Last Updated on November 12, 2021 by Jahangir

I’m sure you’ve realized that the **power factor formula** is an important formula for electrical fields that needs to be understood. The power factor of a circuit could vary wildly, and it could be high, low, or somewhere in the middle. The objective of this article is to discuss what a power factor is, how it is calculated, and the factors that affect it.

## An introduction to power factor

Electrical engineers place a high value on power factor; it is used across all electrical and electronic equipment. It is first important to understand what the power factor is all about because it is basically the ratio between the amount of actual power consumed (measured in watts) and the amount of apparent power consumed (measured in volt-amperes). Real power refers to the actual amount of energy being consumed by a load, while apparent power refers to the voltage and current that appear to flow through a circuit.

By definition, the power factor is the relationship between actual and apparent powers, typically between 0 and 1. There is a power factor of one which indicates that actual and apparent power is the same.

## What is the power factor?

In a circuit, the power factor is calculated by dividing the real power by the apparent power. In a power factor, it pertains to how well a source of electrical energy is being utilized by a load. During a power supply, the power factor compares the incoming power provided to the power used by the load. The power factor is most commonly 0.85 in India/Bangladesh, although it can be much lower or higher.

It depends on the type of load and how much current is drawn to figure out what power factor the load has. The power factor of a circuit is its ratio of delivered to consumed energy. There is a direct correlation between the power factor and the amount of power delivered per unit of a circuit that is active. The power factor is employed to judge the power that an AC circuit gets from its real power compared with the apparent power that it produces.

It is often referred to as volt-ampere power (VA) or real power (W), but usually, they are measured separately. Using this formula, one can calculate the power factor as the cosine of the angle between current and voltage. Angles of 0 degrees produce a power factor of 1; those of 90 degrees produce a power factor of 0. It is considered poor if the power factor is less than 0.7. It is considered good if the power factor is greater than 0.80. 1.0 is the perfect power factor.

**What is the power factor formula? How to calculating power factor 2021? **

An electrical load’s power factor is an indicator of how efficiently electric power that has been delivered to the load is being used. Comparing two loads with different power factors, a load with a greater power factor draws a small current, reducing power consumption and lowering an energy bill. Having an understanding of a load’s power factor is valuable since it tells us about the conditions under which it operates. When calculating the power factor of an electric load, a power factor formula is used.

There is no dimension to the PF. The PF of an ideal power source is 1.0. The power factor (pf cos) of a circuit can be obtained by using the power formula of a circuit as described below.

Power factor=Fp= cosφ

P=V*I*power factor

P=V*I*PF

PF=P/VI

## How to calculate power factor in your home/office

According to the IEEE, the power factor is regarded as the proportion of true or active power or real power consumption by the load to the apparent power consumption of the load. Understanding power factor is useful, especially for sensitive equipment. Whenever the power factor is low, a large electric motor is going to use a lot more electricity. Electricity supplied by providers may be billed at a higher rate in some countries with poor power factor. Electric engineers use power factor to judge the efficiency of the electrical circuit.

Figure 1: Resistive load circuit

The phase angle between V and I is zero degrees, if we were dealing with a purely resistive load like the load shown in the figure, then the power factor would be 1. **cos φ**; PF=Cos0=1

P=V*I*PF

Here total power is

P=50*5*1

P=250watts

The phase angle between V and I is 90 degrees, if we were dealing with a purely reactive load (inductive load or capacitive load) like the load shown in the figure, then the power factor would be 0. PF=Cos90=0

Figure 2: Reactive load circuit

Here total power is

P=50*5*0=0watts

### Single-Phase Calculations

In 1-phase, line voltage, current, power as well as power factor are correlated. In order to calculate the power of 1-phase circuits, the following equation is usually used:

P = pf × I × V.

Power Triangle is another method what we can use for determining the PF.

**Example of single-phase system for calculating power factor 2021:**

Figure 3: Circuit diagram considering single phase circuit

If we consider Voltage 220voltage, current 5amp, and power 935watts i.e 0.935 kilowatts kw, then the power factor would be as-

PF= (935watt)/ (220volts*5amp)=935watts/1100VA=0.85

Furthermore, you can utilize the calculation for the **motor power factor**. As an example, if your motor has 2hp, voltage 220volts and the current of the motor is 7amp, then we can easily find out the motor power factor using the below formula.

We know 1 Horse Power=746watts

so, 2horse power=746*2=1492watts

Again we know PF=Power/(Volts*Current)

PF=1492/(220*7)=1492/1540=0.96

In this way, you can utilize the above equation to determine the motor power factor formula 2021.

**Effect on power factor to the actual power**

In this paragraph, we will see how the current changes according to the power factor. Here, I have considered 220voltage, and power 500watt for the below single-phase system. Then I assumed different values of power factor in order to check the required current for constant power.

Sl | Voltage in V | Power in watt | PF | Current in amp |

1 | 220 | 500 | 0.3 | 7.575758 |

2 | 220 | 500 | 0.4 | 5.681818 |

3 | 220 | 500 | 0.5 | 4.545455 |

4 | 220 | 500 | 0.6 | 3.787879 |

5 | 220 | 500 | 0.7 | 3.246753 |

6 | 220 | 500 | 0.75 | 3.030303 |

7 | 220 | 500 | 0.8 | 2.840909 |

8 | 220 | 500 | 0.85 | 2.673797 |

9 | 220 | 500 | 0.9 | 2.525253 |

10 | 220 | 500 | 1 | 2.272727 |

Table 1: PF in single-phase system

I then entered the value of power factor and current on a graph to find the required current for the single-phase system for specific power. The graph is shown below.

Figure 4: Power factor versus current in single-phase system

From the above graph, we can see when the power factor is 1/unity of the single-phase system, the required current is 2.27amp. On the other hand, when the power factor is 0.3 of the single-phase system, the required current is 7.57amp. This means when the power factor is low, then we need more current to operate the same capacity/power of equipment. Hence, a greater power factor is required in order to reduce the system loss of power system.

**Three-Phase Power Factor Formula 2021**

Figure 5: Circuit diagram considering single phase system

In 3-phase, voltage, current, power as well as power factor are correlated. In order to calculate the power of three-phase circuits, the following equation is usually used:

P = √3 × pf × I × V.

**Example of the three-phase system:**

If we consider Voltage 220voltage, current 5amp and power 935watts of a three-phase system, then the power factor would be as-

PF= (935watt)/ (220volts*5amp*1.73)=935watts/ (1.73*1100VA)=0.49

**Effect on power factor to the actual power**

In this paragraph, we will look at how the current changes if the power factor of the load varies. For the following three-phase system, I have taken 220volts and power p of 500watts into account. Therefore, I assumed that the power factor would be different in order to determine the current needed for a constant power supply.

Sl | Voltage in V | Power in watt | PF | Current in amp |

1 | 220 | 500 | 0.3 | 4.379050622 |

2 | 220 | 500 | 0.4 | 3.284287966 |

3 | 220 | 500 | 0.5 | 2.627430373 |

4 | 220 | 500 | 0.6 | 2.189525311 |

5 | 220 | 500 | 0.7 | 1.876735981 |

6 | 220 | 500 | 0.75 | 1.751620249 |

7 | 220 | 500 | 0.8 | 1.642143983 |

8 | 220 | 500 | 0.85 | 1.545547278 |

9 | 220 | 500 | 0.9 | 1.459683541 |

10 | 220 | 500 | 1 | 1.313715187 |

Table 2: Power factor versus current in three-phase system

Figure 6: Power factor versus current in single-phase system

Using that information along with the value of power factor and current that was entered into the graph, I was able to find the required current for a three-phase system for a given power. Below you can see a graph of the data.

Figure: Power factor versus current in three-phase system

When the power factor of the three-phase system is 1/unity, we can see that the required current is 1.13amps. The required current for a three-phase system is 4.37 amps when the power factor is 0.3. The low power factor, the higher the current required for a piece of equipment to run. Power systems need to have a higher power factor in order to reduce their system losses.

### Single-Phase Two-Phases (2 p) and Three-Phase (3 p) System

In electrical engineering, alternating current (AC) can be as both single-phase and three-phase power. AC systems have a continuous amplitude (i.e., size) and direction of current variations, which are typically characterized by sine waves. Sine function describes a smooth variation with peaks and valleys. Such waves do not exist in single-phase systems.

In a two-phase system, this would be divided into two parts. In each phase of current, the phase difference is half a cycle out of phase with the others. A wave, which describes the first part of the alternating current, reaches its maximum value at the same time as another reaches its minimum.

There isn’t much 2 phase power, however. A system with three phase circuit splits the current into three components out of phase, rather than two. A third of a cycle separates each of the parts of the current. As a result, the pattern is more complex than with two-phase power, but the cancellation is the same. In spite of being identical in size, each component has a different direction from the others.

### Converting kW to Amps

In this paragraph, we will learn how to convert KW to Amp. To determine the ampere/current of a three-phase system, we need to know KW, Voltage, and power factor.

If we consider Voltage 220voltage, Power Factor 0.8, and power 0.935Kws of a three-phase system, then the current of the system would be as-

P = √3 × pf × I × V; I=P/(1.73*PF*V)=0.935/(1.73*0.8*220)=0.935/304.48 Kamp=3.07Amp

### Converting Amps to kW

In this paragraph, we will learn how to convert Amps to Kw. To determine the KW of a three-phase system, we need to know Amp, Voltage, and power factors.

If we consider Voltage 220voltage, Amp 5amp, and power factor o.8 of a three-phase system, then the power of the system would be as-

P = √3 × pf × I × V=1.73*0.8*5*220=1522watts=1522/1000Kw=1.522Kw

## Advantages of Power Factor Correction System

Power factor correction is a system that improves the power quality by reducing energy losses and harmonics. The main reason for using PFC in an electrical distribution system is to reduce the amount of reactive power (VARs) generated by induction motors or inductive loads, which are commonly used as drives on electric motors in industry and process industries. A PFC circuit can be installed at the point where the utility voltage enters a facility or building, or it can be installed downstream of inductive loads such as heavy-duty industrial motors. The advantages of installing a Power Factor Correction capacitor system include: -improved power quality for critical electrical loads -reduced harmonic distortion levels across the frequency spectrum (50/60Hz) -increased transformer life.

## Real and reactive powers and complex power

### The effect of Reactive power on power factor

Reactive power is a measurement of energy that flows back and forth between an electric circuit, typically due to inductance or capacitance. Power Factor (PF) is the ratio of total real power to total reactive power in an AC circuit. This power reactive power affects PF and what you can do to improve our PF if it’s close to unity. Reactive load on a grid causes more currents than desired which in turn leads to overloading, voltage sags, brownouts, and blackouts. To prevent these events from happening we must maintain our PF. Reactive power (var or kvar) is an important consideration when analyzing the electrical load of a system. Power factor is the ratio of real/ active power to reactive power, and the higher this ratio, the better for your system. To determine what effect reactive power has on your system’s power factor, you’ll need to calculate how much reactance there is in your circuit component or network. It will be expressed in ohms because reactance opposes current flow just like resistance does. The more reactance there is in a circuit or network, the greater its opposition to current flow which will result in less efficiency and wasted power energy as heat loss from equipment not being used productively.

### The effect of apparent power on power factor

In this blog post, I will discuss the effect of apparent power (va or kva or volt amps) on power factors. When you’re working with AC circuits and components it’s important to know what the difference is between real or true power and apparent power (sometimes also called apparent current). Apparent current is calculated by multiplying voltage (in volts) times current (in amperes), then dividing that product by impedance in ohms. A higher apparent current means a lower true or real power factor, which can lead to losses in your system because efficiency decreases as the circuit load increases. The main point is that if you want to reduce these potential losses in your electrical distribution system, try increasing your use of energy-efficient lighting.

## Conclusion

Calculating power factor 2021 is very important and this simple formula needs to know everyone because now these days most of the countries are adding extra charges for lower power factor. This is a very simple formula that everyone can easily determine their power factor. Even you can easily determine the motor power factor formula 2021 with the help of the above formula.

## FAQs

*Having seven years of experience in the Engineering field, Md Jahangir Alam is qualified in the electrical and electronics engineering field. He is the Chief of our organization and he has provided guidance to a hundred and fifty Engineers in their migration skills assessment process for Engineers Australia. He has played a significant role in the organization CDRFOREA since it was established back in 2013.*