Three-Phase Power

Formula

Description

Three-phase power systems are the standard for industrial and commercial power distribution because they deliver constant instantaneous power (unlike single-phase which pulsates) and use less conductor material for the same power delivery. The √3 factor arises from the 120-degree phase relationship between the three phases. Line-to-line voltage is √3 times the phase voltage. Three-phase motors are simpler and more efficient than single-phase equivalents. This formula gives the total real power delivered by all three phases combined.

Variables

• P — Total three-phase real power (W)
• VLL — Line-to-line RMS voltage (V)
• IL — Line current RMS (A)
• cos(φ) — Power factor

Practical Notes

Common three-phase voltages: 208V (US commercial), 380V (EU), 400V (EU newer), 480V (US industrial). Three-phase apparent power is S = √3 × VLL × IL (without power factor). For balanced loads, each phase carries one-third of the total power. Variable frequency drives (VFDs) convert single or three-phase input to three-phase output for motor speed control.