Voltage Drop Formula: How to Calculate Step by Step
Voltage Drop Formulas
Single-Phase (120V or 240V)
VD = 2 × L × I × R ÷ 1000
- VD = voltage drop (volts)
- L = one-way circuit length (feet)
- I = current (amps)
- R = wire resistance (ohms per 1,000 feet) from NEC Table 8
The factor of 2 accounts for the round-trip (hot + neutral).
Three-Phase
VD = √3 × L × I × R ÷ 1000
√3 ≈ 1.732. The three-phase formula uses √3 instead of 2 because the return path is shared across phases.
Worked Example
Scenario: 120V circuit, 20A load, 100 ft run, 12 AWG copper wire.
Step 1: Find resistance from NEC Table 8: 12 AWG copper = 2.01 ohms/1000ft (DC resistance at 75°C)
Step 2: VD = 2 × 100 × 20 × 2.01 ÷ 1000 = 8.04V
Step 3: %VD = 8.04 ÷ 120 × 100 = 6.7%
Result: 6.7% exceeds the NEC 3% recommendation. Use 10 AWG (1.24 ohms/1000ft): VD = 2 × 100 × 20 × 1.24 ÷ 1000 = 4.96V = 4.1%. Still above 3%? Try 8 AWG: VD = 3.12V = 2.6% ✓
NEC Voltage Drop Recommendations
| Circuit Type | Max Voltage Drop | 120V Circuit | 240V Circuit |
|---|---|---|---|
| Branch circuit (NEC recommendation) | 3% | 3.6V | 7.2V |
| Feeder + branch combined | 5% | 6.0V | 12.0V |
| Fire alarm circuits (NFPA 72) | 10% | 12.0V | 24.0V |
Note: NEC 210.19 and 215.2 use "shall" for ampacity but "should" for voltage drop — it's a recommendation, not a code violation. However, exceeding 3% causes equipment problems and energy waste.
Frequently Asked Questions
What is the voltage drop formula?
Single-phase: VD = 2 × L × I × R ÷ 1000. Three-phase: VD = √3 × L × I × R ÷ 1000. Where L = length (ft), I = current (amps), R = resistance (ohms/1000ft) from NEC Chapter 9 Table 8.
What is the allowable voltage drop?
NEC recommends (not requires) max 3% voltage drop on branch circuits and 5% total (feeder + branch). For a 120V circuit: 3% = 3.6V drop, 5% = 6V drop. For 240V: 3% = 7.2V, 5% = 12V.
How do I reduce voltage drop?
Use larger wire (lower gauge), shorter circuit runs, or higher voltage (240V instead of 120V). For a given load: doubling the wire size halves the voltage drop. Moving from 120V to 240V halves the current, which halves the drop.