Voltage Drop Calculation Cable Sizing: Formulas and Worked Examples

The standard single-phase voltage drop calculation cable formula is VD = (2 × K × I × L) / CM. If you are sizing a 120V, 15A branch circuit running 100 feet using 14 AWG copper wire, the calculated voltage drop is 9.41V (7.8%). This immediately tells you the wire is undersized, as it violates the NEC recommendation of a maximum 3% drop for branch circuits. To fix it, you must rearrange the formula to solve for Circular Mils (CM) and step up to 10 AWG or 8 AWG. Below is the complete derivation, symbol breakdown, and real-world application of this essential electrical formula.

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

Before you can size a feeder or branch circuit, you must understand the physics of the voltage drop calculation cable equation. The formula calculates the exact number of volts lost as current pushes through the resistance of a conductor over a specific distance. For single-phase AC or DC circuits, the formula is:

Here is the exact definition of every symbol used in the equation, including the assumptions baked into the constants:

The constant K represents the resistance of a 1-foot length of wire with a cross-sectional area of 1 circular mil at a specific temperature. We use 12.9 for copper and 21.2 for aluminum based on a 75°C operating temperature, which aligns with the ampacity columns used for most modern THHN and NM-B terminations.

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

On the jobsite, you rarely use the formula to find the voltage drop itself. Usually, you know your maximum allowable drop (e.g., 3.6V on a 120V circuit) and need to find the required wire size. By applying basic algebra, we can isolate any variable in the voltage drop calculation cable 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 Chapter 9, 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 determine the maximum load an existing buried cable can handle without excessive drop.
• Three-Phase Adjustment: For 3-phase circuits, replace the 2 in the numerator with √3 (1.732). The rearranged forms remain identical, just swap the multiplier.

Worked Examples: From Basic Branch Circuits to Long Feeder Runs

Abstract formulas are useless without unit tracking. Let us walk through two distinct scenarios, showing every intermediate step and how the units cancel out to leave us with Volts or Circular Mils.

Problem 1: Finding the Voltage Drop on an Existing 14 AWG Circuit

Setup: You have a 120V single-phase branch circuit supplying a 15A non-continuous receptacle load. The one-way distance is 100 feet. The wire is 14 AWG solid copper.

1. Identify Knowns: K = 12.9, I = 15A, L = 100 ft. From NEC Chapter 9 Table 8, the CM for 14 AWG is 4,110.
2. Plug into Formula: VD = (2 × 12.9 × 15 × 100) / 4,110
3. Calculate Numerator: 2 × 12.9 × 15 × 100 = 38,700 (Unit tracking: Ω·cmil/ft × A × ft = Ω·A·cmil, which simplifies to V·cmil)
4. Divide by CM: 38,700 / 4,110 = 9.41 Volts
5. Calculate Percentage: (9.41V / 120V) × 100 = 7.84%

Verdict: A 7.84% drop vastly exceeds the NEC Informational Note recommendation of 3%. You must upsize the wire.

Problem 2: Sizing a Feeder for a 240V Load

Setup: You are running a 240V, 30A continuous load (like an EV charger) to a detached garage 150 feet away. You want to limit the voltage drop to exactly 3%.

1. Identify Knowns: K = 12.9 (Copper), I = 30A (Note: for continuous loads, some engineers calculate drop at 125% of the load, but NEC 210.19(A)(IN4) calculates drop based on the actual load current of 30A), L = 150 ft. Max VD = 3% of 240V = 7.2V.
2. Rearrange for CM: CM = (2 × K × I × L) / VD
3. Plug in Values: CM = (2 × 12.9 × 30 × 150) / 7.2
4. Calculate Numerator: 2 × 12.9 × 30 × 150 = 116,100
5. Divide by VD: 116,100 / 7.2 = 16,125 CM

Verdict: Looking at NEC Chapter 9, Table 8, 10 AWG is only 10,380 CM (too small). 8 AWG is 16,510 CM. Therefore, 8 AWG copper is the minimum size required to keep the drop under 3%.

Real-World Scenario Walkthrough: The 240V Well Pump Failure

Formulas assume steady-state resistive loads, but motors introduce complex physics. Here is a real-world bench-to-jobsite scenario where ignoring the nuances of the voltage drop calculation cable formula resulted in a burned-out motor.

The Numbers: Let us run the math on the running load.
VD = (2 × 12.9 × 20 × 250) / 10,380 (CM for 10 AWG).
VD = 129,000 / 10,380 = 12.4 Volts.
This is a 5.1% drop. While high, the pump might still run once spinning.

The Outcome: When the pressure switch closed, the pump hummed loudly, failed to spin, and tripped the thermal overload after 10 seconds. The DIYer assumed the pump was defective.

What Went Wrong: The formula was applied to the running current (FLA), but motors draw Locked Rotor Amps (LRA) during startup. For this pump, the LRA was 65A. If we plug 65A into the formula, the startup voltage drop spikes to 40.4 Volts. The voltage at the motor terminals during startup dropped to 199V. Because motor starting torque is proportional to the square of the voltage (T ∝ V²), the 17% voltage sag resulted in a 31% loss of starting torque. The motor physically could not overcome the hydraulic head pressure to start spinning. The fix required upsizing the cable to 6 AWG copper to mitigate the startup drop and installing a soft-start controller.

Assumptions, Unit Traps, and Realistic Magnitudes

To use this formula safely and accurately, you must understand its boundaries. The National Electrical Code provides the framework, but the math requires strict discipline.

When the Formula Applies (and Its Assumptions)

This formula is derived from Ohm’s Law (V = I × R) and assumes a steady-state DC load or a single-phase AC load operating at or very near a unity power factor (1.0). For highly inductive loads (like large transformers or uncorrected fluorescent lighting banks) where the power factor drops below 0.85, this formula will slightly under-calculate the actual voltage drop because it ignores the reactive component (Reactance, X) of the cable impedance. For standard residential NM-B and THHN runs under 250 feet, the error margin is negligible and universally accepted by inspectors.

Unit Mistakes That Break the Math

• The "One-Way" vs "Loop" Trap: The 2 in the formula accounts for the hot and the neutral (the out-and-back loop). If you measure the total physical length of the wire spool used (e.g., 200 feet of 10/2 cable), your L is 100 feet, not 200. Entering the total wire length instead of the one-way distance will double your calculated drop and cause you to overspend on copper.
• Metric Confusion: This formula is strictly for Imperial units (feet, circular mils). If you are working with metric cable sizes (mm²), you cannot use Circular Mils. You must convert mm² to CM (1 mm² = 1,973.5 CM) or use the metric equivalent formula: VD = (2 × ρ × I × L) / A, where ρ is resistivity in Ω·m and A is area in mm².
• Temperature Derating: The K constant of 12.9 assumes 75°C. If your wire is running through a 120°F attic, the resistance increases. For precise engineering in high-ambient environments, increase K by roughly 10% to account for the thermal coefficient of copper.

What a Realistic Answer Magnitude Looks Like

When you finish your calculation, sanity-check the result against real-world baselines. A healthy 120V branch circuit should show a calculated drop between 1.5V and 3.6V (1.25% to 3%). If your math spits out a 0.2V drop on a 20A circuit, you likely forgot a zero in your CM value. If it spits out a 25V drop, you either entered the distance in inches instead of feet, or you are trying to pull 50A through 14 AWG wire. Always verify your final AWG selection against NEC Article 310 ampacity tables; voltage drop calculations can dictate a larger wire, but they can never override the minimum ampacity requirements for breaker sizing and overcurrent protection.