Three-Phase Line vs Phase Voltage

Formula

Description

In a balanced three-phase wye (star) connected system, the line-to-line voltage is √3 (approximately 1.732) times the phase-to-neutral voltage. This fundamental relationship arises from the 120° phase displacement between phases. In a 208/120 V system (common in North America), V_phase = 120 V and V_line = 208 V. In a 400/230 V system (common in Europe), V_phase = 230 V and V_line = 400 V. Understanding this relationship is essential for three-phase power system design, motor connections, and transformer configurations.

Variables

• V_line — Line-to-line (phase-to-phase) voltage (V)
• V_phase — Phase-to-neutral voltage (V)

Practical Notes

For delta connections, the line voltage equals the phase voltage (V_line = V_phase), but the line current is √3 times the phase current. Three-phase power is P = √3 × V_line × I_line × cos(φ) regardless of wye or delta connection. In a balanced system, the neutral carries zero current.