Free engineering tool
Three-Phase Power Calculator
Calculate active, apparent, and reactive power in balanced three-phase systems using power factor.
Calculator
Calculate three-phase power
For balanced, sinusoidal three-phase systems using RMS line-to-line voltage and line-current values.
RMS voltage measured between two lines, such as 400 V — not line-to-neutral voltage.
RMS current in one line of the balanced three-phase system.
A value from 0 to 1. For non-sinusoidal loads, true power factor can differ from cos φ.
The ratio P₂/P₁. It affects useful mechanical output, not the electrical quantities P₁, Q, and S.
The selection determines the sign of reactive power Q and phase angle φ.
S = √3 × ULL × IL; P₁ = S × cos φ; P₂ = η × P₁
With line-to-line voltage and line current, the √3 formulas apply to both wye and delta connections under balanced loading.
Electrical active power P₁: 5.889 kW
Results
Line current IL
10 A
Apparent power S
6.928 kVA
Electrical active power P₁
5.889 kW
Reactive power Q
3.65 kvar
positive: inductive / lagging
Useful shaft output P₂
5.3 kW
Phase angle φ
31.79 °
Efficiency
90 %
For balanced, sinusoidal systems only. Harmonics or unbalanced loading require measurement or a per-phase calculation.
Formula and calculation method
This calculator uses RMS line-to-line voltage and line current for a balanced sinusoidal three-phase system. With those line quantities, the formulas apply independently of star or delta connection.
Apparent power: S = √3 × ULL × IL
Electrical active power: P₁ = S × cos φ
Reactive power: Q = ±S × √(1 − cos² φ) · Shaft output: P₂ = η × P₁
Assumptions and limitations
- Entered voltage is line-to-line voltage, not phase voltage.
- Efficiency changes mechanical output power, not electrical active, apparent, or reactive power.
- Inductive loads use positive Q and capacitive loads negative Q.
- With harmonics or unbalanced loads, true power factor can differ from cos φ; per-phase measurement is then required.
Technical sources
Formulas and conventions were checked against these primary and manufacturer references.