Power Systems calculator
Power Factor Triangle Calculator
Visualize and calculate the power triangle relationship between Real Power (kW), Reactive Power (kVAR), and Apparent Power (kVA). Enter any two known values to find all power components, phase angle, and capacitor sizing for power factor correction.
Updated August 4, 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)
| Power Factor | Rating | Action |
|---|---|---|
| ≥ 0.95 | Excellent | No correction needed |
| 0.90 - 0.94 | Good | Consider correction for savings |
| 0.80 - 0.89 | Fair | Correction recommended |
| < 0.80 | Poor | Correction required, likely penalties |
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:
kVAR needed = kW × (tan θ₁ - tan θ₂)
Where θ₁ = current angle, θ₂ = target angle
For detailed PF correction, use the Power Factor Correction Calculator. For penalty analysis, see Power Factor Penalty Calculator.
Common Applications
More applications. Open to review 2 additional use cases.
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?
Low power factor means you draw more current than necessary for your actual work, causing: higher electricity bills (demand charges), larger wire/transformer requirements, increased I²R losses, and possible utility penalties. Most utilities penalize PF below 0.85-0.90.
How do I improve power factor?
Add capacitor banks to supply reactive power locally instead of drawing it from the utility. Size the capacitor bank using kVAR = kW × (tan θ₁ - tan θ₂). Common correction targets are 0.95 to avoid penalties and reduce demand charges.
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 (apparent power), not kW (real power). A facility drawing 100 kW at 0.85 PF requires 117.6 kVA from the transformer — 17.6% more capacity than the actual useful work. Improving PF to 0.95 reduces the required kVA to 105.3 — freeing 12.3 kVA of transformer capacity. This means you can either use a smaller transformer (saving $2,000–$10,000 depending on size) or serve additional load from the existing transformer without upgrading. For facilities approaching transformer capacity limits, PF correction is often cheaper than a transformer upgrade.
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