How Is Voltage Drop Calculated? Formula, Worked Examples, and Wire Sizing

If you need to know how voltage drop is calculated for a DC or single-phase AC circuit, the direct answer is the standard approximate formula: V_d = (2 × K × I × L) / CM. This equation balances the resistivity of your conductor material against the physical distance and the current draw to tell you exactly how many volts will be lost as heat before reaching the load.

While software and online calculators can spit out an answer in milliseconds, relying on them without understanding the underlying math is how you end up with undersized feeders, dimming lights, and tripped breakers under load. Below is the complete derivation, reference data, and step-by-step worked examples with explicit unit tracking so you can verify your own bench and jobsite calculations.

The Core Voltage Drop Formula and Symbol Definitions

The formula used for standard single-phase AC and DC voltage drop calculations is derived directly from Ohm’s Law (V = I × R), expanded to account for the physical dimensions and material properties of the wire.

Every symbol in this equation represents a specific physical property. If you swap the wrong value into the wrong slot, your calculation will fail silently, giving you a mathematically correct but physically dangerous answer.

Essential Reference Data: Circular Mils and Resistivity Constants

You cannot solve the formula without the correct CM and K values. The National Electrical Code (NEC) Chapter 9, Table 8 provides the exact cross-sectional area for standard wire gauges. The K factor is derived from the material's resistivity; for copper at 75°C, K is approximately 12.9, and for aluminum, it is 21.2 (Engineering Toolbox).

Keep this data-dense table on hand when sizing branch circuits and feeders. Note that these values assume standard stranded or solid copper conductors at an operating temperature of 75°C.

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

On the jobsite, you rarely solve for V_d directly. Usually, the voltage drop limit is dictated by code or equipment requirements, and you need to find the physical constraints. Here are the algebraic rearrangements of the core formula:

• Solving for Wire Size (CM): Use this when you know your load, distance, and maximum allowable drop, and need to pick an AWG size.
  CM = (2 × K × I × L) / Vd
• Solving for Maximum Distance (L): Use this when placing a subpanel or remote outlet to find the maximum run length before you must upsize the wire.
  L = (Vd × CM) / (2 × K × I)
• Solving for Maximum Current (I): Use this to verify if an existing wire run can handle a new piece of equipment without exceeding voltage drop limits.
  I = (Vd × CM) / (2 × K × L)

Worked Examples with Unit Tracking

Abstract formulas are useless if you don't track your units. Let's walk through two real-world scenarios, explicitly showing how the units cancel out to leave you with Volts or Circular Mils.

Problem 1: Calculating Drop on an Existing 120V Branch Circuit

Scenario: You are powering a 15A continuous load (like a space heater or server rack) located 80 feet from the panel. The circuit is wired with 12 AWG copper wire. What is the voltage drop, and does it meet the NEC 3% recommendation?

1. Identify Variables:
   K = 12.9 Ω·cmil/ft (Copper)
   I = 15 A
   L = 80 ft
   CM = 6,530 cmil (12 AWG from reference table)
2. Set Up the Equation with Units:
   V_d = [ 2 × (12.9 Ω·cmil/ft) × 15 A × 80 ft ] / 6,530 cmil
3. Calculate the Numerator:
   2 × 12.9 × 15 × 80 = 30,960 (Ω·cmil·A)
   Note: The 'ft' in the denominator of K cancels with the 'ft' in L.
4. Divide by the Denominator:
   V_d = 30,960 / 6,530 = 4.74 V
   Note: The 'cmil' cancels out. We are left with Ω × A, which equals Volts (Ohm's Law).
5. Calculate Percentage:
   (4.74 V / 120 V) × 100 = 3.95%

Problem 2: Sizing a 240V Feeder for a Subpanel

Scenario: You are running a 240V single-phase feeder to a detached garage subpanel. The calculated continuous load is 40A, and the one-way distance is 150 feet. You want to limit the voltage drop to exactly 3% (7.2V). What size copper wire do you need?

1. Identify Variables:
   V_d = 7.2 V (3% of 240V)
   K = 12.9 Ω·cmil/ft
   I = 40 A
   L = 150 ft
2. Use the Rearranged Formula for CM:
   CM = (2 × K × I × L) / V_d
3. Calculate the Numerator:
   2 × 12.9 × 40 × 150 = 154,800
4. Divide by Target Voltage Drop:
   CM = 154,800 / 7.2 = 21,500 cmil
5. Select Wire Size:
   Looking at our reference table, 8 AWG is only 16,510 cmil (too small). 6 AWG is 26,240 cmil, which safely exceeds our 21,500 cmil requirement.

Assumptions, Unit Traps, and Realistic Magnitudes

The formula V_d = (2 × K × I × L) / CM is an approximation. It is highly accurate for most residential and light commercial work, but it relies on specific assumptions. Ignoring these assumptions is where DIYers and junior electricians make critical errors.

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

This formula assumes a DC circuit or a single-phase AC circuit where the power factor is close to 1.0 (purely resistive loads like heaters or incandescent lighting). It also assumes the wire is smaller than 1/0 AWG.

For conductors 1/0 AWG and larger, or when wires are pulled through steel conduit, inductive reactance (X_L) and the skin effect become significant. The AC resistance is higher than the DC resistance. In those cases, you must use the exact vector formula: Vd = I × (R cosθ + X sinθ) × 2 × L, referencing the AC resistance and reactance tables in NEC Chapter 9, Table 9.

Unit Mistakes That Break the Math

• Using Total Length Instead of One-Way Length: The '2' in the numerator accounts for the hot wire out and the neutral/ground wire back. If you measure 80 feet of trench and plug 160 feet into 'L' (thinking you need to account for both wires), you will double your calculated voltage drop and buy wire that is massively oversized.
• Plugging in the AWG Number: I have seen apprentices plug "12" into the CM slot because they are using 12 AWG wire. This results in a calculated voltage drop in the thousands of volts. Always use the Circular Mils value (6,530 for 12 AWG).
• Mixing K-Factors: Using the Copper K (12.9) when calculating for Aluminum SER cable (which requires K = 21.2). Aluminum has higher resistivity; using the copper constant will result in an undersized, dangerous aluminum feeder.

What a Realistic Answer Magnitude Looks Like

According to NFPA 70 (NEC) Informational Notes, the recommended maximum voltage drop is 3% for the farthest outlet on a branch circuit, and 5% total for the feeder and branch circuit combined.

• On a 120V circuit: 3% is 3.6V. If your math yields a 15V drop, you either made a calculation error, or you are about to start a fire.
• On a 240V circuit: 3% is 7.2V.
• On a 12V DC solar system: 3% is 0.36V. This is why 12V DC systems require massive, expensive wire for anything more than a few feet of run. The allowable V_d is tiny, forcing the CM (wire size) to be huge.

Always verify your final calculated voltage against the nominal source. If your calculated drop leaves the load with less voltage than its nameplate minimum tolerance (usually -10% for motors and compressors), the equipment will draw excess amperage to compensate for the missing wattage, leading to thermal overload and premature failure. Do the math, track your units, and size the wire for the distance, not just the breaker.