Calculate real, apparent, and reactive power in three-phase AC electrical circuits. Essential for industrial motor, transformer, and power system analysis, electrical design, and power factor correction.
Last Updated: 5/6/2026
Three-phase: 208V, 277V, 380V, 480V, 600V typical
Residential: <50A; Industrial: 100–500A
1.0 = pure resistive; 0.7–0.95 = typical inductive loads (motors, transformers)
Electrical power in AC (alternating current) circuits is far more complex than in DC (direct current). The watt (W), the SI unit of power, measures real power—the actual energy transferred per unit time to do useful work (e.g., spinning a motor, heating a resistor, lighting a bulb). Real power P = V × I × cos(θ) = V × I × PF, where PF (power factor) is the cosine of the phase angle θ between voltage and current. A power factor of 1.0 (resistive loads: heaters, incandescent bulbs) means voltage and current are in phase; all supplied power becomes work. However, inductive loads (motors, transformers, inductors) and capacitive loads (capacitors, power electronics) create phase lag or lead, decoupling voltage from current. This creates reactive power Q (measured in volt-amperes reactive, VAR), which oscillates between the source and load without being consumed—energy sloshes back and forth on the circuit, heating wires and reducing the system's ability to deliver real power. Apparent power S = V × I (measured in volt-amperes, VA) is the vector sum of real and reactive components: S² = P² + Q². The power factor PF = cos(θ) = P / S quantifies the ratio of real work to total power supplied. Low power factor (e.g., 0.7) means a significant portion of the utility company's electrical infrastructure (large transformers, thick power lines, expensive generation capacity) is dedicated to moving reactive power rather than delivering real power. Utilities charge penalties for low power factor; motor-driven facilities often install capacitor banks to "correct" power factor by injecting capacitive reactive power to cancel inductive reactive power, bringing PF close to 1.0. Understanding the power triangle (P-Q-S right triangle) is essential for electrical engineers, facility managers, and anyone designing power distribution systems, applying correctly-sized transformers, and avoiding equipment overheating.
Industrial power systems often use three-phase AC (three voltage sinusoids 120° apart), which is more efficient for motors and reduces ripple compared to single-phase AC used in households. Three-phase power calculations are identical conceptually but use line-to-line voltage, line current, and power factor to compute P_total = √3 × V_LL × I_line × PF, and apparent power S = √3 × V_LL × I_line. Motors are inherently inductive; a 10 kW three-phase motor at 0.85 PF draws Q = √(S² − P²) ≈ 6.3 kVAR of reactive power, requiring larger conductors, transformers, and switchgear than a 10 kW resistive heater at 1.0 PF (zero reactive). Power factor correction capacitors (typically 5–50 kVAR) are installed in parallel with motors to offset reactive current, reducing line current, power losses (I²R heating in wires), and utility charges. Non-sinusoidal waveforms (square-wave inverters, LED drivers, laptop PSUs with diode bridges) introduce harmonics, which complicate power calculations by adding harmonic power components beyond the fundamental 50/60 Hz; true power factor (PF_true) differs from displacement power factor (cos θ) when harmonics are significant. This calculator assumes sinusoidal (no harmonics) three-phase AC voltage and current with balanced line conditions; for more complex scenarios (unbalanced loads, harmonics, DC circuits), use dedicated power analyzers or spreadsheets accounting for such effects.
Use a digital multimeter (DMM) set to AC voltage (V~) across two phase lines (line-to-line, NOT line-to-neutral) and AC current (A~) in series through one phase line. For three-phase industrial circuits, line-to-line voltages are: 208V, 277V, 380V, 480V, or 600V depending on region and system configuration. Current is per-phase line current. The calculator applies the three-phase formula P = √3 × V_LL × I × PF, making results directly comparable across industrial systems. For single-phase AC or DC circuits with the same formula (without √3), use a dedicated single-phase calculator.
For pure resistive loads (incandescent light, electric heater), PF ≈ 1.0. For inductive loads (induction motors, transformers), PF is typically 0.7–0.95; the motor nameplate often lists the PF. For capacitive loads (capacitor banks, power factor correction devices), PF would again approach 1.0. Industrial loads are usually mixed; a facility with many motors might have overall PF = 0.85, meaning 15% of supplied power is reactive. Many utility bills include PF or allow you to calculate it from real/reactive power measurements.
Input voltage (V), current (A), and power factor (0–1). If only two values are known (e.g., apparent power in kVA and real power in kW from a nameplate), calculate the third: cos(θ) = P / S gives the PF; then enter that into the calculator. Alternatively, if you have impedance Z and phase angle θ, use Z = V / I and PF = cos(θ) directly.
Real power (W or kW) is the actual usable power—this is what you pay for and what does work. Apparent power (VA or kVA) is what the utility must generate and deliver; your wiring and transformer must be sized for this. Reactive power (VAR or kVAR) indicates inductive lag; if substantial, power factor correction might reduce utility costs. Phase angle θ and reactive loss % show how much capacity is "wasted" on reactive components. If reactive loss exceeds 25%, consider installing capacitor banks to bring PF closer to 1.0.
Transformers and switchgear must handle apparent power, not real power—undersizing for real power alone will overheat equipment. Conductors and breakers are sized by current and voltage, which are independent of PF; however, reactive power increases line current (I = S / V = √(P² + Q²) / V), requiring larger wires. If an industrial facility's PF drops below 0.95, utilities often charge reactive power penalties; installing capacitor banks (50–500 kVAR) can restore PF to >0.95, reducing bills by 2–10% annually.
Scenario: A 50 kW three-phase induction motor (nameplate: 50 kW, 380V, 92A, PF 0.88, 60 Hz) is operating at full load. Calculate: (1) real power delivered, (2) apparent power drawn, (3) reactive power, (4) phase angle, (5) power correction capacitor size needed to bring PF to 0.95.
Watts (W) measure real power—the actual energy consumed per unit time, doing useful work (heats, light, motion). Volt-amperes (VA) measure apparent power, the product V × I, which includes both real and reactive components; utilities must generate and transport this. Volt-amperes reactive (VAR) measure reactive power, the oscillating component that is not consumed. In AC, they form a right triangle: VA² = W² + VAR². A 100W resistive heater at 120V draws 100W real, 100VA apparent, 0 VAR reactive. A 100VA inductive load at 0.8 PF draws 80W real, 100VA apparent, 60 VAR reactive.
Low PF means high reactive power losses that don't produce work but require large wires, transformers, and generation capacity. Utilities must overbuild infrastructure to serve VAR flow. A facility drawing 100kW at 0.7 PF requires 143 kVA infrastructure vs. only 100 kVA at 1.0 PF—43% more investment! Utilities recover this cost by charging reactive power penalties (e.g., $0.02–0.10/kVAR·month) for PF < 0.95. Installing capacitors to raise PF pays for itself within 1–3 years and improves reliability (reduced voltage drop), equipment lifespan, and efficiency.
Inductive loads (motors, transformers) create lagging reactive current (leading voltage). Adding capacitors in parallel injects leading reactive current that cancels the inductive lagging current. The net phase lag decreases, reducing apparent power and line current. For example, a 10 kW motor at 0.8 PF lagging draws 12.5A line current; adding a 6.25 kVAR capacitor (parallel) creates leading reactive current that cancels the motor's lagging portion, effectively raising PF to >0.95 and dropping line current to ~8.5A (32% reduction). No real power is added or removed; energy is just re-routed more efficiently.
Power factor ranges 0–1.0 for sinusoidal waveforms; it cannot exceed 1.0 conceptually (cos(θ) ≤ 1). Lagging PF occurs when current lags voltage (inductive loads: motors, coils, inductors); common PF = 0.7–0.95. Leading PF occurs when current leads voltage (capacitive loads: capacitor banks, some power electronics); PF might read 0.95 leading. Utilities prefer PF close to 1.0 (unity) regardless of leading/lagging. Some specs state leading/lagging explicitly (e.g., 0.88 PF lagging).
Simple method: Measure voltage (V), current (I), and real power or apparent power. If you know real power (e.g., kWh meter or named watts), PF = P / (V × I). If you know only V and I, assume PF and verify against typical loads (resistive ≈ 1.0, motor ≈ 0.85–0.95, mixed facility ≈ 0.8–0.9). Advanced: Use a true RMS multimeter and power analyzer (≈$100–500) to measure phase shift or PF directly. Many utility bills show PF now; check the breakdown.
During startup, induction motors draw 5–7× rated current for a fraction of a second while accelerating from zero RPM. At low speed, impedance Z = V/I is lowest, so current peaks; additionally, the motor is still not optimized for PF (high slip = high reactive current). Once running, PF improves to nameplate (0.85–0.95). This transient inrush causes voltage dips on the electrical system, which utilities and facility engineers monitor. Soft starters or variable frequency drives (VFDs) reduce inrush, protecting downstream equipment and PF stability
Three-phase AC supplies three sinusoidal voltages 120° apart, creating instantaneous power output that is nearly constant (vs. pulsating in single-phase). This enables smaller, more efficient motors (no start capacitors or auxiliary windings needed), better power delivery without voltage ripple, and 1.732× power density per conductor. Industrial and large commercial use 3-phase; residential typically uses 2-phase (120/240V split-phase, which is derived from 3-phase utility). Three-phase motor power: P = √3 × V_line × I_line × cos(θ) ≈ 1.732 × V × I × PF.
Traditional power calculations assume pure 50/60 Hz sinusoids. However, modern loads (LED drivers, computers, VFDs) draw non-sinusoidal current with harmonics (multiples of fundamental frequency: 3f, 5f, 7f, etc.). Harmonics increase RMS current (I_RMS = √(I_1² + I_3² + I_5² + ...)) without increasing fundamental power, distorting PF measurement. True power factor (PF_true) accounts for harmonic content; displacement power factor (cos θ fundamental) is the traditional PF. Utilities penalize high harmonic distortion (>5% THD); filters and modern switching PSUs minimize harmonics.
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