Three-Phase Power Calculator

Frequently Asked Questions

What is the three-phase power formula?

For a balanced load, P (watts) = √3 × V_line × I_line × power factor. Apparent power S = √3 × V × I (VA) and reactive power Q = √(S² − P²). The √3 (≈1.732) accounts for the 120° phase offset between the three phases.

Is the formula different for delta vs wye?

No - using line voltage and line current, P = √3·V_L·I_L·PF holds for both wye and delta. The configuration only changes the relationship between line and phase quantities, not the total power.

Why is three-phase used over single-phase?

It delivers constant power (no zero-crossings in total), needs less conductor material for the same power, and runs motors more smoothly - which is why industrial and commercial loads are three-phase.

How is single-phase power different?

Single-phase uses P = V × I × PF (no √3). Treat this as an estimate; consult a licensed electrician for design or code-compliant sizing.

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How This Calculator Works

For a balanced three-phase system the real power delivered to a load is P = √3 × V_L × I_L × PF, where V_L is the line-to-line voltage, I_L is the line current, and PF is the power factor (cosine of the angle between voltage and current). The √3 (≈1.732) factor appears because line and phase quantities differ between wye and delta connections, yet the three-phase power expression in line terms is identical for both. Apparent power is S = √3 × V_L × I_L in volt-amps, and reactive power is Q = S × √(1 − PF²) in VAR. This tool solves for power, line current, or power factor depending on which two of the three quantities you supply.

Worked Numeric Example

A 480 V (line-to-line) motor draws 100 A at a power factor of 0.85. Apparent power S = √3 × 480 × 100 = 83,138 VA ≈ 83.14 kVA. Real power P = 83.14 × 0.85 = 70.67 kW. Reactive power Q = 83.14 × √(1 − 0.85²) = 83.14 × 0.527 = 43.8 kVAR. By contrast a single phase of that load at 480 V would deliver only V×I×PF = 480×100×0.85 = 40.8 kW - the three-phase total is √3 larger, not 3×, because the per-phase voltage in a wye is V_L÷√3.

Real-World Use

Three-phase power is the backbone of industrial and commercial electrical distribution: motors, HVAC compressors, pumps, elevators, and large UPS systems all run on it. Engineers use this calculation to size conductors and breakers, verify generator and transformer loading, estimate utility demand charges (billed on kW and often kVA), and check whether a motor is operating within nameplate ratings. A drop in measured power factor at constant kW signals rising current - useful for predictive maintenance on aging motor windings.

Common Mistakes

The single biggest error is confusing line voltage with phase voltage. The √3 formula always uses line-to-line voltage and line current. Mixing a phase voltage into a line formula introduces another √3 error. A second mistake is treating power factor as optional - omitting it (PF = 1) overstates real power for any inductive load. Do not multiply single-phase power by 3 to get three-phase power; the correct relationship between per-phase and total uses the line quantities directly. Finally, kVA and kW are not interchangeable: a 100 kVA transformer at 0.8 PF delivers only 80 kW.

Limitations & Related Tools

This calculator assumes a balanced three-phase system with sinusoidal voltages. Real installations with significant phase imbalance, harmonic distortion from variable-frequency drives, or non-linear loads require true-RMS instruments and per-phase analysis. It does not account for conductor voltage drop, transformer impedance, or starting inrush, which can be several times running current. For low power factor seen here, pair this with a power-factor correction (capacitor kVAR) calculator; for conductor sizing use a voltage-drop or ampacity tool; and for transformer loading see the transformer sizing calculator.

Three-Phase Power Calculator

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