Apparent power
S = √3 V_L I_L
Balanced three-phase apparent power from line voltage and line current.
Three-Phase Power Calculator
Calculate balanced three-phase apparent power, real power, reactive power, delivered power, phase angle, and estimated conversion loss from line-to-line voltage and line current.
Access: Free to use, no installation, and No account required. Calculations run in your browser.
Inputs
Results
Three-phase power equations
For a balanced three-phase system using line-to-line voltage and line current, apparent power is S = √3 VLLIL. Real power is P = S·PF, and reactive power is Q = S√(1−PF²).
The optional efficiency input estimates delivered output power as Pout = P·η. It does not model motor slip, harmonics, phase imbalance, nonlinear loads, or detailed converter loss mechanisms.
Engineering reference
Three-Phase Power Calculator: background and worked detail
Use the Three-Phase Power Calculator to calculate apparent power, real power, reactive power, delivered power, phase angle, and estimated losses from line voltage, line current, power factor, and efficiency.
Line, phase, and power relationships
Real power
P = S cosφ = S·PF
Power factor converts apparent power to real input power.
Reactive power
Q = S sinφ = S√(1−PF²)
Reactive power follows from the right-triangle relationship among S, P, and Q.
Balanced three-phase assumptions
For a balanced three-phase system, apparent power is based on line-to-line voltage and line current. Power factor resolves apparent power into real and reactive components, while the efficiency input estimates how much real electrical power reaches the output.
The calculator treats the system as balanced and sinusoidal. It is appropriate for quick power-flow estimates, not harmonic analysis or unbalanced phase-by-phase load studies.
480 V motor load
A balanced 480 V three-phase load draws 30 A at 0.85 power factor with 95% efficiency.
- Apparent power is about 24.9 kVA.
- Real input power is about 21.2 kW and reactive power about 13.1 kVAR.
- Applying 95% efficiency gives about 20.1 kW delivered power and about 1.06 kW estimated loss.
Result: The example corresponds to a phase angle of about 31.8°.
Validation checks
Balanced-load identities make these checks easy to verify by hand.
Unity power factor
Case: Set PF to 1.0.
Expected: Reactive power should be zero and real power should equal apparent power.
100% efficiency
Case: Set efficiency to 1.0.
Expected: Delivered power should equal real input power and estimated loss should be zero.
Assumptions and model boundaries
Assumptions
- Balanced three-phase voltages and currents.
- Sinusoidal steady-state quantities expressed as RMS values.
- Efficiency is represented as a single scalar applied to real power.
Limitations
- Does not resolve phase imbalance, harmonics, neutral currents, or sequence components.
- Does not determine motor torque, transformer thermal loading, or power-quality compliance.
Three-Phase Power Calculator FAQ
Should I enter line-to-line voltage?
Yes. The three-phase mode uses line voltage and line current in S = √3 V_L I_L.
What is the difference between kW and kVA?
kVA is apparent power; kW is the real power doing net work. Power factor links them.
Does efficiency change reactive power?
In this calculator, efficiency is applied to real power to estimate delivered power. Reactive power is calculated from voltage, current, and power factor.
Where this calculation comes from
Shared with the Electrical Design Workbench, which also covers unbalanced loads and harmonic effects this route omits.
Open the source workbench →Read calculation and source methodology →