Beginner
Voltage Drop Formulas (1Φ & 3Φ)
Single-phase and three-phase voltage drop formulas with conductor resistance values — calculate VD% for any circuit length and load.
Formulas
VD = 2 × L × I × R / 1000
Single-phase voltage drop (volts)
VD = √3 × L × I × R / 1000
Three-phase voltage drop (volts)
VD% = (VD / V_source) × 100
Voltage drop as percentage of source voltage
Variable Definitions
VD=Voltage drop(volts (V))
L=One-way conductor length(feet (ft))
I=Load current(amperes (A))
R=Conductor resistance per 1000 ft(ohms/1000ft (from NEC Ch9 T8))
√3=Square root of 3(1.732 (three-phase factor))
Worked Examples
Example 1
150 ft run, 20A load, 12 AWG copper (R=1.93Ω/1000ft), 120V single-phase.
- VD = 2 × 150 × 20 × 1.93 / 1000 = 11.58V
- VD% = 11.58 / 120 × 100 = 9.65%
- Exceeds 3% NEC recommendation — upsize to 10 AWG
Answer: 11.58V (9.65%) — must upsize conductor
Example 2
200 ft run, 30A load, 10 AWG copper (R=1.21Ω/1000ft), 480V three-phase.
- VD = 1.732 × 200 × 30 × 1.21 / 1000 = 12.58V
- VD% = 12.58 / 480 × 100 = 2.62%
Answer: 12.58V (2.62%) — within 3% limit ✓
When to Use
- •Sizing branch circuit conductors for long runs
- •Verifying feeder conductor sizing meets NEC recommendations
- •Comparing conductor sizes to find the most cost-effective option
- •Designing outdoor/parking lot lighting circuits with long cable runs
Standards & References
- NEC 210.19(A) Informational Note No. 4 — 3% branch circuit VD recommendation
- NEC 215.2(A) Informational Note No. 2 — 5% total VD recommendation
- NEC Chapter 9, Table 8 — DC Resistance
- NEC Chapter 9, Table 9 — AC Impedance