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.
What NEC reference covers the voltage drop formula?
The NEC voltage drop recommendation is in Article 210.19(A)(1) Informational Note No. 1 for branch circuits and 215.2(A)(1) for feeders: keep combined voltage drop within 3% for supply conductors and 5% total from panel to the furthest load. These are fine-print recommendations, not mandatory limits.