Three-phase power calculator converts line voltage, current, and power factor into real, apparent, and reactive power values used for equipment, conductor, plus generator sizing.
Calculate Three-Phase Power (kW, kVA, kVAR) From Voltage, Current, and Power Factor
This tool calculates real, apparent, and reactive power for a balanced three-phase electrical load from line voltage, line current, and power factor. Electricians, industrial electrical engineers, and facility maintenance teams use it to size conductors, transformers, generators, and switchgear for three-phase motors and equipment.
How to Use the Three-Phase Power Calculator
Enter the supply voltage and select whether it’s line-to-line or line-to-neutral. Enter the line current in amps and the load’s power factor (between 0 and 1.0). The calculator returns real power (kW), apparent power (kVA), reactive power (kVAR), phase angle, per-phase impedance, and the active/reactive current split.
Three-Phase Power Formula
For a balanced three-phase load, real power is calculated per IEEE Std 141 (the IEEE Red Book, the standard industry reference for power system analysis in commercial and industrial facilities):
$$P_{kW} = \frac{\sqrt{3} \times V_{LL} \times I \times PF}{1000}$$
Apparent power (the total capacity the source must supply):
$$S_{kVA} = \frac{\sqrt{3} \times V_{LL} \times I}{1000}$$
Reactive power, using the phase angle $\phi = \cos^{-1}(PF)$:
$$Q_{kVAR} = S_{kVA} \times \sin(\phi)$$
$V_{LL}$ is line-to-line voltage. If you only have line-to-neutral voltage, convert first with $V_{LL} = \sqrt{3} \times V_{LN}$ — this √3 relationship between line and phase quantities is the same one documented in IEEE Std 141 for wye-connected systems.
Common input mistake: confusing line current with phase current. In a wye connection, line current equals phase current. In a delta connection, line current equals $\sqrt{3} \times$ phase current. Plugging a phase-current reading into a line-current field (or vice versa) throws the result off by 73%.
Less obvious nuance: the √3 formula only holds for a balanced load — equal current on all three lines. If a clamp meter reads different amps per phase (say 62 A, 58 A, 65 A on an unevenly loaded panel), entering one averaged current into this calculator will understate the power actually drawn on the most heavily loaded leg. For unbalanced loads, calculate each phase separately using phase voltage × phase current × PF, then sum the three results — don’t average the currents first.
Three-Phase Power Diagram (Power Triangle)
P sits on the horizontal leg, Q on the vertical leg, and S is the hypotenuse. The angle phi between P and S is the same phase angle used to derive PF = cos(phi) in the formula above.
Standard Three-Phase Voltages (ANSI/NEMA MG-1)
ANSI/NEMA MG-1 (Motors and Generators standard) lists the preferred voltage ratings that three-phase equipment in North America is built around. Use these to sanity-check whatever voltage a nameplate or utility service reports.
| Voltage Class | Preferred Voltage (per NEMA MG-1) |
|---|---|
| Low voltage | 115 V, 230 V, 460 V, 575 V |
| Medium voltage | 2,300 V, 4,000 V, 4,600 V, 6,600 V, 7,200 V |
Three-Phase Power Calculator FAQs
What’s the difference between line-to-line and line-to-neutral voltage?
Line-to-line voltage is measured between any two of the three phase conductors. Line-to-neutral is measured between one phase conductor and neutral. In a balanced wye system, $V_{LL} = \sqrt{3} \times V_{LN}$.
Does this formula work for both delta and wye connections?
Yes. $P = \sqrt{3} \times V_{LL} \times I \times PF$ uses line voltage and line current for both configurations. The internal phase relationships differ between delta and wye, but the total power formula stays the same.
Why must power factor be between 0 and 1?
Power factor is the ratio of real power to apparent power, and real power can never exceed apparent power in a passive load. A PF above 1.0 or below 0 isn’t physically valid for this calculation.
Can I use this calculator for unbalanced three-phase loads?
Not directly. The formula assumes equal current on all three phases. For unbalanced loads, calculate power on each phase separately using phase voltage and that phase’s current, then add the three results together.
What’s the difference between kW and kVA in the results?
kW is real power — the portion actually doing work. kVA is apparent power — the total capacity the source must be sized to deliver. kVA is always equal to or greater than kW; they’re equal only at PF = 1.0.