If you are sizing a feeder or running a long branch circuit, the fundamental single-phase voltage drop formula you need is VD = (2 × K × I × L) / CM. Guessing wire sizes based purely on ampacity tables will leave you with dim lights, tripping breakers, and overheated motors at the end of a long run. To design reliable circuits, you must calculate the exact voltage lost as heat in the conductors.

Below, we break down the core voltage drop formulas, rearrange them for practical wire sizing, and walk through solved problems with strict unit tracking so you can confidently size your next project.

The Core Voltage Drop Formulas and Symbol Definitions

The standard formulas used in NEC-style calculations (specifically referencing the informational notes in NFPA 70 Article 210.19) rely on the basic physics of resistance. For direct current (DC) and single-phase alternating current (AC) with a high power factor, the formula is:

Single-Phase / DC: VD = (2 × K × I × L) / CM

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

Every symbol in these equations represents a specific physical property or measurement. Mixing up the units here is the most common reason calculations fail on the bench.

Symbol Definition Standard Unit / Value
VD Voltage Drop (the absolute voltage lost in the wire) Volts (V)
2 Multiplier for the out-and-back return path in single-phase/DC Dimensionless constant
√3 Multiplier for 3-phase systems (approx. 1.732) Dimensionless constant
K Specific resistance of the conductor material at a specific temperature Ohm-circular mils per foot (Ω·cmil/ft)
I Current flowing through the circuit Amperes (A)
L One-way length of the circuit from source to load Feet (ft)
CM Circular Mils (the cross-sectional area of the wire) Circular Mils (cmil)

Note on K values: At the standard 75°C operating temperature column used for most THHN/NM-B sizing, K = 12.9 for Copper and K = 21.2 for Aluminum. If you are calculating for cold wire (20°C), K drops to 10.8 for copper, but using the 75°C value is the safer, code-compliant assumption for loaded circuits.

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

On the jobsite, you rarely need to find the voltage drop of an existing wire; you usually know your maximum allowable drop and need to find the right wire size. By algebraically rearranging the single-phase formula, we get three highly practical variations:

  1. Solving 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 size in NEC Chapter 9, Table 8.
  2. Solving for Maximum Length (L): L = (CM × VD) / (2 × K × I)
    Use this to find how far you can run a specific wire gauge before exceeding your drop limit.
  3. Solving for Maximum Current (I): I = (CM × VD) / (2 × K × L)
    Use this to determine the maximum safe load for an existing buried feeder of known length and gauge.

Worked Examples with Strict Unit Tracking

Let’s run two scenarios. We will track every unit to ensure the math holds up. According to Fluke's electrical testing guidelines, maintaining voltage within 3% to 5% of nominal is critical for equipment longevity.

Problem 1: Calculating Voltage Drop on an Existing Branch Circuit

Given: A 120V single-phase circuit using 12 AWG copper wire (THHN). The one-way length (L) is 80 feet. The continuous load current (I) is 15 Amps. Find the voltage drop (VD) and the percentage drop.

  1. Identify Constants: K = 12.9 (Copper at 75°C). From NEC Chapter 9, Table 8, the Circular Mils (CM) for 12 AWG is 6,530 cmil.
  2. Plug into Formula: VD = (2 × 12.9 × 15 × 80) / 6530
  3. Calculate Numerator: 2 × 12.9 = 25.8. → 25.8 × 15 = 387. → 387 × 80 = 30,960
  4. Divide by Denominator: 30,960 / 6,530 = 4.74 Volts
  5. Calculate Percentage: (4.74V / 120V) × 100 = 3.95%

Result: A 3.95% drop exceeds the NEC's recommended 3% maximum for branch circuits. You should upsize to 10 AWG (10,380 cmil) to bring the drop down to 2.5%.

Problem 2: Sizing Wire for a New 240V Feeder

Given: A 240V single-phase subpanel feeder. The maximum load (I) is 30 Amps. The one-way distance (L) is 150 feet. We want a maximum voltage drop of 3%.

  1. Calculate Target VD: 3% of 240V = 7.2 Volts.
  2. Identify Constants: K = 12.9 (Copper).
  3. Use Rearranged Formula for CM: CM = (2 × K × I × L) / VD
  4. Plug in Values: CM = (2 × 12.9 × 30 × 150) / 7.2
  5. Calculate Numerator: 2 × 12.9 × 30 × 150 = 116,100
  6. Divide by VD: 116,100 / 7.2 = 16,125 cmil

Result: We need a wire with at least 16,125 Circular Mils. Checking the AWG table: 10 AWG is 10,380 cmil (too small). 8 AWG is 16,510 cmil. Therefore, 8 AWG copper is the minimum required size to maintain a 3% drop.

Real-World Scenario: The 240V Well Pump Feeder Mistake

Scenario Setup: A DIYer runs a 240V single-phase feeder to a 1.5 HP well pump located 250 feet from the main panel. The pump’s nameplate lists a Full Load Amps (FLA) of 10A. The builder uses the formula to size for 10A at a 3% drop (7.2V) and calculates a requirement of roughly 10,750 cmil. They install 10 AWG copper wire (10,380 cmil), which is close enough and rated for 30A.

The Numbers (Steady State):
Once the pump is running at 10A, the voltage drop is:
VD = (2 × 12.9 × 10 × 250) / 10380 = 6.21 Volts (2.5% drop).
The system appears to be working perfectly on paper.

The Outcome and What Went Wrong:
When the pump tries to start, the motor draws Locked Rotor Amps (LRA), which for this 1.5 HP pump is 45 Amps. During the 2-second startup phase, the voltage drop spikes massively:
VD = (2 × 12.9 × 45 × 250) / 10380 = 27.96 Volts.

The voltage at the pump terminals momentarily sags to 212V (240V - 27.96V). Because AC motor starting torque is proportional to the square of the voltage, this 11.6% voltage sag causes a 22% loss in starting torque. The pump fails to overcome the static head pressure of the well, stalls, continues drawing 45A, overheats the windings, and eventually trips the breaker or destroys the motor.

The Fix: The builder failed to account for transient starting currents. To fix this, they must either upsize the wire to 6 AWG (26,240 cmil) to keep startup drop under 5%, or install a soft-start device at the well head to limit the inrush current. Tools like the Southwire Voltage Drop Calculator can help verify these complex scenarios, but they still require you to input the correct starting current, not just the running current.

Assumptions, Unit Traps, and Realistic Magnitudes

The formulas above are highly accurate for typical residential and light commercial wiring, but they rely on specific assumptions. Ignoring these assumptions or falling for common unit traps will yield useless data.

When the Formula Applies (and When it Doesn't)

  • High Power Factor: The standard K constant assumes the load has a power factor (PF) near 1.0 (like resistive heating or incandescent lighting). If you are running long feeders to large inductive loads (like big HVAC compressors) with a low PF, the reactive component of impedance (X) matters. For conductors larger than 1/0 AWG, you must use the full AC impedance formula: VD = I × (R cosθ + X sinθ) × L, pulling R and X values from NEC Chapter 9, Table 9.
  • Steady-State Temperatures: The K=12.9 value assumes the wire is operating at 75°C. If the wire is in a freezing environment and lightly loaded, its actual resistance will be lower, meaning your real-world voltage drop will be slightly less than calculated.

Unit Mistakes That Break the Math

  • Using AWG instead of CM: Plugging '12' into the denominator instead of '6530' will result in a calculated voltage drop that is hundreds of times too high. Always convert AWG to Circular Mils.
  • Forgetting the '2' Multiplier: In single-phase and DC circuits, current must travel to the load and return to the source. If you use the physical length of the cable without multiplying by 2 (or without using the formula that explicitly includes the 2), you are only calculating the drop on the hot leg, ignoring the neutral.
  • Mixing Metric and Imperial: The K values of 12.9 and 21.2 are strictly for feet and circular mils. If you measure your run in meters, you must convert to feet (multiply by 3.281) before plugging into this specific formula.

What a Realistic Answer Magnitude Looks Like

When you finish your calculation, do a quick sanity check on the magnitude. For a standard 120V branch circuit, a 3% drop is 3.6 Volts. For a 240V feeder, a 3% drop is 7.2 Volts.

If your math spits out 0.04V, you likely forgot to multiply by the current or length. If your math spits out 45V on a 120V circuit, you either used the AWG number instead of Circular Mils, or you are attempting to push 50 Amps through 14 AWG wire (which would melt the insulation long before the voltage drop mattered). Keep your expected magnitudes in the single digits for standard residential runs, and always verify your dead circuit with a multimeter before terminating.