Balanced Three-Phase Power Calculator

Use this calculator to connect line-to-line voltage, line current, power factor, and reactive-power direction in an ideal balanced three-phase system.

Updates instantly

|S| = √3 VLLILP = |S| cos φQ = |S| sin φ

Model controls

System values

Line-to-line voltageVLine currentAPower factor

Power triangle

The triangle is redrawn to scale with every change.

Calculated readout

Apparent power

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Real power

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Reactive power

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Power-factor angle

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!Theory model only — do not use it to size, approve, or perform electrical work.

Model assumptions

The calculator assumes a balanced sinusoidal system and uses line-to-line voltage with line current. Its apparent-power relationship is |S| = √3 VLL IL. Lagging reactive power is positive and leading reactive power is negative.

The model does not account for unbalance, harmonics, transients, losses, efficiency, demand, protection, metering conventions, or electrical-code requirements.

Try these theory checks

• Keep voltage and current fixed, then lower the power factor and compare apparent power with real power.
• Switch between lagging and leading and identify which calculated values change sign.
• Set the power factor to one and explain why reactive power and the power-factor angle become zero.

These are original study prompts written for this site.