Three-phase power calculator
Solve a balanced three-phase system from line-to-line voltage, line current and power factor—with electrical input power and useful output kept separate.
Power factor acts between apparent and real electrical input power. Efficiency acts after that, between electrical input and useful output.
Balanced sinusoidal three-phase line values only. No unbalance, harmonics, conductor or protection sizing, installation advice or compliance verdict.
Included
- Balanced sinusoidal three-phase systems
- Line-to-line voltage and line current only
- Real, apparent and reactive power with separate output efficiency
Not included
- Phase-to-neutral inputs, unbalanced loads and harmonics
- Cable, breaker, transformer or protection sizing
- Installation, code-compliance or safety approval
What this means
For a balanced three-phase system, apparent power is S = √3 × V<sub>LL</sub> × I<sub>L</sub>. Real electrical input power is P₁ = S × PF. Reactive power follows the power triangle: Q = √(S² − P₁²).
Efficiency is deliberately separate from power factor. Power factor describes the relationship between real and apparent electrical power; efficiency compares useful output power with real electrical input power.
Every voltage and current field is a line value. The calculator does not accept or infer phase-to-neutral voltage, so the √3 factor is never mixed with an ambiguous phase convention.
Formula & worked example
S = √3 × VLL × IL P₁ = S × PF Q = √(S² − P₁²) P₂ = P₁ × η
400 V line-to-line, 10 A line current, 0.80 power factor and 90% efficiency
- Apparent power
- √3 × 400 × 10 = 6.928 kVA
- Electrical input real power
- 6.928 × 0.80 = 5.543 kW
- Useful output power
- 5.543 × 0.90 = 4.988 kW
Power factor reduces real power relative to apparent power; efficiency then reduces useful output relative to real electrical input.
How this calculation works
The calculation follows the formulas, definitions and assumptions explained on this page. The references below support the method and any stated boundaries.
Official sources
- Schneider Electric — three-phase transformer kVA formula — Public line-to-line voltage × line current × √3 formula and power-factor relationship
- U.S. Department of Energy — basic AC power — Public power-triangle definitions for real, apparent and reactive power and power factor
- NIST — SI units for electric current — Volt, ampere and watt unit relationships used for normalized calculations