When you are pulling wire for a 3-phase motor or feeding a subpanel, guessing the wire size based solely on ampacity tables is a fast track to overheated conductors and tripped breakers. You must calculate the voltage drop to ensure the equipment receives adequate voltage under load. The standard 3 phase voltage drop equation used in North American NEC-style design is:
VD = (1.732 × K × I × D) / CM
This formula is the workhorse for journeymen and engineers alike. Below, we break down every variable, show you how to rearrange it for any unknown, and walk through two exact field calculations so you can size your next feeder with confidence.
The Core Equation and Symbol Definitions
The formula above is the NEC Chapter 9 approximate method. It assumes a balanced, sinusoidal steady-state load and uses the DC resistance constant adjusted for standard AC operating temperatures. Here is the exact spec-sheet definition for every symbol in the equation.
| Symbol | Definition | Standard Units / Values |
|---|---|---|
| VD | Voltage Drop | Volts (V) |
| 1.732 | Square root of 3 (√3) | Dimensionless constant for 3-phase vector math |
| K | DC Resistance Constant | 12.9 for Copper, 21.2 for Aluminum (at 75°C) |
| I | Load Current | Amperes (A) |
| D | One-Way Distance | Feet (ft) from source to load |
| CM | Circular Mils | Cross-sectional area of the wire (from NEC Table 8) |
Rearranged Forms for Sizing and Troubleshooting
You rarely use the formula just to find the voltage drop. Usually, you know your maximum allowable drop and need to find the wire size, or you are troubleshooting an existing run and need to find the maximum allowable distance. Here are the algebraic rearrangements you need on the jobsite:
- Solving for Wire Size (CM):
CM = (1.732 × K × I × D) / VD - Solving for Max Distance (D):
D = (VD × CM) / (1.732 × K × I) - Solving for Max Current (I):
I = (VD × CM) / (1.732 × K × D) - Solving for K (Material Check):
K = (VD × CM) / (1.732 × I × D)
Assumptions, Limits, and Unit Traps
Before you punch numbers into your calculator, you must understand the boundaries of this formula. Using it outside its assumptions or mixing up units will yield wire sizes that are dangerously undersized.
When the Formula Applies
This equation assumes a balanced 3-phase load (like a 3-phase motor or a perfectly balanced wye-connected heater bank). If your load is heavily unbalanced (e.g., a multi-tap transformer feeding single-phase 120V loads where one phase is maxed out and the others are empty), this formula will under-report the voltage drop on the heavily loaded phase. It also assumes a power factor near 0.85 to 1.0; highly inductive loads without power factor correction will experience slightly higher actual drops than this formula predicts.
Unit Mistakes That Break the Math
- The Metric Trap: The constant K = 12.9 is strictly derived for feet and circular mils. If you measure distance in meters or wire area in mm², this formula fails completely. (For metric, use VD = √3 × I × ρ × L / A, where ρ is 0.022 Ω·mm²/m for Cu).
- The Distance Trap: D is the one-way distance from the breaker to the load. Do not double it for the out-and-back path. The √3 factor already accounts for the 3-phase return path geometry. Doubling the distance will result in wire that is massively oversized.
- The Percentage Trap: When calculating percentage drop, divide the VD by the line-to-line voltage (e.g., 480V or 208V), not the line-to-neutral voltage (277V or 120V).
What a Realistic Answer Magnitude Looks Like
NEC-style guidance recommends a maximum of 3% voltage drop for branch circuits and 5% total for feeder plus branch.
• On a 480V system, 3% is 14.4V.
• On a 208V system, 3% is 6.24V.
If your calculation spits out a 45V drop on a 208V system, your wire is severely undersized. If it spits out 0.05V, you have massively overspent on copper.
Worked Example 1: Calculating Drop on an Existing 480V Feeder
Scenario: You are auditing an existing workshop. A 480V, 3-phase dust collector motor draws 60A under full load. The feeder is 4 AWG Copper THHN, and the one-way run from the panel is 250 feet. Is the voltage drop acceptable?
Step 1: Identify knowns.
- K = 12.9 (Copper)
- I = 60A
- D = 250 ft
- CM = 41,740 (from NEC Chapter 9, Table 8 for 4 AWG)
Step 2: Plug into the core equation.
VD = (1.732 × 12.9 × 60 × 250) / 41,740
Step 3: Track the units and solve.
- Numerator: 1.732 × 12.9 × 60 × 250 = 334,710
- Denominator: 41,740
- VD = 334,710 / 41,740 = 8.02 Volts
Step 4: Calculate percentage.
(8.02V / 480V) × 100 = 1.67%.
Verdict: Well under the 3% limit. The existing 4 AWG wire is perfectly adequate.
Worked Example 2: Sizing Wire for a New 208V Motor Run
Scenario: You are installing a new 208V, 3-phase air compressor. The motor draws 40A continuous. The one-way distance from the subpanel is 150 feet. You need to size the wire to stay under a 3% voltage drop.
Step 1: Determine maximum allowable VD.
Max VD = 208V × 0.03 = 6.24 Volts
Step 2: Identify knowns for the rearranged formula.
- K = 12.9 (Copper)
- I = 40A
- D = 150 ft
- VD = 6.24V
Step 3: Solve for required Circular Mils (CM).
CM = (1.732 × 12.9 × 40 × 150) / 6.24
- Numerator: 1.732 × 12.9 × 40 × 150 = 134,056.8
- CM = 134,056.8 / 6.24 = 21,483 CM
Step 4: Select the wire size.
Looking at NEC Table 8, 8 AWG is 16,510 CM (too small). 6 AWG is 26,240 CM (meets the requirement).
Verdict: You must pull a minimum of 6 AWG Copper.
Decision Path: Picking the Exact Wire and Breaker
Calculating the wire size for voltage drop is only half the job. You must also satisfy NEC ampacity rules and continuous load multipliers. Use this decision tree to finalize your exact bill of materials. We will use the 40A continuous 208V compressor from Example 2 as the baseline.
| Condition / Check | If YES (Action) | If NO (Action) |
|---|---|---|
| Is the load continuous (runs 3 hours or more)? | Multiply load by 1.25 for breaker sizing. (40A × 1.25 = 50A minimum breaker). | Size breaker at 100% of load. (40A minimum breaker). |
| Does the VD-calculated wire (6 AWG) meet the 75°C ampacity table for the breaker? | Proceed to termination check. (6 AWG at 75°C is 65A, which safely handles a 50A breaker). | Upsize wire to match breaker terminal ratings. |
| Are the panel and equipment terminals rated for 90°C? | You can use the 90°C column for derating, but terminations are still limited to 75°C. | Strictly use the 75°C column for all sizing (Standard practice). |
| Is the run in a conduit with more than 3 current-carrying conductors? | Apply NEC 310.15(C)(1) derating factors. Upsize wire if derated ampacity drops below breaker size. | No derating required. Final wire size stands. |
Based on the decision path above (40A continuous load, 150ft run, 208V 3-phase):
• Wire: 6 AWG THHN Copper (e.g., Cerrowire Part #10458 or Southwire equivalent). Pull 3 current-carrying conductors plus a 10 AWG green ground.
• Breaker: 50A 3-Pole Breaker (e.g., Eaton BR250 or Square D QOB350, matching your specific panel brand).
Do not downgrade to 8 AWG just because an 8 AWG wire's 50A ampacity 'matches' the breaker; the 8 AWG wire will fail the 21,483 CM voltage drop requirement, causing the motor to overheat and trip its internal overloads on startup.
For further reading on conductor properties and code compliance, refer to the NFPA 70 National Electrical Code guidelines, and consult EC&M (Electrical Construction & Maintenance) for advanced field derating scenarios. Always verify final designs with your local Authority Having Jurisdiction (AHJ), as local amendments may dictate stricter voltage drop limits than the baseline NEC recommendations.
