Calculation sequence
Step-by-step method
- Use line-to-line RMS voltage and representative line current.
- Calculate apparent power using √3VI.
- Multiply apparent power by true power factor to obtain real power.
ElectricalIntermediateElectrical Fundamentals
Three-Phase Power Calculator
Calculate balanced three-phase real, apparent, and reactive power from line voltage, line current, and true power factor.
Why it matters: kW and kVA are not interchangeable. The distinction affects loading, generator capacity, transformer utilization, and equipment performance.
Calculated result
Engineering evaluation
Three-phase real power (P)74.8 kW
- Apparent power (S)
- 83.1 kVA
- Reactive power (Q)
- 36.2 kvar
- Power factor (PF)
- 0.9
Engineering interpretation
The entered balanced three-phase measurements represent approximately 74.8 kW and 83.1 kVA. For unbalanced or distorted systems, use a three-phase power analyzer and evaluate each phase.
Engineering knowledge center
Understand the calculation—not just the answer
Governing relationships
S = √3 × VLL × I / 1000
P = S × PF
Q = √(S² − P²)
Current substitution
P = √3 × VLL × I × PF / 1000 = √3 × 480 × 100 × 0.9 / 1000 = 74.8 kW.
Equation legend
Inputs and calculated quantities
- VLL
- Line-to-line voltage — V
- I
- Line current — A
- PF
- True power factor — 0–1
- P
- Three-phase real power — kW
- S
- Apparent power — kVA
- Q
- Reactive power — kvar
- PF
- Power factor
Applications
How this calculation is used
Building design
Screen balanced three-phase load relationships.
Construction
Check startup readings against equipment and distribution expectations.
Commissioning
Evaluate measured electrical loading using a true three-phase power analyzer.
Quality controls
Assumptions and limitations
Assumptions
- Balanced three-phase system.
- Sinusoidal or power-analyzer measurements represented by true RMS and true PF.
Limitations
- Unbalanced systems require per-phase analysis.
- Does not include efficiency unless measured at the intended boundary.
Field use
Verification procedure
- Follow electrical-safety requirements.
- Use a correctly rated three-phase power analyzer.
- Confirm phase rotation and connections.
- Record phase values, kW, kVA, kvar, PF, and operating mode.
Common engineering mistakes
- Using phase-to-neutral voltage in the line-voltage equation.
- Using displacement PF when true PF is needed.
- Confusing kW and kVA.
Technical basis
References and source standards
- NIST Guide to the SIElectrical quantity and unit conventions.
- NEMA StandardsMotor and electrical equipment terminology; project-specific edition requires review.
Engineering calculation disclaimer
These engineering tools are provided for educational, preliminary evaluation, field verification, and commissioning support. Results depend on the accuracy of user-entered information and the assumptions stated for each calculation. Every colored status and comparison is a screening indicator only; project criteria, contract requirements, applicable codes, manufacturer instructions, measurement uncertainty, and authorized engineering judgment govern. The tools do not replace project-specific engineering analysis or the judgment of a licensed professional engineer.
Read the full use and limitation statement