# Power Factor Correction Calculator

Size the shunt capacitor needed to raise the power factor: C = P·(tanφ₁ − tanφ₂)/(2π·f·U²). Returns compensated reactive power Qc, capacitive reactance Xc, capacitor current Ic, and the required capacitance in F/μF.

> Canonical page: https://elysiatools.com/en/tools/power-factor-correction

- **Category:** Math & Numbers

- **Keywords:** power factor correction, PFC, capacitor sizing, reactive power compensation, cosφ, tanφ, Qc, electrical engineering, power systems

## Overview

The Power Factor Correction Calculator helps electrical engineers and facility managers size the shunt capacitor required to improve system efficiency. By entering the active power, initial and target power factors, line frequency, and voltage, you can instantly calculate the compensated reactive power (Qc), capacitive reactance (Xc), capacitor current (Ic), and the exact capacitance needed in farads and microfarads.

## Inputs

- **Active Power P (W)** (number): Real (active) power drawn by the load.
- **Initial cosφ₁** (number): Initial power factor (lagging). 0 < cosφ₁ < 1.
- **Target cosφ₂** (number): Target power factor (lagging). Must be > cosφ₁.
- **Frequency f (Hz)** (number): AC line frequency (50 or 60 Hz typical).
- **Voltage U (V)** (number): Voltage across the capacitor (line-to-line for a 3-phase bank, or phase voltage for single-phase).
- **Decimal Places** (number)

## When to use

- Designing capacitor banks for industrial facilities to avoid low power factor penalties from utility companies.
- Sizing shunt capacitors for electrical systems to reduce line losses and voltage drops.
- Analyzing reactive power compensation requirements during electrical system upgrades or equipment installations.

## How it works

- Enter the active power (P) in Watts, the initial lagging power factor (cosφ₁), and your desired target power factor (cosφ₂).
- Input the AC line frequency (f) in Hz and the voltage (U) across the capacitor in Volts.
- The calculator computes the initial and target tangent angles (tanφ₁ and tanφ₂) to determine the required compensated reactive power (Qc).
- It outputs the required capacitance in Farads and Microfarads, along with the capacitive reactance (Xc) and capacitor current (Ic).

## Use cases

- Calculating capacitor sizing for a manufacturing plant to eliminate utility billing surcharges.
- Determining the reactive power compensation needed for a large induction motor installation.
- Specifying component values for electrical distribution panel upgrades.

## Frequently asked questions

### What is power factor correction?

It is the process of improving a low power factor by adding capacitors to offset inductive reactive power, reducing overall current draw.

### Why should I target a power factor below 1.0 instead of exactly 1.0?

Targeting exactly 1.0 requires an impractical amount of capacitance and risks overcorrection, which causes high voltage and resonance issues.

### What voltage value should I enter for a three-phase system?

Enter the voltage that will be applied directly across the capacitor terminals, which depends on whether the capacitor bank is connected in delta or star.

### How does frequency affect the required capacitance?

Higher AC frequencies require less capacitance to achieve the same reactive power compensation because capacitive reactance decreases as frequency increases.

### What is the difference between active power (P) and reactive power (Q)?

Active power performs the actual work in a circuit, while reactive power sustains the electromagnetic fields in inductive loads like motors.

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