Voltage Drop Calculation for 3-Phase Systems
Three-Phase Voltage Drop Formula
VD = √3 × L × I × R ÷ 1000
- √3 ≈ 1.732
- L = one-way length (feet)
- I = current per phase (amps)
- R = resistance (ohms/1000ft) from NEC Chapter 9 Table 8 (DC) or Table 9 (AC)
Worked Example: 3-Phase 208V Circuit
Scenario: 208V 3-phase, 40A load, 150 ft run, 8 AWG copper.
Step 1: R for 8 AWG copper = 0.778 ohms/1000ft (reference assumption; verify the adopted edition, conductor construction and installation method)
Step 2: VD = 1.732 × 150 × 40 × 0.778 ÷ 1000 = 8.09V
Step 3: Line-to-line voltage drop = 8.09V. Line-to-neutral = 8.09 ÷ √3 = 4.67V
Step 4: %VD = 8.09 ÷ 208 × 100 = 3.89% (exceeds 3%)
Fix: Use 6 AWG (R=0.491): VD = 1.732 × 150 × 40 × 0.491 ÷ 1000 = 5.10V = 2.45% ✓
Single-Phase vs 3-Phase Comparison
| Factor | Single-Phase (240V) | Three-Phase (208V) |
|---|---|---|
| Power at 40A | 9,600 W | 14,400 W |
| Wire needed | Same gauge | Same gauge |
| VD factor | 2 × L × I × R | √3 × L × I × R |
| VD for 150ft, 8 AWG, 40A | 9.34V (3.9%) | 8.09V (3.9%) |
| Power per volt of drop | 1,028 W/V | 1,780 W/V |
Frequently Asked Questions
How do you calculate voltage drop for 3-phase?
VD = √3 × L × I × R ÷ 1000. Where √3 ≈ 1.732, L = length (ft), I = current per phase (amps), R = resistance per 1000ft (NEC Table 9). For balanced loads, calculate for one phase.
What is the difference between single-phase and 3-phase voltage drop?
Single-phase: VD = 2 × L × I × R ÷ 1000 (factor of 2 for hot + neutral round trip). Three-phase: VD = √3 × L × I × R ÷ 1000 (factor of √3 because return path is shared). Three-phase has ~13% less voltage drop for the same power.
When should I use 3-phase power?
Three-phase is used for: motors >5 HP, large commercial loads, industrial equipment, and when voltage drop is a concern on long runs. Three-phase delivers more power with less copper and lower voltage drop.