Three-Phase Power Calculations: kVA, kW, Power Factor, and Transformer Sizing

Three-phase power calculations show up at every level of commercial and industrial electrical work: sizing a service transformer, checking whether a panel can handle additional load, reading a utility bill, and selecting a generator. The confusion is usually about kVA vs. kW—and when each number matters.

This guide covers the three-phase power formulas that come up in NEC calculations, the relationship between kVA, kW, kVAR, and power factor, and a worked example for transformer sizing on a commercial load.

Why Three-Phase Uses a √3 Factor

In a balanced three-phase system, three conductors each carry current at 120 degrees apart. The total power is not simply three times the single-phase value—it’s multiplied by the square root of 3 (1.732), because the phase voltages add as vectors, not scalars.

The practical consequence: a three-phase circuit at 480V and 100A delivers 83.1 kVA, not 48 kVA (single-phase equivalent at the same voltage and current).

The Three-Phase kVA Formula

To solve for line current from a known kVA rating (used when sizing transformer secondary conductors or generator output connections):

kVA, kW, and kVAR: The Power Triangle

kVA is apparent power—the total power the circuit must supply, including both the useful work done (kW) and the reactive power that inductors and capacitors absorb and release each cycle (kVAR). The relationship:

Transformers, generators, and conductors are all sized in kVA, not kW—because they must supply the full apparent power, regardless of how much of it is reactive. A 100 kVA transformer running at 0.70 power factor is only delivering 70 kW of useful work, but its conductors and windings carry current proportional to all 100 kVA.

Power factor in commercial buildings typically ranges from 0.80 to 0.95. Large inductive loads (motors, transformers, fluorescent ballasts) pull PF down; power factor correction capacitors push it back up toward 1.0. The utility charges for reactive power on larger commercial accounts through demand charges—low PF means higher utility bills for the same kW of useful work.

Common Three-Phase Voltage Systems

Worked Example: Sizing a Three-Phase Transformer

A commercial office space has the following connected three-phase loads at 480V:

• HVAC air-handling units: 60A total (three-phase)
• Lighting panelboard (480V feeder): 40A total
• Miscellaneous motor loads: 50A total
• Total line current: 150A at 480V, three-phase

Solving for Secondary Current (Conductor Sizing)

Once the transformer is selected, the secondary conductors must be sized to carry the full transformer output at maximum load. For a 150 kVA, 480V secondary:

From NEC Table 310.16, 75°C copper: 3/0 AWG = 200A ampacity. This is the minimum secondary conductor size for a 150 kVA, 480V transformer under continuous load conditions.

For the primary conductors at 13.8 kV (typical utility service), the same formula applies with the primary voltage substituted. High-voltage conductors are sized and installed by the utility—but the electrician needs the primary current to verify the service disconnecting means rating required by NEC 450.3.

Three-Phase kVA in Load Calculations

When performing a panel load calculation for a three-phase commercial panel, loads are commonly listed in VA or kVA on the panel schedule. To convert between three-phase kVA and amperes—which is what the breakers and conductors are rated in:

This is the same formula as above, rearranged. A 45 kVA three-phase load at 208V draws:

Which rounds to 125A—a common service size for a 208V, three-phase panelboard in a commercial tenant space.

These conversions are the foundation of electrical load calculations for new circuits and the full service sizing calculations covered in the subpanel sizing guide. The electrical load calculator handles the kVA-to-ampere conversions and demand factor applications when building out a complete panel schedule.