3-Phase Power Calculator

To calculate three-phase real power, use P(kW) = √3 × V × I × PF ÷ 1000, where V is line-to-line voltage and I is line current. For a 480 V system drawing 20 A at power factor 0.9: √3 × 480 × 20 × 0.9 ÷ 1,000 = 14.96 kW. The apparent power is √3 × 480 × 20 ÷ 1,000 = 16.63 kVA. The calculator above returns real power (kW), apparent power (kVA), and reactive power (kVAR) together.

The defining feature of three-phase math is the √3 factor (approximately 1.732). It appears because the three phases are offset 120° from one another, and when you use the line-to-line voltage (the voltage measured between any two of the three lines), the combined power is √3 times the naive line-voltage-times-current product. Getting this factor and the line-versus-phase voltage right is the crux of every three-phase calculation.

Balanced three-phase systems have three interrelated power quantities:

The terms:

• V (line-to-line voltage) — measured between any two lines, e.g., 208 V, 480 V, or 600 V.
• I (line current) — the current in each supply line.
• PF (power factor) — the cosine of the phase angle between voltage and current, 0 to 1.
• √3 — the constant 1.7320508, arising from the 120° phase geometry.

Real power (kW) does actual work; apparent power (kVA) is what the transformer and conductors carry; reactive power (kVAR) circulates without doing work. The three form a right triangle — the "power triangle" — where kVA is the hypotenuse. To convert three-phase amps straight to kilowatts, this same formula underlies the amps to kW calculator. For single-phase equivalents, use the volts to watts calculator.

These examples work through the full power triangle with arithmetic shown.

Example 1 — 480 V industrial motor: Line current 20 A, power factor 0.9. Apparent power = √3 × 480 × 20 = 16,628 VA = 16.63 kVA. Real power = 16.63 × 0.9 = 14.96 kW. Reactive power = √(16.63² − 14.96²) = 7.25 kVAR. This ~15 kW motor is roughly 20 HP of shaft output.

Example 2 — 208 V commercial load: 30 A per line at PF 0.85. Apparent = √3 × 208 × 30 = 10,808 VA = 10.81 kVA. Real = 10.81 × 0.85 = 9.19 kW. The 0.85 power factor means 15% of the apparent power is reactive.

Example 3 — 240 V three-phase heater (resistive): 25 A at PF 1.0. Real = √3 × 240 × 25 × 1.0 = 10,392 W = 10.39 kW. With unity power factor, kVA equals kW and there is no reactive power.

Example 4 — 600 V large motor: 40 A at PF 0.88. Real = √3 × 600 × 40 × 0.88 = 36,564 W ≈ 36.6 kW. Higher voltage lets this ~49 HP motor draw modest current, keeping conductors small.

A frequent source of error is confusing line and phase quantities. Three-phase systems come in two configurations:

• Wye (star, Y): Line-to-line voltage = √3 × phase voltage. Line current = phase current. A 208 V wye system has 120 V phases (208 ÷ √3 ≈ 120).
• Delta (Δ): Line voltage = phase voltage. Line current = √3 × phase current.

Regardless of connection, the total three-phase power is the same: P = √3 × V(line) × I(line) × PF. This is the beauty of the line-to-line formula — you do not need to know whether the load is wye or delta, only the line voltage and line current, which are what you actually measure at the panel or with a clamp meter.

Common line-to-line voltages: 208 V and 480 V (US wye systems), 240 V (US delta), 400 V (European), and 600 V (Canadian industrial). Always confirm you are entering line-to-line voltage, not phase voltage, into the calculator, because a wye phase voltage is √3 times smaller and would understate power by 42%. The relationship between these voltages and currents traces back to Ohm's law explained.

Three-phase power dominates commercial and industrial installations for concrete engineering reasons:

1. More power per conductor. Three-phase delivers √3 times more power than single-phase for the same line voltage and current, so conductors and equipment are smaller and cheaper per kilowatt.
2. Constant power delivery. The three phases overlap so total instantaneous power is nearly constant, unlike single-phase which pulses at twice line frequency. This gives smoother motor torque and less vibration.
3. Self-starting motors. Three-phase induction motors create a rotating magnetic field naturally, needing no start capacitor or auxiliary winding, making them simpler and more reliable.
4. Efficiency. Balanced three-phase systems carry no neutral current, reducing losses.

For a given real-power demand, moving from single-phase to three-phase (or to a higher line voltage) reduces line current, which shrinks wire size and voltage drop. This is why factories, data centers, EV fast-chargers, and large HVAC systems are three-phase. To size the resulting current, rearrange the formula: I = P ÷ (√3 × V × PF), or convert amperage directly with the amps to kW calculator.

1. Enter the line-to-line voltage. Use the voltage measured between any two lines (208 V, 240 V, 480 V, 600 V). Do not use phase voltage.
2. Enter the line current in amps. Use the current in one supply line, measured with a clamp meter or read from the nameplate full-load amps.
3. Enter the power factor. Use 1.0 for resistive loads (heaters), 0.8–0.9 for motors, or the nameplate value. Poor power factor lowers real kW relative to kVA.
4. Read the results. Real power (kW) is the useful output; apparent power (kVA) sizes transformers and conductors; reactive power (kVAR) shows the non-working component.

The calculator updates live. Use kVA to size a transformer or generator, kW to estimate energy use, and kVAR to gauge power-factor-correction needs.

Three-phase power analysis is essential across industry:

Motor and equipment sizing. Industrial motors, compressors, and pumps are three-phase. Converting nameplate voltage, current, and power factor into kW confirms the load and, with the HP to watts calculator, relates it to mechanical horsepower.

Transformer and generator selection. These are rated in kVA, not kW, because they must handle apparent power. Knowing both kW and kVA ensures the unit is neither undersized nor wastefully oversized.

Power-factor correction. The kVAR figure tells you how much capacitance to add to raise power factor, reduce utility penalties, and free up transformer capacity.

Data centers and EV charging. Large IT loads and DC fast-chargers run on three-phase for density. Accurate kW and kVA figures drive electrical infrastructure and cooling design, and feed energy-cost estimates via the watts to kWh calculator.

Building services and panel scheduling. Electrical engineers building a panel schedule tally every three-phase load in kVA to size feeders, the main breaker, and the service transformer, then track kW separately for energy and demand-charge estimates. A load that reads 37 kW but 41 kVA forces the feeder and transformer to be sized for the larger apparent figure, while the utility's demand charge keys off the kW (and sometimes kVA) peak. Running each motor, chiller, and rooftop unit through the √3 formula, then rolling the results into a total, is the routine that keeps a building's service neither dangerously undersized nor expensively overbuilt.

The three power quantities in a three-phase (or any AC) system are not independent — they form a right triangle that makes the relationships easy to visualize and remember. Understanding this "power triangle" is the key to power-factor correction and correct equipment sizing.

Place real power (kW) along the horizontal leg, reactive power (kVAR) along the vertical leg, and apparent power (kVA) as the hypotenuse. By the Pythagorean theorem, kVA² = kW² + kVAR². The angle between kW and kVA is the phase angle φ, and the power factor is its cosine: PF = cos φ = kW ÷ kVA. A small angle (near 0°) means power factor near 1.0 and almost no reactive power; a large angle means poor power factor and a lot of circulating reactive power.

This geometry has direct financial consequences. Utilities bill large customers for kVA (or penalize low power factor) because their transformers and lines must carry the full apparent current, reactive component included. Adding power-factor-correction capacitors supplies the reactive power locally, shrinking the kVAR leg, pulling the hypotenuse (kVA) closer to the real-power leg (kW), and reducing both the current drawn and the utility penalty. The calculator's kVAR output tells you exactly how much reactive power you would need to offset — for our 480 V, 20 A, 0.9 PF example, that is 7.25 kVAR of correction to reach unity power factor.

The same triangle applies to single-phase AC; three-phase simply scales every side by √3 when using line-to-line voltage. To size the capacitors or evaluate a correction project, compute the existing kVAR here, then the target kVAR at your desired power factor, and install capacitors for the difference. For the underlying single-phase relationships, the volts to watts calculator reports both watts and VA side by side.

• Omitting the √3 factor. Treating three-phase like single-phase understates power by about 42%.
• Using phase voltage instead of line voltage. The formula expects line-to-line voltage; using phase voltage on a wye system gives a result √3 too low.
• Confusing kW and kVA. Sizing a transformer on kW instead of kVA leaves it undersized for reactive loads.
• Ignoring load imbalance. The √3 formula assumes balanced phases; badly unbalanced loads need per-phase analysis.
• Using unity power factor for motors. Motors run at 0.8–0.9 PF, so assuming 1.0 overstates real power.

For related conversions, use the volts to watts calculator, the watts to amps calculator, and the amps to kW calculator.