# Power Factor Calculator

Created by Luciano Mino
Last updated: Aug 16, 2022
Table of contents:

Our power factor calculator is a handy tool that will help you calculate the real power (P), reactive power (Q), and apparent power (S) in an AC circuit.

This all-in-one tool also works as a:

• Power triangle calculator;
• Active power calculator;
• Reactive power calculator;
• Apparent power calculator; and as a
• Phase angle calculator.

Below, we've added a short text explaining everything you need to calculate the power factor using the power factor formula. Let's start!

## Real, reactive, and apparent power

Let's start with the definitions of real, reactive, and apparent power:

• Real power (P): also called true power, active power, or useful power, is the amount of power used or dissipated in the circuit. Its unit is the watt (W).
• Reactive power (Q): this type of power does no real work. Instead, it flows back and forth between the source and load. It is related to inductors and capacitors, and its unit is the volt-ampere reactive (VAR).
• Apparent power (S): the combination of real and reactive powers. It is the product of the RMS (root mean square) values of the voltage (V) and current (I) values. We measure apparent power in volt-amperes (VA).

## Power factor formula

Given the above definitions, we are ready to introduce the power factor definition.

The power factor $pf$ in an AC circuit is the ratio between the real and apparent power:

$pf = \frac{P}{S}$

Thus, it ranges from -1 to 1.

This definition relates the power factor of a device to its efficiency since a power factor closer to one means the device will require less current to produce work.

So, how do you calculate the power factor of a device? Simply replace the real and apparent power values in the formula above (or use our power factor calculator instead).

## How to calculate power factor using the power triangle

As we said before, this tool also works as a power triangle calculator. But, what is the power triangle?

The power triangle is a graphical method to represent the real, reactive, and apparent power and their relations.

Here, the legs represent the real and reactive powers, with the hypotenuse as the apparent power.

As in any right-angle triangle, the Pythagorean theorem holds, and thus the following expression is true:

$S^{2} = P^{2} + Q^{2}$

Lastly, the angle between the real and apparent power is called the phase angle denoted by $φ$. This angle gives us another way of finding the power factor:

$pf = \cos{φ}$
Luciano Mino
Current (I)
A
Power triangle
True power (P)
W
Reactive power (Q)
VAR
Apparent power (S)
VA
Phase angle
deg
Power factor
R, X, and Z
Resistance (R)
Reactance (X)
Ω
Impedance (Z)
Ω
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