Power Factor Calculator – Compute PF, Reactive Power, and Capacitor kVAr

The power factor calculator helps you quantify how efficiently electrical power is used by your load or facility. It computes power factor (PF), phase angle (φ), real power (P), apparent power (S), reactive power (Q), and the capacitor bank size (kVAr) needed to correct a low power factor to a chosen target. Whether you work with single-phase motors or three-phase industrial systems, this tool translates voltage, current, and power data into actionable numbers for performance and savings.

What Is Power Factor?

Power factor represents the ratio of real power to apparent power in an AC circuit and ranges from 0 to 1. Mathematically, PF = P/S = cosφ, where φ is the phase angle between voltage and current. A lagging power factor (typical for inductive loads such as motors and transformers) indicates that current lags voltage, drawing reactive power (Q). The power factor calculator exposes these relationships so you can diagnose inefficiencies and plan corrective actions.

Key Quantities and Formulas

• Real Power (P): P = S × PF (kW) — the useful work done.
• Apparent Power (S): For single-phase, S = V × I; for three-phase (balanced), S = √3 × V_LL × I (kVA).
• Reactive Power (Q): Q = √(S² − P²) (kVAr) — oscillates between source and reactive elements.
• Power Factor (PF): PF = cosφ = P/S (dimensionless).
• Phase Angle (φ): φ = arccos(PF) (degrees).

By combining these, the power factor calculator can infer any missing quantity from two known values.

Power Factor and Energy Costs

Utilities may apply penalties when PF falls below a threshold (e.g., 0.9 or 0.95). Low PF increases current for a given real power, driving higher I²R losses and requiring larger conductors and transformers. Correcting PF with capacitors (or active filters) reduces reactive power demand and can lower utility charges. See general background in U.S. EIA – Delivery & Use of Electricity.

How the Power Factor Calculator Works

1. PF from P, V, I: Enter voltage and current (and either P or PF); the tool computes S, P, Q, PF and φ.
2. Power relationships: From any two (P, S, Q, PF), the calculator solves the rest using Pythagorean power triangle.
3. PF correction sizing: Enter initial PF, target PF, and real power; the power factor correction calculator outputs kVAr = P × (tanφ₁ − tanφ₂).

This workflow reflects typical plant maintenance tasks—measure currents and voltages, estimate load power, then size correction capacitors.

Single-Phase vs Three-Phase

In single-phase systems, apparent power is simply V × I. In balanced three-phase systems, apparent power is √3 × V_LL × I, where V_LL is line-to-line voltage. The power factor calculator switches formulas automatically when you choose the phase option. If your three-phase system is unbalanced or heavily distorted, consider per-phase measurements or a power quality analyzer.

Reactive Power and Capacitor Banks

Most industrial loads are inductive and draw positive (lagging) reactive power. Capacitors supply negative (leading) reactive power to cancel part of Q, raising PF closer to 1. The required compensation is:

kVAradd = P × (tanφ₁ − tanφ₂),  where φ = arccos(PF)

After computing kVAr, choose the nearest standard capacitor step (e.g., 5, 10, 25, 50 kVAr), and ensure voltage, kvar rating, detuning for harmonics, and switching method (fixed vs automatic PFC). High-quality application notes are available from Schneider Electric – Reactive energy compensation and Fluke – What is power factor.

Worked Examples

Example 1 – PF from P, V, I (Single-Phase)

Given V = 230 V, I = 10 A, measured P = 1.5 kW. Apparent power S = 230 × 10 / 1000 = 2.30 kVA. PF = 1.5 / 2.30 ≈ 0.652; φ ≈ arccos(0.652) ≈ 49.2°. Reactive power Q = √(2.30² − 1.50²) ≈ 1.71 kVAr.

Example 2 – Three-Phase Motor

Balanced 400 V (line-to-line), 50 Hz, I = 120 A, PF ≈ 0.82. S = √3 × 400 × 120 / 1000 ≈ 83.1 kVA. P = 83.1 × 0.82 ≈ 68.1 kW. Q = √(83.1² − 68.1²) ≈ 46.8 kVAr. If target PF is 0.95: φ₁ = arccos(0.82), φ₂ = arccos(0.95). kVAr_add = 68.1 × (tanφ₁ − tanφ₂) ≈ 24.2 kVAr.

When to Correct Power Factor

• Utility penalties or demand charges tied to PF thresholds (often <0.95).
• Overheating cables/transformers due to higher RMS current at low PF.
• Voltage drop issues under motor starts or variable loads.
• Desire to free up transformer capacity or reduce line losses.

Use the power factor calculator to quantify the gap and estimate kVAr before you request quotes for capacitor banks or active filters.

Common Pitfalls

• Ignoring harmonics: Capacitors can resonate with network impedance. Consider detuned banks (e.g., 189 Hz at 50 Hz systems).
• Seasonal variation: PF varies with load mix; fixed kVAr may overcorrect at light load. Automatic PFC stages help.
• Unbalanced systems: Measure per phase for accuracy; PF on a single phase may differ from overall.
• PF < 0 or leading PF: Overcorrection leads to leading PF, which can also incur penalties or create instability.

Measuring Power Factor

Clamp meters with PF, true-RMS voltmeters, and portable power quality analyzers provide direct PF readings along with harmonics. Refer to Fluke power quality resources. For engineering standards and definitions, see relevant IEEE publications.

Related Electrical Calculators

• Watts to Amps Calculator
• Watts to Volts Calculator
• Ohm’s Law Calculator
• Inductance Calculator

Key Takeaways

• PF = P/S = cosφ; low PF increases current and losses.
• Use capacitors to supply leading kVAr: kVAr_add = P × (tanφ₁ − tanφ₂).
• Size for operating scenarios; consider detuning for harmonics and staged control.
• The power factor calculator gives fast estimates to guide design and vendor discussions.

Further reading: Schneider Electric – Reactive energy compensation • Fluke – What is power factor • EIA – Delivery & Use of Electricity

Disclaimer: This power factor calculator is for educational purposes only. Always verify ratings, safety margins, and standards with a qualified engineer before implementing PF correction equipment.