Calculations 13 min read Updated 2024-11-10

Three-Phase Voltage Drop Calculations Explained

Master three-phase voltage drop calculations for commercial and industrial applications. Covers balanced loads, line vs phase voltage, and the √3 factor.

Three-Phase Power Fundamentals

Three-phase power is the backbone of commercial and industrial electrical distribution. Unlike single-phase power, three-phase systems use three conductors carrying currents that are 120 degrees out of phase with each other. This configuration provides significant advantages: more efficient power transmission, smaller conductors for equivalent power, and smoother power delivery to motors and other rotating equipment.

Understanding three-phase voltage drop is essential for designing feeders, motor circuits, and distribution systems in commercial and industrial facilities. The calculations differ from single-phase because of the phase relationships between conductors.

The √3 Factor Explained

The key difference in three-phase voltage drop calculations is the use of √3 (approximately 1.732) instead of the factor of 2 used in single-phase calculations. This factor emerges from the vector relationship between the three phases. In a balanced three-phase system, the voltages are equal in magnitude but displaced by 120°.

Three-Phase Voltage Drop Formula

Vd = (√3 × I × L × R) / 1000
√3 = 1.732
I = Line current (amps)
L = One-way length (ft)
R = Resistance (Ω/kft)

Line vs Phase Voltage

Understanding the relationship between line and phase voltages is critical for three-phase calculations. Line voltage is measured between any two phase conductors, while phase voltage is measured from any phase to neutral.

Wye (Star) Configuration

  • • VLine = VPhase × √3
  • • ILine = IPhase
  • • Common: 208Y/120V, 480Y/277V
  • • Neutral available

Delta Configuration

  • • VLine = VPhase
  • • ILine = IPhase × √3
  • • Common: 480V, 240V delta
  • • No inherent neutral

Common Three-Phase Systems

SystemConfigurationLine VoltagePhase Voltage
Small Commercial208Y/120V208V120V
Industrial480Y/277V480V277V
Heavy Industrial480V Delta480V480V
Medium Voltage4160V4160V2400V

Three-Phase Voltage Drop Calculator

Calculate voltage drop for your three-phase circuits with our professional calculator. Select three-phase mode for automatic application of the √3 factor and accurate results for balanced loads.

Three-Phase Calculator

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