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# What’s common for Beer Mug and Power Factor?

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Understanding power factor is not that hard. We have some very common example from the real life you will understand for sure, but first let’s start with some introduction of power factor.

To understand power factor, we’ll first start with the definition of some basic terms:

kW is Working Power (also called Actual Power or Active Power or Real Power). It is the power that actually powers the equipment and performs useful work.

kVAR is Reactive Power. It is the power that magnetic equipment (transformer, motor, relay etc.) needs to produce the magnetizing flux.

kVA is Apparent Power. It is the “vectorial summation” of KVAR and KW.

## Example From the Real Life ;)

Let’s look at a simple analogy in order to better understand these terms….

Let’s say it’s friday evening, and you are with your friends at your favorite pub after really hot day. You order up a big mug of your favorite beer for you and for your friends. The thirst-quenching portion of your beer is represented by KW (the big pic on top).

Unfortunately, life isn’t perfect. Along with your ale comes a little bit of foam. (And let’s face it…that foam just doesn’t quench your thirst.) This foam is represented by KVAR.

The total contents of your mug, KVA, is this summation of KW (the beer) and KVAR (the foam).

So, now that we understand some basic terms, we are ready to learn about power factor:

Power Factor (P.F.) is the ratio of Working Power to Apparent Power.

Looking at our beer mug analogy above, power factor would be the ratio of beer (KW) to beer plus foam (KVA).

Thus, for a given KVA:

1. The more foam you have (the higher the percentage of KVAR), the lower your ratio of KW (beer) to KVA (beer plus foam). Thus, the lower your power factor.
2. The less foam you have (the lower the percentage of KVAR), the higher your ratio of KW (beer) to KVA (beer plus foam). In fact, as your foam (or KVAR) approaches zero, your power factor approaches 1.0.

Our beer mug analogy is a bit simplistic. In reality, when we calculate KVA, we must determine the “vectorial summation” of KVAR and KW. Therefore, we must go one step further and look at the angle between these vectors.

## Power Triangle

The “Power Triangle” illustrates this relationship between KW, KVA, KVAR,  and Power Factor:

Note that in an ideal world looking at the beer mug analogy:

1. KVAR would be very small (foam would be approaching zero)
2. KW and KVA would be almost equal (more beer; less foam)

There are dosen of tools and technical articles/guides published at EEP that can help you to understand power factor and its controlling. Hope these can help:

Resource: powerstudies.com

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### Edvard Csanyi

Electrical engineer, programmer and founder of EEP. Highly specialized for design of LV/MV switchgears and LV high power busbar trunking (<6300A) in power substations, commercial buildings and industry facilities. Professional in AutoCAD programming.

1. Jessica Ortiz
Mar 27, 2023

I’m trying to use the power triangle to “do some beer math” but I am not getting the same answer. Using “beer math” (If KVA =300 Kw = 270 & PF= .9) my Kvar should be 30kw. Using the power triangle however, Kvar = √(300²-270²) which happens to equal 130.7 kvar. So I’m wondering what I’m missing because Kvar in beer math =30 but using the power triangle Kvar = 130. Help please, examples on this page would be helpful to explain finding a solution for Kvar/Kw/Kva would make understanding much easier. Thank you!

2. Amar Nath Mishra
Aug 25, 2022

Beer glass analogy will impart wrong concept among the students as real power is vector sum of active power and reactive power but, beer glass analogy suggests real power as algebraic sum of active power and reactive power.Requesting to delete beer glass analogy to describe the power factor.

3. Nazar Ahamed.j
May 21, 2022

We have 2000KVAR shunt capacitor
We need to convert KW kindly workout formula and share me to given mail ID
33KV supply
HT current 75Amps

4. Stanley Osao
Jun 25, 2021

Thank you for the simplest explanation and beer analogy to help me understand P.F. As a non electrical engineer, this is a very handy information.

5. Fernando
Jun 12, 2018

Thanks for the simple and easy explanation by the author and by the corrections by readers.

6. Olga Neiman
Mar 13, 2018

Man, there is a Mistake. PF with the sin is kw/kva=cos(Θ)=sin(90°-Θ)

• Alun Williams
Mar 18, 2018

The p.f. shown here with sin is indeed correct. SinΘ = perp/hyp = KVAR/KVA

7. Server Room UPS
Mar 10, 2018

What a great way to describe and explain the power factor. I like this style of learning.

8. WALTER MARTINS DA JUNIOR
Dec 20, 2017

The correct unit for reactive power is kvar, not kVAr.

• Raman
Jan 25, 2020

No, actually its kVAr not kvar

9. Engr.I.F.Ogbuty
Oct 29, 2016

Well said,good job

10. Ramakrishna
Feb 17, 2016

Very clear answer . Thank you

11. Dinu Alex
Dec 21, 2015

good

12. Stuart
Sep 04, 2015

Instructions unclear. Beer now empty.

13. Robin Koffler
Aug 17, 2015

It is amazing how this how often this graphic turns up when you need to discuss reactive power and explain how it can affect electricity bills. With the ESOS deadline on the horizon it is even more relevant.

14. Jason Koffler
Apr 25, 2015

been using this way to explain kva and real power since the mid 90’s.

15. Alex Damaso
Apr 16, 2015

I would like to ask what is the appropriate KW rating of a generator set to used for 5 tonner aircondioning unit? Thanks

16. Jagdish Aggarwal
Apr 16, 2015

this is so simple and interesting. examples are just from day to day life.

17. Denis mchau
Apr 15, 2015

Am student and iwant to know the way of achive my goal to be a engineer .

18. nick
Apr 14, 2015

VERY EDUCATIVE

19. jorge mosquera
Apr 14, 2015

Excelente analogía. Interesante el portal

20. Saravanan
Apr 14, 2015

I didn’t see like this example wow its very help full

21. ezhil
Jan 29, 2015

Analogy of Kirchoffs law

22. sontakke
Jan 04, 2015

Dear Sir,Greetings.
Its a really interesting Practical Example.
Congrants for \an \idea.

• Lui
Jan 29, 2015

Greatest description ever! ;) Thanks..

23. PETER
Dec 29, 2014

Very good example

Dec 11, 2014

Good Illustration. Hope people donot forget after having a beer. Cheers

25. Romona Davidson
Sep 15, 2014

merci d’un million de… Really appreciate this example……..

26. Dejan
Jun 22, 2014

Jelen Beer FTW.
Srsly guys, you could’ve picked some less catastrophic Serbian beer :D

• perendev
Jun 23, 2014

Palindrome: Jelenovi pivo nelej.

27. Gaudencio Toto
Mar 10, 2014

Excellent example, served me to explain the power factor to my clients.
We need more examples applicable to real life. Thanks

28. Barbara Kerr
Feb 12, 2014

Is it correct to say that the equipment itself ‘eats’ a bit of the electricity that can be generated? So there is always a bit of loss in the generation process, lost to the equipment itself? Thanks much for this helpful article!

29. Loh Kon Min
Feb 03, 2014

Great job….I love your power factor analogy using beer as an example!!!

30. lenin pugal
Feb 02, 2014

i need more very common example from the real life like this.

31. MANI NV
Dec 27, 2012

Good approach to teach a topic in a simple way.

32. SKuchle
Nov 19, 2012

Great article I will never be able to look at me beers the same way again.

33. elbf2801
Nov 15, 2012

Took into this extent, the PUB is the Substation and the Brewerei is the Power Plant.

34. PowertothePeople
Nov 15, 2012

Good article. Easy to read and great analogy. However, the equation P.F. = KW/(KW + KVAR) needs to be corrected to P.F. = KW/(KW^2 + KVAR^2)^(1/2) since KVA=(KW^2 + KVAR^2)^(1/2). I understand how the author wanted to keep it simple by associating his beer equation (P.F.= Beer/(Beer + Foam) ) with the actual power factor equation, but this is misleading and will lead to errors. People who aren’t comfortable with this topic will use P.F. = KW/(KW + KVAR) and will not obtain a correct answer.

35. laxmi
Nov 15, 2012

cool…. yesterday only i was questioned on this by laboratory viva examiner!! wish i read this before….