Calculate real, apparent, and reactive power for balanced three-phase electrical systems.
Last updated: March 2026 | By Summacalculator
Common: 208V, 480V, 600V
Resistive: 1.0, Motor: 0.8 - 0.9
Three-phase power is an AC (alternating current) electrical power generation and distribution system using three conductors carrying sinusoidal currents phase-shifted 120° from each other. It is the dominant method for bulk power transmission and industrial applications worldwide. In three-phase systems, power flows continuously and uniformly to the load, unlike single-phase systems where power fluctuates at twice the frequency, causing vibration and inefficiency in motors.
Three-phase systems are vastly superior to single-phase for industrial and utility-scale applications. They require lighter and smaller conductors than single-phase to transmit the same power (reducing copper costs), provide constant power delivery enabling efficient smooth motor operation, and consume significantly less reactive power. Power companies prefer three-phase because it provides better voltage regulation and stability. Almost all large industrial motors, generators, and grid-level transmission use three-phase. Understanding three-phase power calculations is essential for electrical engineers, facility managers, industrial maintenance technicians, and power system designers. The terms real power (kW), apparent power (kVA), and reactive power (kVAR) form the power triangle fundamental to all grid operations.
Step 1: Enter the line-to-line voltage (V_L) in Volts. This is the voltage measured between any two of the three power lines. Common industrial voltages: 208V (single buildings), 480V (factories, large facilities), 600V (heavy industrial). Residential three-phase is sometimes 208V or 240V split-phase.
Step 2: Enter the line current (I_L) in Amperes. This is the current flowing in each of the three lines. Measure with a clamp meter on any line; in a balanced system, all three carry the same current.
Step 3: Enter the Power Factor (PF) between 0 and 1. This indicates how much of the apparent power is actually doing useful work. Resistive loads (heaters, lights) have PF = 1.0. Inductive loads (motors, inductors) typically have PF = 0.8-0.9. Leading phase (capacitive) and lagging phase (inductive) are tracked separately, but by convention the displayed PF magnitude is always between 0 and 1.
Step 4: The calculator instantly displays three power values: Real Power (kW)—the useful work done, Apparent Power (kVA)—the total supplied, and Reactive Power (kVAR)—the magnetic oscillations. These form the power triangle: P² + Q² = S².
A factory has a three-phase system with a line-to-line voltage of 480V. When running its production machinery, the line current is 100A, and the power factor of the load is 0.85 (typical for motors). Calculate the real power consumption, apparent power demand, and reactive power in the system.
kW (kilowatts) is real power—the actual work being done, measured in Watts. Your electricity bill charges for kW-hours. kVA (kilovolt-amperes) is apparent power—the total power the utility must supply and infrastructure must handle. If PF = 1, then kVA = kW. If PF = 0.8, then for every kW of work, 1.25 kVA must be supplied. Utilities assess demand charges on kVA.
In a balanced three-phase system, the three voltage waveforms are 120° phase-shifted. The line-to-line voltage (V_L, typically quoted) is √3 times the line-to-neutral voltage (V_N). Since power is proportional to voltage, the three-phase formula includes this factor. Mathematically: V_L = √3 × V_N, so P_total = 3 × P_per_phase = 3 × V_N × I × PF = √3 × V_L × I × PF.
Power factor > 0.95 is excellent; 0.90-0.95 is good; 0.85-0.90 is acceptable but utilities may charge penalties; < 0.85 is poor and triggers surcharges. Motors typically operate at PF 0.8-0.9. Utilities sometimes require industrial customers to maintain PF > 0.9 to avoid penalties. Power factor correction equipment (capacitor banks) can improve PF toward unity (1.0).
Reactive power is the portion of apparent power that oscillates back and forth without doing net work, measured in VAR (volt-ampere-reactive). It's essential for creating magnetic fields in motors, transformers, and inductors. However, it requires the utility to provide extra infrastructure (larger cables, transformers) with no revenue benefit. This is why utilities penalize low power factors via 'PF surcharges' or require power factor correction.
On demand charges: utilities multiply by kVA (apparent power), not kW. If PF is low, your kVA is higher than necessary for the same kW, increasing demand charges. Some utilities impose 'reactive power surcharges' for PF < 0.9. Installing capacitor banks for power factor correction can reduce apparent power and lower bills. Payback periods are typically 1-3 years for industrial facilities.
Motors contain inductance (electromagnetic coils). Inductive loads lag the voltage by some angle, creating reactive power consumption. This is why motor-heavy facilities naturally have PF around 0.8-0.9. The percentage of time the motor runs at full load also affects PF: running at lower load worsens PF. Power factor correction (parallel capacitors) supplies leading reactive power to counteract the motor's inductive lagging current.
No, by definition PF is between 0 and 1.0. However, the leading/lagging phase angle matters: negative angles (capacitive, leading) and positive angles (inductive, lagging) are distinct. By convention, we report absolute PF value between 0 and 1. At PF = 1, the load is purely resistive (no phase shift). PF > 0.95 is considered excellent, rarely exceeded in practice.
Use a power quality meter (PQ meter) or multi-function digital meter that displays cos(φ). Most meters show voltage, current, power factor, real power, reactive power, and apparent power. For rough estimation: if you know total power and line values, calculate theoretical power and compare. PF meters give instantaneous or averaged readings (typically over 15-60 min). Industrial standard measurement is per IEC 61000-4-7.
Related Tools
Calculate current divider.
Calculate power transmission.
Size transformers.
Calculate transistor biasing.
Convert volts to electron volts.
Calculate voltage divider.