Three-Phase Power Calculator

What Is Three-Phase Power? Three-phase AC power uses three alternating currents, each 120° apart in phase, delivered on three separate conductors. It is the standard for industrial and commercial electrical systems worldwide. Three-phase is more efficient than single-phase for transmitting large amounts of power — motors are smoother, transformers are smaller, and wiring uses less copper for the same power. Most industrial motors, HVAC compressors, and manufacturing equipment run on three-phase power.

Star (Y) vs Delta (Δ) Connections Star (Y) connection: each phase connects between one line and a neutral conductor. Line voltage (V_L) = √3 × Phase voltage (V_ph) ≈ 1.732 × V_ph. Delta (Δ) connection: each phase connects between two lines, no neutral. Line voltage = Phase voltage (V_L = V_ph). Most utility distribution uses star for 4-wire systems (3 phases + neutral). Motors use delta or star internally.

Three-Phase Power Formulas Real Power (P): P = √3 × V_L × I_L × PF (in watts or kW). Apparent Power (S): S = √3 × V_L × I_L (in VA or kVA). Reactive Power (Q): Q = √3 × V_L × I_L × sin(θ) (in VAR or kVAR). Line Current: I_L = P / (√3 × V_L × PF).

Common Three-Phase Voltages United States industrial: 480V (line-to-line), 277V (line-to-neutral). Used for motors and HVAC. United States commercial: 208V (line-to-line), 120V (line-to-neutral). Office buildings, restaurants. European industrial: 400V (line-to-line), 230V (line-to-neutral). High voltage transmission: 11 kV, 33 kV, 66 kV, 132 kV, 400 kV (all line-to-line RMS).

Power Factor in Three-Phase Systems Power factor (PF) = cos(θ) = P / S = real power / apparent power. Three-phase induction motors at full load: PF ≈ 0.85–0.92. At partial load: PF drops significantly (a motor at 25% load may have PF = 0.50). Low power factor causes higher current for the same useful power — increasing line losses and requiring larger conductors. Power factor correction capacitors are installed in factories to bring PF toward unity.

Balanced vs Unbalanced Loads A balanced three-phase load has equal impedance on all three phases — industrial motors are typically balanced. An unbalanced load (common in commercial buildings with mixed single-phase loads) causes neutral current to flow. These formulas apply to balanced loads. Unbalanced systems require per-phase analysis.

Efficiency and Three-Phase Motors NEMA Premium efficiency motors (IE3) at full load: 93–96% efficient. A 100 kW motor at 95% efficiency draws 105 kW from the supply (100/0.95). Variable frequency drives (VFDs) control three-phase motor speed — they draw distorted current, often requiring de-rating of conductors and transformers.