The standard single-phase voltage drop formula is VD = (2 × K × I × L) / CM. For a 120V, 15A circuit running 60 feet on 14 AWG copper wire, the voltage drop is 5.65V (4.7%), which exceeds the NEC recommended 3% maximum for branch circuits. To fix this, you must increase the wire size to 12 AWG. Below is the complete derivation, symbol breakdown, and the exact decision path to size your next wire run without guessing.
The Exact Voltage Drop Formula (and What Every Symbol Means)
This formula calculates the approximate voltage lost as current travels through a conductor and back. It is derived directly from Ohm's Law (V = I × R), substituting the specific resistance properties of wire based on its material and cross-sectional area.
| Symbol | Definition | Standard Unit | Notes & Bench Values |
|---|---|---|---|
| VD | Voltage Drop | Volts (V) | The actual volts lost in the wire pair. Target <3% for branch, <5% total. |
| 2 | Multiplier | Dimensionless | Accounts for the hot wire out and the neutral/ground wire back (single-phase). |
| K | Specific Resistance | Ω·cmil/ft | 12.9 for Copper, 21.2 for Aluminum (at 75°C operating temp). |
| I | Current | Amperes (A) | The actual continuous load current, not the breaker rating. |
| L | Length | Feet (ft) | One-way distance from source to load. Do not double this for the return path. |
| CM | Circular Mils | cmil | Cross-sectional area. 14 AWG = 4,110; 12 AWG = 6,530; 10 AWG = 10,380. |
Rearranged Forms: Solving for Wire Size, Distance, and Current
On the jobsite, you rarely need to find the voltage drop itself; you already know your maximum allowable drop (e.g., 3.6V on a 120V circuit) and need to find the wire size that keeps you under that limit. Here are the algebraic rearrangements of the core formula:
- To find Wire Size (CM):
CM = (2 × K × I × L) / VD - To find Max Distance (L):
L = (VD × CM) / (2 × K × I) - To find Max Current (I):
I = (VD × CM) / (2 × K × L)
Worked Example 1: Calculating Drop on an Existing 120V Branch Circuit
Scenario: You are troubleshooting a 120V receptacle at the end of a garage run. The load is a 15A table saw. The wire is 14 AWG copper, and the one-way distance from the panel is 60 feet. Will the saw experience excessive voltage drop?
Step 1: Identify known variables.
- K = 12.9 (Copper at 75°C)
- I = 15A
- L = 60 ft
- CM = 4,110 (Standard 14 AWG)
Step 2: Plug into the formula with unit tracking.
VD = (2 × 12.9 (Ω·cmil/ft) × 15 (A) × 60 (ft)) / 4,110 (cmil)
Step 3: Solve the numerator.
2 × 12.9 × 15 × 60 = 23,220
Step 4: Divide by the denominator.
VD = 23,220 / 4,110 = 5.65V
Step 5: Calculate percentage and evaluate.
Percentage Drop = (5.65V / 120V) × 100 = 4.7%
Worked Example 2: Sizing a 240V Feeder for a Subpanel
Scenario: You are running a 240V feeder to a detached workshop subpanel. The continuous calculated load is 50A. The one-way trench distance is 150 feet. You want to limit voltage drop to 3% (7.2V). What size copper wire do you pull?
Step 1: Identify known variables.
- K = 12.9 (Copper)
- I = 50A
- L = 150 ft
- VD = 7.2V (3% of 240V)
Step 2: Use the rearranged formula for CM.
CM = (2 × K × I × L) / VD
Step 3: Plug in values with unit tracking.
CM = (2 × 12.9 (Ω·cmil/ft) × 50 (A) × 150 (ft)) / 7.2 (V)
Step 4: Solve numerator and divide.
Numerator = 2 × 12.9 × 50 × 150 = 193,500
CM = 193,500 / 7.2 = 26,875 cmil
Step 5: Select the wire.
Looking at standard AWG tables, 6 AWG is 26,240 cmil (too small, it will yield a 3.07% drop). The next size up is 4 AWG at 41,740 cmil. Pull 4 AWG THHN copper in your conduit.
Assumptions, Unit Traps, and Realistic Magnitudes
The formula is highly accurate for DC and single-phase AC circuits with a power factor near 1.0 (like resistive heating or incandescent lighting). For heavy inductive loads (large motors with a power factor below 0.85), the wire's reactance matters, and you should use the exact impedance (Z) from manufacturer voltage drop tables rather than the simple K constant.
Unit Mistakes That Break the Math
- Using Meters for Length: The K constant (12.9) is strictly calibrated for feet. If you measure in meters, you must convert to feet first, or use the metric K value (0.0424 for copper) and square millimeters for area.
- Using AWG Numbers as CM: Plugging '12' into the CM slot instead of '6530' will result in a mathematically absurd voltage drop of hundreds of volts. Always convert AWG to Circular Mils.
- Doubling the Length: The '2' in the numerator already accounts for the return path. If L is 50 feet, use 50. Do not use 100.
What a Realistic Answer Looks Like
If your calculated VD is larger than your source voltage, you made a math error (likely the AWG vs CM trap). In a properly designed 120V residential circuit, your VD should be between 0.5V and 3.6V. In a 240V circuit, it should be between 1.0V and 7.2V. If your formula spits out 0.01V for a 100-foot run, check your decimal placement.
Decision Tree: Picking the Right AWG for Your Next Run
Stop guessing at the hardware store. Use this decision matrix to terminate your planning phase with a concrete wire pick. This assumes standard 75°C copper (THHN/THWN-2) in a normal ambient temperature (under 86°F/30°C).
| Circuit Voltage | Max Continuous Load | One-Way Distance | Concrete Wire Pick (AWG) |
|---|---|---|---|
| 120V | 15A | Under 50 ft | 14 AWG (Standard NM-B) |
| 120V | 15A | 50 ft to 85 ft | 12 AWG (Upsize for drop) |
| 120V | 20A | Under 40 ft | 12 AWG (Standard NM-B) |
| 120V | 20A | 40 ft to 70 ft | 10 AWG (THHN in conduit) |
| 240V | 30A (Dryer/Tool) | Under 100 ft | 10 AWG (Standard NM-B) |
| 240V | 30A (Dryer/Tool) | 100 ft to 170 ft | 8 AWG (THHN in conduit) |
| 240V | 50A (Subpanel/Range) | Under 110 ft | 6 AWG (Standard NM-B or THHN) |
| 240V | 50A (Subpanel/Range) | 110 ft to 180 ft | 4 AWG (THHN in conduit) |
Default Recommendation: If your specific load or distance falls outside this table, or if you are running aluminum SER cable underground, default to using the rearranged CM formula above. However, for 90% of residential DIY branch circuits under 75 feet, 12 AWG copper is the ultimate baseline. It provides a 20A ampacity rating while offering 58% more cross-sectional area than 14 AWG, virtually eliminating voltage drop complaints on standard 120V runs up to 70 feet. Buy the 12 AWG.
