To calculate voltage drop in a single-phase AC or DC circuit, use the formula VD = (2 × K × I × L) / CM. For a standard 120V, 15A branch circuit using 12 AWG copper wire over an 80-foot one-way distance, the voltage drop is 4.74V (3.95%). If your calculated drop exceeds 3% for branch circuits or 5% for feeders, you must increase the wire gauge (lower the AWG number) to increase the Circular Mil (CM) area.
The Core Voltage Drop Formula and Symbol Definitions
The fundamental equation for single-phase voltage drop derives from Ohm's Law (V = I × R), adapted to account for the physical dimensions and material properties of the conductor. Because current must travel to the load and return to the source, the one-way distance is multiplied by 2.
| Symbol | Variable Name | Unit | Definition & Bench Notes |
|---|---|---|---|
| VD | Voltage Drop | Volts (V) | The absolute voltage lost as heat across the wire. Not a percentage. |
| 2 | Multiplier | Dimensionless | Accounts for the out-and-back path in single-phase/DC. (Use 1.732 for 3-phase). |
| K | Specific Resistance | Ohm-cmil/ft | Material constant. Use 12.9 for Copper at 75°C (standard for THHN/THWN-2 AC). Use 21.2 for Aluminum at 75°C. |
| I | Current | Amperes (A) | The actual continuous load current, not the breaker size. |
| L | Length | Feet (ft) | The one-way distance from the breaker panel to the load. |
| CM | Circular Mils | cmil | Cross-sectional area of the wire. (e.g., 12 AWG = 6,530 cmil; 10 AWG = 10,380 cmil). |
Rearranged Forms for Wire Sizing and Distance Limits
On the jobsite, you rarely solve for VD directly; you usually know your maximum allowable drop and need to find the right wire size or maximum run length. Here are the algebraically rearranged forms:
- To find Wire Size (CM):
CM = (2 × K × I × L) / VD
Use this to size a new feeder. Convert the resulting CM to the next largest standard AWG size. - To find Maximum Distance (L):
L = (VD × CM) / (2 × K × I)
Use this to determine if an existing wire reel is long enough for a specific load without exceeding code drop limits. - To find Maximum Current (I):
I = (VD × CM) / (2 × K × L)
Use this to see if an existing long circuit can handle an added appliance without dimming lights or tripping thermal overloads.
Worked Example 1: Calculating Drop on an Existing 120V Branch Circuit
Scenario: You are extending a 120V receptacle circuit to a detached garage workshop. The one-way distance is 80 feet. The continuous load is a 15A air compressor. You plan to use 12 AWG copper THHN wire. What is the voltage drop, and is it acceptable?
- Identify knowns and constants:
K = 12.9 (Copper, 75°C)
I = 15A
L = 80 ft
CM = 6,530 (from NEC Chapter 9, Table 8 for 12 AWG) - Plug into the formula:
VD = (2 × 12.9 × 15 × 80) / 6,530 - Calculate the numerator (total resistance factor):
2 × 12.9 = 25.8
25.8 × 15 = 387
387 × 80 = 30,960 - Divide by CM:
VD = 30,960 / 6,530 = 4.74 Volts - Calculate percentage:
(4.74V / 120V) × 100 = 3.95%
Verdict: At 3.95%, this exceeds the NEC-recommended 3% maximum for branch circuits (NEC Informational Note 210.19(A)). The compressor will see 115.26V. While it will likely run, the motor will draw slightly higher amperage to compensate, running hotter. Fix: Upsize to 10 AWG (CM = 10,380), which drops the VD to 2.98V (2.48%).
Worked Example 2: Sizing Wire for a 240V Subpanel Feeder
Scenario: You are running a 240V feeder to a subpanel for an EV charger and a welder. The maximum continuous load is 40A. The one-way distance is 150 feet. You want to limit the voltage drop to exactly 3%. What size copper wire do you need?
- Calculate the maximum allowable Voltage Drop (VD):
VD = 240V × 0.03 = 7.2 Volts - Identify knowns:
K = 12.9 (Copper)
I = 40A
L = 150 ft
VD = 7.2V - Use the rearranged formula for CM:
CM = (2 × K × I × L) / VD - Calculate the numerator:
2 × 12.9 × 40 × 150 = 154,800 - Divide by the target VD:
CM = 154,800 / 7.2 = 21,500 cmil - Select the wire gauge:
Look at the AWG chart. 8 AWG is 16,510 cmil (too small). 6 AWG is 26,240 cmil (sufficient).
Verdict: You must pull 6 AWG copper THHN. If you use 8 AWG, your drop will be 4.68% (11.25V), which will cause the EV charger to throttle its charging speed or throw a low-voltage fault.
Assumptions, Limitations, and Unit Mistakes That Break the Math
The formula above is an incredibly reliable approximation for 95% of residential and light commercial work, but it relies on specific assumptions. Ignoring them leads to melted lugs or nuisance tripping.
When the Formula Applies
- Steady-State Loads: It calculates drop under continuous, steady current. It does not account for the massive instantaneous voltage sag caused by the locked-rotor amperage (LRA) of a large motor starting up.
- Unity Power Factor: It assumes a power factor (PF) of roughly 1.0 (resistive loads like heaters or incandescent lights). For highly inductive loads (large transformers, uncorrected fluorescent banks), the exact AC formula requires adding reactance (X) and power factor angles, though for wires 1/0 AWG and smaller, the reactance is negligible.
- Temperature: The K=12.9 constant assumes the wire is operating at 75°C under load. If the wire is in a freezing environment and barely loaded, K drops closer to 10.8 (20°C), meaning your actual drop will be slightly lower than calculated.
Unit Mistakes That Break the Math
- Mixing Metric and Imperial: The constant K=12.9 is strictly for Ohm-circular mils per foot. If your length is in meters, you must convert to feet first (multiply meters by 3.281), or use the metric formula:
VD = (2 × ρ × I × L) / A, where ρ is resistivity in Ω·m and A is area in mm². - Using Breaker Size for 'I': Never use the breaker rating for 'I'. A 20A breaker protecting a 12 AWG wire might only be carrying a 4A LED lighting load. Calculating drop based on 20A will tell you to use 8 AWG wire, wasting hundreds of dollars on copper.
- Confusing Circular Mils with Square Mils: CM is not the physical area in square mils. 1 CM is the area of a circle with a 1-mil diameter. Always pull the CM value directly from NEC Chapter 9, Table 8 rather than trying to calculate it from the wire diameter manually.
Decision Path: Picking the Right Wire Gauge for Your Run
Use this decision tree to quickly determine your wire sizing strategy before pulling out the calculator. With copper prices stabilizing in early 2026, the material cost penalty for upsizing one gauge is often less than the labor cost of pulling a second run if the first fails inspection or causes equipment faults.
| Condition / Run Parameter | Action / Wire Sizing Rule |
|---|---|
| One-way distance is under 50 feet | Size wire strictly to NEC ampacity tables (e.g., 14 AWG for 15A, 12 AWG for 20A). Voltage drop is mathematically negligible. |
| One-way distance is 50 to 100 feet, 120V circuit | Calculate drop. If load is >80% of breaker rating, upsize one AWG step (e.g., use 10 AWG for a 20A circuit). |
| One-way distance is over 100 feet, any voltage | Mandatory calculation. Use the CM = (2 × K × I × L) / VD formula targeting a strict 3% max drop. |
| Load is a large motor or compressor (High LRA) | Upsize wire two AWG steps from minimum ampacity to mitigate starting voltage sag, regardless of distance. |
| Wire is bundled with more than 3 current-carrying conductors | Apply NEC 310.15(C)(1) derating factors to ampacity first, then calculate voltage drop based on the derated ampacity. |
Hard Default Recommendation
If you are in the field without a calculator and the run exceeds 75 feet on a 120V branch circuit, default to 10 AWG copper THHN for 20A circuits, and 8 AWG copper for 30A circuits. Terminate these on 75°C rated breakers and receptacles. This single heuristic keeps you under the 3% drop threshold for almost all standard residential distances up to 120 feet, eliminates motor-startup dimming, and satisfies the strictest local inspectors without requiring you to pull out your phone on the ladder.
For further reference on conductor properties, consult the NFPA National Electrical Code (NEC) Chapter 9 tables, and verify complex runs using manufacturer tools like the Southwire Voltage Drop Calculator. For deeper theory on DC and AC resistance, review the All About Circuits textbook chapter on voltage drop.
