3-Phase Power Calculator

Calculate balanced three-phase AC real power (kW), apparent power (kVA), reactive power (kVAR), line current, and power factor correction.

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Formula · assumptions · example(IEEE 141 (Red Book) · IEC 60038 · NFPA 70 (NEC))

Formula

P = \sqrt{3} \cdot V_L \cdot I_L \cdot \cos\phi, \quad S = \sqrt{3} \cdot V_L \cdot I_L, \quad Q = \sqrt{3} \cdot V_L \cdot I_L \cdot \sin\phi

Balanced three-phase active real power P (kW), apparent power S (kVA), reactive power Q (kVAR), and power factor cosφ.

Assumptions

  • · Symmetrical balanced three-phase AC system with 120° phase displacement between line voltages
  • · Line-to-line voltage VL and line current IL measured as RMS values
  • · Linear balanced electrical load across all three phases

Worked example

Worked example — 3-Phase Power Calculator

Deterministic calculation verified against international engineering standards.