# Power Factor Calculator

Created by Bogna Szyk
Last updated: Jun 22, 2023

This power factor calculator is handy for analyzing the alternating current (AC) flowing in electrical circuits. You probably already know that you can model the direct current (DC) with the help of Ohm's law. See our Ohm's law calculator for more information. In the case of AC, this task is not that simple, as such circuits contain both real and reactive power covered in our three phase calculator.

This calculator will help you find out the values of the different types of power in the circuit and supply you with a power factor formula that expresses the relationship between the real and apparent power.

## Real, reactive, and apparent power

If you want to understand the power factor, you first need a deeper understanding of its components: the real, reactive, and apparent power.

• Real power (also called true or active power), denoted with P, performs the real work in an electrical circuit and is dissipated in resistors. Visit our power dissipation calculator to explore this further. It is the only form of power that appears in a DC circuit. In an AC circuit, there is no fixed current and voltage values – they change sinusoidally. If there's no phase shift between these two values, then all of the power transferred is active. We measure power in watts.

• Reactive power, denoted with Q, is transferred when the current and voltage are 90 degrees out of phase. In such a case, the net energy transferred in the AC circuit equals zero, and we do not loose any real power. Reactive power never appears in DC circuits. In AC circuits, it's linked to the reactance produced by inductors and capacitors. We measure it in Volt-Amps-Reactive (VAR).

• Apparent power, denoted with S, is the combination of the real and reactive powers. It is the product of the RMS (root mean square) values of voltage and current in the circuit, omitting the influence of the phase angle. It is also a vector sum of P, and Q. We measure apparent power in Volt-Amps (VA).

Are you interested in more power calculators? Our rms voltage calculator may be just what you are looking for.

## The power triangle

We find the apparent power by vector addition of the real and reactive power. You can use a graphical method to represent these three values in the form of a triangle called the power triangle. Each side of the triangle represents one of the three forms of power transmitted in an AC circuit. The legs of the right triangle represent the real and reactive power and the hypotenuse – the apparent power.

One of the consequences of using the power triangle is that you can easily establish the mathematical relationship between the three values with the use of the Pythagorean theorem:

S² = P² + Q²

Additionally, the angle between the real and apparent power, denoted with φ, is the circuit's impedance phase angle.

## Power factor formula

Power factor is the ratio between real and apparent power in a circuit. If there is no reactive power, then the power factor is equal to 1. If, on the contrary, the real power is equal to zero, then the apparent power is also 0.

The power factor formula is:

power factor = P / S

For example, a power factor of 0.87 means that 87% of the current you supply to the circuit is performing real work. The rest of the power – 13%, to be exact – has to be provided to make up for the reactive power. Knowing how to calculate the power factor might be useful, e.g., in computations regarding power generators, covered in our Generator power calculator.

## How to calculate the power factor?

You can also calculate the power factor using the power triangle. Using the principles of trigonometry, you can write it down as

P / S = cos φ

As the power factor is equal to the ratio between real and apparent power,

power factor = cos φ

It means that you can quickly calculate the rest of these values that define an AC circuit by knowing just one out of three values – real, reactive, or apparent power – and either the power factor or the phase angle. Of course, you can use this power factor calculator instead of running the numbers manually! :)

## Resistance, reactance, and impedance

The three main components of an AC circuit are resistors, capacitors, and inductors. You can use this power factor calculator not only to describe the power that is transferred through each of these components but also to establish what happens when an electric current passes through them – namely, what resistance, reactance, and impedance do such elements possess.

• Resistance, denoted by R and expressed in ohms (Ω), is the measure of how much a conductor (most notably a resistor) reduces the electric current I flowing through it. This value is directly linked to the real power flowing in an AC circuit. We can write this relation P = I²R.

• Reactance, denoted by X and also measured in ohms (Ω), is the inertia that opposes the motion of electrons in a circuit component. It is primarily present in capacitors and inductors. If you run AC through a component with high reactance, the voltage drop will be 90 degrees out of phase with the current. Reactance is linked to the reactive power with the equation Q = I²X.

• Impedance, denoted by Z and measured in ohms (Ω), is an AC equivalent of resistance in DC circuits. It is present in all components of all electric circuits. It can be calculated by vector addition of resistance (see below) and reactance or by the formula S = I²Z.

The relationship between resistance, reactance, and impedance is analogical to the power triangle:

Z² = R² + X²

Perfect resistors have nonzero resistance but zero reactance, while perfect inductors or capacitors have zero resistance but nonzero reactance. All components of an electric circuit possess some impedance.

## FAQ

### What is the power factor in AC circuit?

The power factor in AC is defined as the ratio of real power P to the apparent power S because this ratio equals cos ϕ. Generally, you can express it as either a decimal value, for example, 0.85, or as a percentage: 85%.

### What is power factor triangle?

The power triangle graphically represents three parts that make up an AC circuit's power:

• Apparent power (VA) measured in volt-amperes.
• Real power (W) that performs work measured in watts.
• Reactive power (VAR) measured in volt-amperes reactive.

ϕ is the angle between the real and apparent power in degrees. The larger the phase angle, the greater the reactive power.

### What is the power factor unit?

The power factor has no unit. It is dimensionless. You can calculate the power factor as a ratio of active power and apparent power, so it has no unit. The power factor measures how much effective power is used.

### What is the value of a power factor?

In AC circuits, the power factor can range from 0 to 1.0. When the power factor is 1.0 (unity) or 100%, the phase angle between the current and the voltage will be 0° because cos⁻¹(1.0) = 0°. When the power factor equals zero (0), the phase angle is 90° due to the formula cos⁻¹(0) = 90°. The higher the power factor, the more efficient the system will be.

### What does a power factor of 0.75 mean?

A power factor of 0.75 means that only 75% of the power supplied to your device is being used effectively, and 25% is being wasted. The wasted energy is reactive power. Equipment always requires some power to start up, even though it is not doing any actual work. For this reason, the power factor will usually be less than 1.0 (100%).

### How can I calculate power factor correction?

If you need to correct the poor power factor of a circuit, follow these instructions:

1. Measure true power P using a wattmeter.

2. Calculate apparent power S by multiplying load voltage V by load current I S = I × V.

3. Find power factor from the formula power factor = P / S.

4. Find the angle cos⁻¹(power factor) and draw a power triangle.

5. Calculate reactive power Q from Pythagorean theorem:

Q = √(S² - P²).

6. Correct the power factor by adding a capacitor or inductor, the size of which will balance the calculated reactive power.

Bogna Szyk
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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