Calculation sequence
Step-by-step method
- Combine real and signed reactive power by root-sum-square.
- Divide absolute real power by apparent power.
- Use signed kvar to preserve leading or lagging angle.
ElectricalIntermediateElectrical Fundamentals
AC Power Triangle Calculator
Reconcile signed real and reactive power into apparent power, power-factor magnitude, and power angle.
Why it matters: The signed reactive-power convention distinguishes lagging from leading operation while preserving the measured apparent-power relationship.
Calculated result
Engineering evaluation
Apparent power (S)100 kVA
- Power-factor magnitude (PF)
- 0.8 0–1
- Power angle (φ)
- 36.87 degrees
Engineering interpretation
The entered powers yield 100 kVA at PF 0.8 and angle 36.8699°. Positive kvar is lagging; negative kvar is leading.
Important limitations
- Nonsinusoidal conditions may require additional IEEE 1459 power quantities.
Engineering knowledge center
Understand the calculation—not just the answer
Governing relationships
S = √(P²+Q²)
PF = |P|/S
φ = atan2(Q,P)
Q>0 lagging
Q<0 leading
Current substitution
S = √(80²+60²) = 100 kVA; PF = |80|/100 = 0.8; φ = 36.8699°.
Equation legend
Inputs and calculated quantities
- P
- Real power — kW
- Q
- Signed reactive power — kvar
- S
- Apparent power — kVA
- PF
- Power-factor magnitude — 0–1
- φ
- Power angle — degrees
Applications
How this calculation is used
Building design
Screen power-factor and kvar relationships.
Construction
Check meter sign conventions and phase relationships.
Commissioning
Reconcile measured kW and signed kvar from a power analyzer.
Quality controls
Assumptions and limitations
Assumptions
- Positive kvar is lagging and negative kvar is leading.
- Real and reactive power use the same meter convention and interval.
Limitations
- A displacement-angle interpretation does not fully describe nonsinusoidal conditions.
- Negative real power requires confirmation of the meter export convention.
Field use
Verification procedure
- Follow the approved electrical-safety program and use correctly rated instruments.
- Confirm wiring, ratios, units, operating mode, and measurement boundaries.
- Document simultaneous readings and compare with approved project and manufacturer data.
Common engineering mistakes
- Combining values from different time intervals, phases, or measurement boundaries.
- Treating a screening result as equipment selection, protective-device coordination, or code compliance.
Technical basis
References and source standards
- IEEE Standards AssociationPower quantity, harmonic, transformer, motor, battery, and metering standards; verify the current applicable edition during professional review.
- NIST Guide for the Use of the International System of UnitsElectrical quantity, unit, symbol, and conversion context.
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