Engineering
Three-Phase Power Calculator
Calculate balanced three-phase apparent, real, reactive, useful, and loss power from line-to-line voltage, line current, power factor, and load efficiency. Extend real input power across operating hours to audit energy use and cost.
Apparent power (kVA)-
Real input power (kW)-
Reactive power (kvar)-
Useful load output (kW)-
Energy over entered hours (kWh)-
Energy cost over entered hours-
Modeled conversion loss (kW)-
Line current per real kW (A/kW)-
Decision view
Three-phase power triangle and real-power conversion
Three-phase power triangle and real-power conversionThe electrical triangle separates kVA, kW, and kvar while the output bar reconciles useful power and modeled loss.
Exact scenario comparisonPower factor changes while all other entered assumptions remain constant.
| Power factor | Apparent power (kVA) | Real input power (kW) | Reactive power (kvar) | Useful load output (kW) | Energy over entered hours (kWh) | Energy cost over entered hours | Modeled conversion loss (kW) | Line current per real kW (A/kW) |
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How to use Three-Phase Power Calculator
- Enter balanced line voltage and line current.
- Enter power factor as a decimal and load efficiency as a percentage.
- Choose operating hours and an energy rate.
- Read the power triangle before interpreting useful output and period cost.
Calculator guide
Understanding Three-Phase Power Calculator
Balanced three-phase power has three related but different magnitudes: apparent power sets electrical capacity, real power performs work, and reactive power sustains alternating fields. This calculator keeps those quantities, load efficiency, energy, and cost on their correct units.
Calculation method
How the calculation works
Apply the square-root-of-three balanced three-phase relationship to line voltage and current, then separate apparent, real, reactive, useful, and loss power. Multiply line voltage and line current by the square root of three for apparent power, apply power factor for real input power, recover reactive power with the power triangle, and apply efficiency only to real power.
Detailed calculation process
Build the three-phase power triangle before applying load efficiency
The defaults use 400 V line voltage, 125 A line current, power factor 0.88, and 92% load efficiency.
General formula: S = sqrt(3) V_L I_L / 1000; P = S PF; Q = sqrt(S^2 - P^2); P_out = P eta; E = P h; C = E r The square-root-of-three factor converts balanced line quantities to total three-phase apparent power. Power factor projects S onto the real-power axis; efficiency then separates useful output from conversion loss.
What each symbol means
Worked substitution with the default inputs
The default system carries 86.603 kVA, consumes 76.210 kW, exchanges 41.134 kvar, delivers 70.113 kW, and loses 6.097 kW in the modeled load.
Power anatomy
Separate electrical capacity from useful work
The diagram combines the power triangle with a real-power output split.
Worked situations
Practical examples
- A 400 V, 125 A balanced load carries 86.603 kVA.
- At PF 0.88, real input power is 76.210 kW.
- At 92% efficiency, modeled conversion loss is 6.097 kW.
Better inputs
Useful tips
- Confirm whether source data uses line-to-line or phase voltage.
- Do not treat kvar as consumed kWh.
- Use measured demand intervals for tariff analysis.
Before relying on the result
Limitations and common mistakes
- The model assumes a balanced sinusoidal three-phase system.
- Harmonics, imbalance, starting current, conductor temperature, and protection are excluded.
- Tariff demand rules and site electrical design require separate review.
Reference
Key terms
- Apparent power
- RMS voltage-current capacity measured in kVA.
- Real power
- Average power converted to work or heat, measured in kW.
- Reactive power
- Oscillating field power measured in kvar.
Important note
Calculated from the entered values using the displayed engineering relationship. Confirm design values, load cases, safety factors, standards, and field conditions with a qualified professional.
Frequently asked questions
Why is sqrt(3) used?
Balanced three-phase line quantities combine across three phases to produce the square-root-of-three relationship.
Is power factor the same as efficiency?
No. Power factor relates kW to kVA; efficiency relates useful output to real input kW.
Does reactive power create energy cost?
It does not directly create kWh, though it can affect capacity and utility charges.
Can I use phase-to-neutral voltage?
Not in this line-to-line formula unless you first convert the voltage convention.