Three-Phase Power Calculator — kW, kVA, kVAR
Enter line-to-line voltage, line current and power factor to get the three-phase apparent power (kVA), real power (kW), reactive power (kVAR) and phase values for wye or delta connections.
Connection type
V
A
Three-phase active power: P = √3 · V_L · I_L · PF
- 1
Apparent power S = √3 × V_L × I_L
1.7321 × 400 × 50 ÷ 1000 = 34.641√3 ≈ 1.7321 accounts for the 120° phase displacement between the three phases. - 2
Real power P = S × PF
34.641 kVA × 0.85 = 29.44
How does this calculator work?
Three-phase apparent power S = √3·V_L·I_L (kVA). Real power P = S·PF (kW). Reactive power Q = S·sin(arccos(PF)) (kVAR). For wye: V_ph = V_L/√3, I_ph = I_L. For delta: V_ph = V_L, I_ph = I_L/√3. The power formulas are the same for both connection types when using line values.
Formula
How this is calculated
A balanced three-phase power system delivers energy through three live conductors carrying currents 120 ° apart. The apparent power (S, in volt-amperes) relates line quantities by S = √3 × V_L × I_L — the factor √3 ≈ 1.732 accounts for the 120-degree phase displacement between phases. The real (active) power P, measured in watts, is the power that does useful work: P = S × cos(φ), where φ is the phase angle between voltage and current and cos(φ) is the power factor (PF). The reactive power Q = S × sin(φ), measured in volt-amperes reactive (VAR), represents energy alternately stored and returned by inductors and capacitors; it does not do useful work but must be supplied by the source.
The connection type determines how line and phase quantities relate. In a wye (star) connection the phase voltage is V_ph = V_L / √3 and the phase current equals the line current. In a delta connection the phase voltage equals the line voltage and the phase current is I_ph = I_L / √3. The three-phase power formulae using line values (S = √3 · V_L · I_L) hold identically for both topologies, so the same formula gives the same power regardless of connection type when you measure at the line terminals.
This calculator assumes a balanced three-phase system, meaning all three phases carry equal currents at the same power factor. For unbalanced loads each phase must be analysed separately. The results are standard engineering approximations; refer to IEEE 1459 for precise power definitions under harmonic and unbalanced conditions.
Frequently asked questions
The factor √3 appears because the line-to-line voltage is not the same as the per-phase voltage. In a wye system V_ph = V_L/√3, and per-phase power is V_ph × I_L. Summing three phases gives 3 × (V_L/√3) × I_L = √3 × V_L × I_L. For delta systems V_ph = V_L but I_ph = I_L/√3, and the arithmetic works out identically.
Reactive power (Q, kVAR) represents energy cycling back and forth between the source and inductive or capacitive loads (motors, transformers, capacitor banks). It does not perform work but flows through cables and transformers, causing losses and voltage drop. Power companies charge large customers for poor power factor because high reactive power requires larger conductors and transformers.
Large induction motors typically run at 0.80–0.90 power factor under full load and drop lower at partial load. Most utilities require industrial customers to maintain a power factor above 0.90–0.95 or face a power-factor surcharge. Capacitor banks are commonly installed to correct low power factor back toward unity.
Also known as
TG we-Calculate Editorial Team. (2026). Three-Phase Power Calculator — kW, kVA, kVAR [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/three-phase-calculator
TG we-Calculate Editorial Team. "Three-Phase Power Calculator — kW, kVA, kVAR." TG we-Calculate. 2026. https://we-calculate.com/calculator/three-phase-calculator.
TG we-Calculate Editorial Team, "Three-Phase Power Calculator — kW, kVA, kVAR," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/three-phase-calculator
@misc{wecalculate_three_phase_calculator, title = {Three-Phase Power Calculator — kW, kVA, kVAR}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/three-phase-calculator}}, year = {2026}, note = {TG we-Calculate} }
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