Solving for Maximum Current (I): I = (CM × V_d) / (2 × K × L)
- Solving for Maximum Length (L): L = (CM × V_d) / (2 × K × I)
- Solving for Actual Voltage Drop (V_d): V_d = (2 × K × I × L) / CM
- Solving for Material Constant (K): K = (CM × V_d) / (2 × I × L) (Useful for verifying conductor purity or temperature derating)
Worked Example 1: Sizing a 40A 240V EV Charger Feed
Let us size the THHN copper conductors for a Level 2 EV charger. The charger draws a continuous 32A, but NEC Article 210.20 requires us to size the conductors and breaker at 125% of the continuous load. Therefore, our design current (I) is 40A. The run from the main panel to the garage subpanel is 150 feet.
- Define the target voltage drop: 3% of 240V = 7.2V.
- Plug values into the master formula:
CM = (2 × 12.9 × 40A × 150ft) / 7.2V - Track the units in the numerator:
2 (dimensionless) × 12.9 (Ω·cmil/ft) × 40 (A) × 150 (ft)
The 'ft' cancels out. Ohms (Ω) × Amps (A) = Volts (V).
Numerator = 154,800 V·cmil. - Divide by the denominator:
CM = 154,800 V·cmil / 7.2 V = 21,500 cmil. - Select the wire size: Looking at NEC Chapter 9 Table 8, 8 AWG is 16,510 cmil (too small). 6 AWG is 26,240 cmil. Therefore, you must pull 6 AWG copper.
Worked Example 2: Finding Maximum Run Length for a 50A Welder
You have a spool of 8 AWG copper wire left over, and you want to install a 240V receptacle for a MIG welder. The welder's nameplate dictates a 50A breaker. Because welders are intermittent, NEC Article 630 allows specific duty-cycle derating, but for a conservative worst-case feeder calculation, we will use the full 50A. We will allow a 5% voltage drop (12V) at the receptacle, as feeders and branch circuits combined can drop up to 5% under NEC informational notes.
- Identify knowns: CM for 8 AWG = 16,510 cmil. V_d = 12V. I = 50A. K = 12.9.
- Use the rearranged length formula:
L = (CM × V_d) / (2 × K × I) - Calculate the numerator:
16,510 cmil × 12 V = 198,120 V·cmil. - Calculate the denominator:
2 × 12.9 (Ω·cmil/ft) × 50 A = 1,290 Ω·cmil·A / ft (which simplifies to V·cmil/ft). - Divide to find Length:
L = 198,120 / 1,290 = 153.58 feet.
Your maximum one-way run length for this 8 AWG setup is roughly 153 feet. Anything longer, and the voltage drop exceeds 5% under full 50A load.
Real-World Scenario: The 100A Subpanel Voltage Drop Disaster
Formulas are clean; jobsites are not. Here is a scenario that highlights what happens when the math is misunderstood.
The Setup: A homeowner wanted to power a detached workshop with a 100A subpanel. The trench was 200 feet long. They used an online calculator but misunderstood the inputs, ultimately purchasing and burying 200 feet of 4 AWG copper USE-2 wire, assuming it was massive enough to handle 100A easily (4 AWG is rated for 85A at 75°C, but they upped the breaker to 100A based on a misreading of the 240.4(B) next-size-up rule, ignoring the termination limits).
The Numbers: Let us calculate the actual voltage drop on that 4 AWG wire (41,740 cmil) at a full 100A load.
V_d = (2 × 12.9 × 100A × 200ft) / 41,740 cmil
V_d = 516,000 / 41,740 = 12.36 Volts.
The Outcome: A 12.36V drop on a 240V system is a 5.15% drop. When the homeowner turned on the table saw and the air compressor simultaneously, the voltage at the subpanel sagged below 225V. The compressor motor stalled, tripped its internal thermal overload, and the LED shop lights flickered violently.
What Went Wrong: The homeowner manually calculated the wire size before buying, but they forgot the '2' multiplier in the numerator. They used the DC formula (CM = K × I × L / V_d), calculating for only the outbound wire and ignoring the return path. Their flawed math yielded a requirement of 35,833 cmil, making 4 AWG look perfectly adequate. Had they used the correct single-phase AC formula, they would have found they needed 71,666 cmil, which requires upgrading to 1 AWG copper (83,690 cmil) or using 1/0 AWG aluminum to stay under the 3% drop target.
Unit Mistakes That Break the Math (And Realistic Magnitudes)
When using a wire size calculator for AC 240V, the math will fail catastrophically if you feed it the wrong units. Here are the most common traps:
- Meters vs. Feet: The constant K=12.9 is strictly calibrated for feet. If your tape measure gave you 60 meters, and you plug '60' into the L variable, your calculated wire size will be roughly 3.28 times too small. Always convert meters to feet (multiply by 3.28084) before using the standard K constant.
- mm² vs. Circular Mils: European and metric calculators use square millimeters (mm²). The NEC uses Circular Mils. 1 mm² is approximately 1,973.5 cmil. If a calculator asks for area and you input '10' thinking of 10 mm², but the formula expects cmil, the output will be nonsensical.
- Line-to-Line vs. Line-to-Neutral: In a 240V split-phase system, a pure 240V load (like a water heater) uses two hot legs. The '2' in our formula accounts for the out-and-back on those two hots. If you are calculating a 120V branch circuit off that same panel, your V_d target is 3.6V (3% of 120V), but the formula structure remains the same.
What does a realistic answer magnitude look like?
If your calculator spits out a CM value, you need a mental sanity check. Refer to this baseline from NEC Chapter 9 Table 8:
- 14 AWG: 4,110 cmil
- 10 AWG: 10,380 cmil
- 6 AWG: 26,240 cmil
- 2 AWG: 66,360 cmil
- 4/0 AWG: 211,600 cmil
If your calculation demands 450,000 cmil, you have exceeded the physical limits of standard single-conductor AWG sizing. You must now transition to kcmil (thousands of circular mils) wire, or parallel two smaller conductors (e.g., two runs of 250 kcmil) per NEC 310.10(G). According to the Copper Development Association, stepping up to larger diameters drastically alters the K constant slightly due to skin effect and stranding, but for standard residential and light commercial 240V runs under 400A, the 12.9 constant remains your most reliable bench tool.
