When to use: Quick balanced 3-phase power calculations from line-to-line voltage, current, and power factor. Use Solve for Power to find kW, kVA, and kVAR from known voltage/current/PF, or Solve for Current to back-calculate amps per phase from a known real power (kW) load.
This calculator solves the standard balanced three-phase power relationships between voltage, current, power factor, and the three power quantities engineers work with daily: real power (kW), apparent power (kVA), and reactive power (kVAR). It supports two directions — computing power from a known voltage/current/PF, or back-calculating the required current from a known kW load — covering the most common 3-phase sizing and verification questions.
For a balanced three-phase system with line-to-line voltage V (in volts) and line current I (in amps), apparent power is kVA = (√3 × V × I) / 1000. Real power is kW = kVA × PF, where PF is the power factor (the cosine of the phase angle between voltage and current). Reactive power is kVAR = √(kVA² − kW²), representing the power triangle relationship between the three quantities. To solve in reverse — finding the current required to deliver a known kW load — rearrange to I = (kW × 1000) / (√3 × V × PF).
A three-phase system has three voltage waveforms spaced 120° apart. The line-to-line voltage measured between any two phases is not simply the sum of two phase voltages — because the waveforms are out of phase, the resultant is found using vector (phasor) addition, which works out to line-to-line voltage = √3 × phase voltage for a wye-connected system. That same √3 factor carries through into the power formula: total 3-phase power is 3 × (phase voltage × phase current × PF), and substituting phase voltage = line voltage / √3 simplifies to √3 × V(line) × I(line) × PF. This is why single-phase power (P = V × I × PF) and three-phase power (P = √3 × V × I × PF) look different even though both come from the same underlying per-phase relationship.
Real power (kW) is the power actually converted into useful work — heat, light, rotation. Apparent power (kVA) is the total power the source must supply, combining real and reactive power, and is what determines the required current-carrying and thermal capacity of conductors, transformers, and generators. Reactive power (kVAR) does no useful work but is exchanged with inductive loads (motors, transformers) and capacitive loads (capacitor banks, long cables) to sustain their magnetic or electric fields. Power factor (PF = kW / kVA) expresses how efficiently apparent power is converted to real power — a PF of 1.0 means all apparent power is real power, while a lower PF means more current is needed to deliver the same real power, increasing losses and required equipment capacity.
The factor of 3 accounts for having three phases, but because the three phase voltages are 120° apart rather than in phase, their line-to-line relationship involves vector addition, not simple arithmetic addition. Working through the phasor math for a balanced wye or delta system reduces the combined three-phase power formula to √3 × V(line) × I(line) × PF rather than 3 × V(phase) × I(phase) × PF — both are mathematically equivalent, but the √3 × line-to-line form is the practical formula engineers use since line-to-line voltage and line current are what get measured in the field.
kW (kilowatts) is real power — the power that actually does work. kVA (kilovolt-amps) is apparent power — the total power the electrical system must supply and the value used to size conductors, transformers, and generators, since it reflects actual current draw regardless of power factor. kVA is always equal to or greater than kW; they are equal only at unity power factor (PF = 1.0).
They use different formulas because of how the phases combine: single-phase power is P = V × I × PF, while three-phase power is P = √3 × V × I × PF for the same line current and voltage magnitude. You cannot directly convert a single-phase kW figure to 3-phase by simply multiplying by 3 unless you are also converting from phase voltage to line voltage — use this calculator's formulas directly with your actual line-to-line voltage and per-phase current rather than trying to scale a single-phase number.
For general industrial and commercial loads with a mix of motors and resistive loads, 0.85–0.9 is a common planning assumption. Purely resistive loads (heating elements) run close to PF = 1.0. Induction motors at partial load can run as low as 0.6–0.7. For any real design, use the power factor from the actual equipment nameplate or a field power quality measurement rather than an assumed value — this calculator uses whatever PF you enter directly.
Yes. All formulas here assume equal voltage magnitude and equal current magnitude across all three phases, which is standard practice for sizing calculations on healthy, evenly-loaded systems. Real-world unbalanced loading, harmonics from non-linear loads (VFDs, electronic ballasts), and asymmetric faults require more detailed per-phase analysis that a single balanced calculation cannot capture.
Try our Electrical Studio
More calculators, simulators, and guides for this discipline.