Three-Phase Power Calculator — Watts, VA and kVA

Calculate three-phase real power (W), apparent power (VA) and kVA from line voltage, line current and power factor using P = √3 × V_L × I_L × PF.

Results are estimates for planning and education, based on your inputs and standard engineering values (AWG resistance, NEC ampacity, resistivity). Electrical work can be dangerous and is governed by the NEC and your local code — verify all sizing with a licensed electrician and your authority having jurisdiction (AHJ). Not a substitute for professional design.

Calculator

Real power8,314 W
Apparent power8,314 VA
Apparent power8.31 kVA

Formula

For a balanced three-phase load the real power is P = 1.732 × V_L × I_L × PF, the apparent power is VA = 1.732 × V_L × I_L, and kVA = VA / 1,000, where V_L is the line-to-line voltage, I_L the line current, 1.732 the square root of 3 and PF the power factor (0–1). Real power (watts) is what the load consumes; apparent power (volt-amps) is what the source and conductors must carry. To find the line current from a known kVA, rearrange to I_L = VA / (1.732 × V_L).

Worked example

480 V line-to-line at 10 A line current with a power factor of 1: VA = 1.732 × 480 × 10 = 8,314 VA = 8.31 kVA, and because PF is 1 the real power is also W = 8,314 W. At a power factor of 0.85 the same 480 V and 10 A still draw 8,314 VA but deliver only W = 8,314 × 0.85 = 7,067 W of real power — the extra current is reactive and does no work, yet the conductors and breaker must still carry it.

Three-phase power is where the factor √3, about 1.732, enters, and getting it wrong is a classic source of sizing errors. This tool relates voltage, current, power factor and either real power in kW or apparent power in kVA for a balanced three-phase load, so line and phase quantities line up correctly. Three-phase delivers more power on smaller conductors than single-phase for the same load, which is why it dominates commercial and industrial installations and larger motors. Keep the distinction between line-to-line and line-to-neutral voltage clear, since mixing them is the usual mistake, and treat the result as a balanced-load estimate — real systems carry some imbalance that a hand calculation does not capture.

Frequently asked questions

How do I calculate three-phase power?
Multiply 1.732 (√3) by the line-to-line voltage, the line current and the power factor: P = 1.732 × V_L × I_L × PF. For apparent power drop the power factor: VA = 1.732 × V_L × I_L. Divide by 1,000 for kW or kVA.
Should I use line or phase voltage?
Use the line-to-line voltage (for example 208 V, 240 V or 480 V) with the line current in P = √3 × V_L × I_L × PF. The √3 factor already accounts for the relationship between line and phase quantities in a balanced system, so you do not also convert to phase voltage.
What is the difference between kW and kVA in three-phase?
kVA is apparent power, the volt-amps the system must supply (√3 × V_L × I_L / 1,000). kW is real power, the part that does work (kVA × PF). The closer the power factor is to 1, the closer kW is to kVA. Transformers, generators and conductors are sized in kVA because they must carry the full current regardless of power factor.
How do I find the line current from kVA?
Rearrange the apparent-power formula: I_L = kVA × 1,000 / (1.732 × V_L). A 50 kVA load at 480 V draws 50,000 / (1.732 × 480) = 60.1 A per line.
Why is three-phase more efficient than single-phase?
For the same power, three-phase delivers it across three conductors at a lower line current, so the conductors can be smaller and motors run more smoothly with a constant power flow. That is why commercial and industrial distribution and larger motors are three-phase.
Does power factor change the current my wires carry?
Yes. Conductors and protective devices carry the full line current set by the apparent power (VA), not the real power. A low power factor means more current for the same useful watts, so always size the circuit from VA and amps, not from kW alone.

Source: P = √3 × V_L × I_L × PF (balanced three-phase) · All sources

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