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 June 21, 2026

Calculator Inputs

Desired PF for correction calculation

Calculation Results

Enter values above to see calculation results

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Calculation history

Example Calculations

100 kW at 0.85 PF

Typical industrial load analysis with correction to 0.95.

Inputs
  • Calculation Mode: kW and power factor
  • Real Power: 100
  • Power Factor: 0.85
  • Target Power Factor: 0.95

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

Load Analysis - Determine actual vs apparent power for billing

Transformer Sizing - Size transformers based on kVA demand

Capacitor Selection - Calculate capacitor bank for PF correction

Motor Analysis - Understand motor power consumption

Utility Billing - Verify demand charges and penalties

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.