Power Systems calculator
Power Factor Triangle Calculator
Calculate the simplified power-triangle relationship between real power (kW), reactive power (kVAR), apparent power (kVA), and power factor. Choose one of the supported input pairs; an optional target power factor adds a preliminary capacitor kVAR estimate when the target is higher than the calculated power factor.
Updated October 29, 2026
Example Calculations
How to Use
Quick Answer
What is the power triangle formula?
S² = P² + Q² where:
- P = Real Power (kW) - does actual work
- Q = Reactive Power (kVAR) - sustains magnetic fields
- S = Apparent Power (kVA) - total from source
Power Factor = P ÷ S = cos(θ). The calculator accepts these input pairs: kW + power factor, kVA + power factor, kW + kVAR, or kVA + kW. It does not accept every possible pair of triangle values.
Power Triangle Relationships
From kW and Power Factor:
kVA = kW ÷ PF
kVAR = √(kVA² - kW²)
Example: 100 kW at 0.85 PF → 117.6 kVA, 61.9 kVAR
From kW and kVAR:
kVA = √(kW² + kVAR²)
PF = kW ÷ kVA
Power Factor Correction Formula:
Estimated capacitor kVAR = kW × (tan θ₁ - tan θ₂), when the optional target PF is greater than the calculated PF. This is a preliminary reactive-power estimate; it does not select capacitor equipment or check harmonics, switching, voltage rise, or utility requirements.
For detailed PF correction, use the Power Factor Correction Calculator. For penalty analysis, see Power Factor Penalty Calculator.
Common Applications
Frequently Asked Questions
What is the difference between kW, kVA, and kVAR?
kW (kilowatts) is real power that does actual work like running motors. kVA (kilovolt-amps) is apparent power - the total power your system draws. kVAR (kilovolt-amps reactive) is reactive power needed to maintain magnetic fields but does no useful work. PF = kW/kVA.
Why is a low power factor bad?
For the same real power and voltage in a comparable operating condition, a lower power factor corresponds to higher current. The calculator does not estimate bill changes or determine whether a utility tariff applies a power-factor threshold or penalty; check the applicable tariff and measured load data.
How do I improve power factor?
A higher target power factor can be used to estimate the reactive kVAR change with kVAR = kW × (tan θ₁ - tan θ₂). Treat that result as a preliminary estimate, then review the operating profile, harmonics, switching, equipment instructions, and applicable utility requirements before selecting capacitor equipment.
What causes low power factor?
Inductive loads cause lagging power factor: lightly loaded motors, welding machines, induction furnaces, fluorescent lighting with magnetic ballasts, and VFDs with poor input filtering. Leading PF (rare) comes from over-corrected capacitors.
How does power factor affect transformer sizing?
Transformers are rated in kVA. At 100 kW, the simplified power-triangle calculation gives about 117.6 kVA at 0.85 PF and 105.3 kVA at 0.95 PF, a 12.3 kVA difference in calculated demand. This comparison alone does not establish transformer suitability, available capacity, or project cost; verify actual load measurements and equipment ratings.
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