Calculating Voltage Drop: Formula Derivation, Worked Examples, and Unit Traps

When calculating voltage drop for single-phase AC or DC circuits, the standard approximate formula is VD = (2 × K × I × L) / CM. This equation tells you exactly how many volts are lost as heat across a wire run before the power reaches your load. The National Electrical Code (NEC) recommends keeping this drop under 3% for branch circuits and 5% total for feeders and branches combined to ensure equipment operates efficiently.

While modern apps and online calculators can do the math for you, understanding the derivation, the assumptions baked into the constants, and how to rearrange the formula is what separates a parts-changer from a competent electrician. Below is the complete breakdown of the math, the unit traps that cause failed inspections, and a real-world scenario where ignoring this formula resulted in a bricked EV charging session.

The Core Voltage Drop Formula and Symbol Definitions

The formula below is derived directly from Ohm’s Law (V = I × R), substituting the physical properties of the wire for resistance. It applies to single-phase AC and DC circuits. For three-phase systems, the multiplier '2' is replaced by the square root of 3 (1.732).

Symbol	Definition & Units	Notes & Standard Values
VD	Voltage Drop (Volts)	The actual volts lost across the entire circuit loop.
2	Multiplier (Dimensionless)	Accounts for the out-and-back path (Line and Neutral/Equipment Ground) in single-phase/DC.
K	Resistivity Constant (Ohm-CM/ft)	12.9 for Copper, 21.2 for Aluminum at 75°C operating temp.
I	Current (Amperes)	The actual continuous load current, not the breaker size.
L	One-way Length (Feet)	Distance from the source breaker to the load. Do not double this.
CM	Circular Mils (Area)	Cross-sectional area of the wire. (e.g., 10 AWG = 10,380 CM).

When the Formula Applies and Its Assumptions

This formula is an approximation that assumes a steady-state DC or single-phase AC load. It intentionally ignores AC reactance (the magnetic resistance caused by alternating current). For wires 2 AWG and smaller, reactance is negligible, and this formula is highly accurate. For wires 1 AWG and larger, AC reactance begins to dominate, and you must use the complex impedance formula (Z = R cosθ + X sinθ) found in NEC Chapter 9, Table 9.

Furthermore, the K constant of 12.9 assumes the copper wire is operating at 75°C. At room temperature (20°C), copper's K is actually 10.8. However, wires heat up under load. Using 12.9 builds in a safety margin that reflects real-world operating temperatures inside a conduit or bundled cable.

Rearranging the Equation: Solving for Wire Size, Distance, and Current

On the jobsite, you rarely solve for VD. Usually, you know your maximum allowable voltage drop (e.g., 3% of 240V = 7.2V) and need to find the minimum wire size (CM) or the maximum distance (L) you can run. Here are the algebraically rearranged forms:

• To find Wire Size (CM): CM = (2 × K × I × L) / VD
  Use this to size a wire when you know the load, distance, and maximum acceptable drop.
• To find Maximum Distance (L): L = (VD × CM) / (2 × K × I)
  Use this to see how far you can push a specific wire gauge before violating the 3% rule.
• To find Maximum Current (I): I = (VD × CM) / (2 × K × L)
  Use this to determine if an existing wire run can handle a new piece of equipment.
• To find the K Constant: K = (VD × CM) / (2 × I × L)
  Mostly used in forensics to determine if a wire is overheating or if the terminations are corroded (which artificially raises K).

Solved Problems: Step-by-Step Calculations with Unit Tracking

Let’s run through two common scenarios. Pay close attention to the unit tracking; dropping a unit is the most common reason these calculations fail.

Problem 1: 120V Branch Circuit for a Workshop Receptacle

Scenario: You are running a 120V, 15A continuous load (a space heater and power tools) to a workshop 100 feet away from the panel using 12 AWG copper THHN wire.

1. Identify Variables:
   • K = 12.9 (Copper at 75°C)
   • I = 15 Amps
   • L = 100 Feet
   • CM = 6,530 (Standard Circular Mils for 12 AWG)
2. Substitute into Formula:
   • VD = (2 × 12.9 × 15 × 100) / 6,530
3. Calculate Numerator:
   • 2 × 12.9 = 25.8
   • 25.8 × 15 = 387
   • 387 × 100 = 38,700
4. Divide by CM:
   • VD = 38,700 / 6,530 = 5.92 Volts
5. Check Percentage:
   • 5.92V / 120V = 4.93%

Verdict: A 4.93% drop exceeds the 3% NEC recommendation for a branch circuit. Your tools will run hot and slow. Fix: Upsize to 10 AWG (10,380 CM), which drops the VD to 3.72V (3.1%), or 8 AWG (16,510 CM) for a 2.34V drop (1.95%).

Problem 2: 240V Feeder to a Detached Garage Subpanel

Scenario: You are feeding a subpanel with a 40A continuous load over a 150-foot underground PVC conduit using 6 AWG copper THHN.

1. Identify Variables:
   • K = 12.9
   • I = 40 Amps
   • L = 150 Feet
   • CM = 26,240 (Standard Circular Mils for 6 AWG)
2. Substitute into Formula:
   • VD = (2 × 12.9 × 40 × 150) / 26,240
3. Calculate Numerator:
   • 2 × 12.9 × 40 × 150 = 154,800
4. Divide by CM:
   • VD = 154,800 / 26,240 = 5.90 Volts
5. Check Percentage:
   • 5.90V / 240V = 2.45%

Verdict: At 2.45%, this is well under the 3% feeder recommendation. 6 AWG copper is perfectly sized for this run, both for ampacity (rated 65A at 75°C) and voltage drop.

Real-World Scenario: The 200-Foot EV Charger Run That Tripped the Breaker

Math on a page is clean; math on a jobsite is messy. Here is a documented failure mode that happens constantly with residential EV charger installations.

Unit Traps and Magnitude Checks: Why Your Math Might Be Wrong

If your calculator spits out a number that looks wrong, you likely fell into one of these common unit traps. Always perform a magnitude check before buying wire.

The Three Unit Mistakes That Break the Formula

1. Forgetting the '2' Multiplier: The formula requires the total loop length. If you measure 100 feet from the panel to the outlet, the current travels 100 feet out on the hot wire and 100 feet back on the neutral. The '2' accounts for this. If you manually double your 'L' variable AND use the '2' in the formula, your voltage drop will be artificially doubled.
2. Using Square Mils Instead of Circular Mils: The 'CM' variable stands for Circular Mils, not square mils or square millimeters. A circular mil is the area of a circle with a diameter of one mil (1/1000th of an inch). The formula relies on the math of circular mils to cancel out the pi in the area calculation. If you look up a wire's cross-sectional area in mm² (metric), the formula will fail completely. Always use the NEC Chapter 9, Table 8 CM values.
3. Mixing Metric and Imperial: The K constant of 12.9 is specifically calibrated for feet and circular mils. If you measure your length in meters, you cannot use 12.9. You must convert your length to feet first (1 meter = 3.28084 feet).

What a Realistic Answer Magnitude Looks Like

Before you trust your math, do a sanity check on the final voltage drop number. For residential and light commercial work, your VD should almost always be a single-digit number or a low double-digit number.

• 120V Circuit: 3% is 3.6V. If your math says the drop is 36V, you missed a decimal point or forgot to divide by the CM properly. A 36V drop means your 120V tool is receiving 84V, which will instantly fry a universal motor.
• 240V Circuit: 3% is 7.2V. 5% is 12V. If you calculate a 45V drop on a 240V feeder, you are either running a multi-mile transmission line or you accidentally used the wire diameter instead of the Circular Mil area.

Calculating voltage drop is not just an academic exercise to satisfy an inspector's informational note; it is the difference between equipment that operates at peak efficiency and equipment that degrades prematurely due to under-voltage conditions. Always run the math, check your CM values against reliable wire tables, and when in doubt, step up one wire size. For further reading on code compliance and derating factors, consult the NFPA NEC guidelines, but remember that your local Authority Having Jurisdiction (AHJ) always has the final say on site-specific installations.