Three-Phase Power and Current Calculator: W, VA, VAR, and PF

Real power (W/kW) is the power that actually performs work and produces heat. Reactive power (VAR/kVAR) circulates between the source and inductive loads (motors, transformers) without performing work — it sustains magnetic fields. Apparent power (VA/kVA) is the vector sum: S = √(P^2 + Q^2). Power factor = P/S = cos(φ). A PF of 0.85 lagging means 85% of the apparent current does real work; 15% circulates reactively.

The √3 factor (1.732) appears because three-phase power is derived from the geometric relationship between line voltages and phase voltages in a balanced wye or delta system. In a wye system: V_LL = √3 * V_LN. In balanced conditions, total three-phase power P = 3 * V_PH * I_PH * cos(φ) = √3 * V_LL * I_L * cos(φ). This single √3 replaces the 3 * (√3) that would otherwise appear.

Current at constant real power: I = P / (√3 * V * PF). At PF=1.0 (purely resistive), current is minimum. At PF=0.7, current increases by 1/0.7 = 1.43x for the same kW. At PF=0.85, current is 1/0.85 = 1.18x the PF=1.0 value. Utilities charge for low PF because it increases line current and I^2R losses without delivering proportional real power.

The power triangle: P (adjacent) + jQ (perpendicular) = S (hypotenuse). Mathematically: S(kVA) = √(P^2 + Q^2), PF = P/S, Q = S * sin(arccos(PF)). Example: 100kW load at PF=0.80 → S = 100/0.80 = 125kVA, Q = 125 * sin(arccos(0.80)) = 125 * 0.6 = 75kVAR.

Three-phase current from kW: I = P(kW) * 1000 / (√3 * V_LL * PF). Example: 50kW, 480V, PF=0.87 → I = 50,000 / (1.732 * 480 * 0.87) = 69.4A. This is the line current in each conductor. For unbalanced loads, calculate each phase separately using the phase voltage.

Low PF is caused by inductive loads: AC motors (especially lightly loaded), transformers, HID lighting, and VFDs without input reactors. Correction uses capacitors (capacitors supply reactive power, reducing Q from the source). PF correction should not over-correct to leading PF. IEEE519 limits total harmonic distortion, which capacitors alone cannot address — use harmonic filters for non-linear loads.