Fibonacci Number Series and Elliott Waves

Fibonacci number series has caught the imagination of almost every serious Elliott Wave trader in the global markets. Unfortunately, many traders seem to think that a knowledge of Fibonacci numbers is the answer to all their trading problems! But first, let us see what this is all about.

Elliott wave analysis of stock market or forex or commodity market would invariably involve the use of some Fibonacci numbers to arrive at targets for corrections or projections. If you had searched the Internet for some information about the Fibonacci number series, you would have found a lot of material, but few explain it clearly enough. So this post aims to fill some of the gaps.

The series takes on a sequence 1,1,2,3,5,8,13,21,34,55,89,144 and so on to infinity. Observe that as we go to larger numbers, the advance becomes closer in ratio to 1.618. (PHI)

Suppose you place two squares of side 1 unit (say 1 inch) side by side, you get a rectangle whose sides measure 1 by 2. Now imagine you have drawn a diagonal on this rectangle, thereby creating two right-angled triangles on either side of the diagonal. If you remember the old Pythagoras theorem that you learned while at school, you will know that the square on the hypotenuse of a right triangle is equal to the sum of the squares on the two sides! So the diagonal
=square root [(1×1)+((2×2)
=square root [1+4]
=square root [5]
Now let us just take the first square (of sides 1 unit each) and draw its diagonal. This diagonal will measure square root of 2 = 1.414

These two ratios, 2.236 and 1.414 are sacred roots. The reciprocals of them are 0.447 and 0.707. You will see a lot of my work is using the ratio 0.707!

Now I have a vague suspicion that some of you are more confused than before reading this article. But don’t despair. There are lots of easy stuff that you will learn as we go forward. For example, you could learn how to use Fibonacci Ratios properly by first exploring possible placements of the Fibonacci grids on your Elliott Wave charts.

I wish you good trading!

Update on 29 August 2019:

If you love my book FWTFF, then you will love my online course even more! That course will take your understanding of Elliott Waves to a whole new level, because it teaches you how to APPLY what you learn in my book to actually make profits in the markets. Here is the link:


Do share if you found this useful


  1. I came here from the link in your book. I have just started reading it and have high hopes that I may finally make some sense of Elliot Waves. I have been intensely studying harmonic trading patterns and have gotten quite deeply in the study of Gann. In the course of referring to various material, I have seen harmonic patterns in charts showing the Elliot Waves. So, I am wondering if the two have been melded together or have been recognized as complimentary by someone.

    My background is a recent student in the Online Trading Academy for stocks, options and futures and some extended learning tracks. I just feel that there is something more as do some instructors and senior students of OTA seem to feel.

    1. Hello Steve, Welcome to WaveTimes. I am unaware of the kind of relationships you seem to have noticed. My suggestion is unless you are aiming to become a technical analyst, a deep knowledge of Elliott Waves is more than enough to make you quite profitable. Seeking out the unknown and new kinds of edges will be very rewarding when you succeed, but the wait could be quite long. I wish you the best of luck in your pursuits.

  2. Dear Ramki,

    Nice and great work and loved your ebook too.

    My software does not support grid and have price extension and we have to choose point a, b and c and then grid comes, so could you throw more light on it.


    1. Hi Sumit, I have been working with Thomson Reuters for over 30 years, but don’t think wave analysis needs any special software. The Fibonacci levels can all be computed using the simple excel workbook I have made available in

  3. I just started on this with help of your book. One question I have
    Wave 2 can never exceed the start of Wave 1
    Is it close or low you are referring to? I have a chart where close is not exceeding wave1 but low is.
    Please advice

  4. Hi Ramki, I am in an online learning space of forex and one teacher shows us Elliot waves. I fell in love and been hooked on it since. I read your book and it made me more excited how much deeper you go. My mentor only practices the absolute basics.

    My real problem is, sometimes I think I labelled wave 3 properly, but I either end up being short or too much after it has developed. Even if I count 5 waves originally.

    Do you have videos or tutorials on how to count 5 waves in impulse wave 3?

    I often use fib extension from 0 to end of wave 1 to see if I have 5 waves within 1.618 extension, or if the wave still needs to expand. Is this correct method?

    Thank you.

  5. Simply excellent blog. You have worked very well as we all know Fibonacci is the golden string which is hosted amazed by maths department. You have enlightened very interesting topic of Elliott Waves. Enjoyed the work you represented.

  6. Hi Ramki,
    OHLC chart is used in your book for wave analysis. But can we use candle stick or line chart also. Can you please tell the best chart for EWP(for easy analysis and counting).

    1. Hello Krishna, I prefer OHLC, but you will get the same result with Candlestick charts. If you use a line chart that connects the closing prices of each period, you miss out the high or low and hence not my recommendation.

  7. Hi Mr. Ramki,
    I read your book but it was a bit confusing about retracements and extensions. At one point you show a pic with fib retracements and then suddenly you jump to another pic of fib extensions without mentioning how to utilise both of them effectively. I hope you update your ebook Five wave to financial freedom about fib retracements and fib extensions. This is why I would like to attend your seminar.

    1. Kumar, Thank you for your feedback which I will keep in mind when I decide to update the book. Meanwhile, I suggest that you try to read some other author’s book on Elliott Waves and come back to FWTFF, at which time you will find that this book makes thing a lot easier to follow. Good luck.

  8. Hello Sir,
    I have read your book twice and I must say that I am very happy that I someone recommended me this lovely piece of jewel. Look forward to read your other book- Dividend growth investing using Elliott waves.
    Also, I must appreciate that the price of the book is very generous. I am a student and could not have afforded a 2-3k book (which I feel should be the true price of it).
    Thanks a lot Sir. Look forward to meet you someday.

    1. Jatin, Thank you for writing. You could pass the favor forward by writing a review of the book on Amazon! Best wishes

  9. Sir while going through bar charts some times I see a swing low has been lower than the previous low so I do not consider them as wave 1 & 2 but when i change the chart to line chart for clearer view i find the same second low has never retraced more than 100% of the 1st wave. So while counting waves which chart is recommended? Bar chart or line chart?

    1. Sudhir, I personally use the OHLC bar chart for my analysis. And if the low comes below the prior low, then it has implications for the wave count.

  10. Hello Ramki
    I read off two times the book and could not understand Is their any rule for the sub-waves ? Do they follow the same rule as the Impulse wave and is it better if I just use fib level on a higher time frame to find out the 1st and 2nd impulse wave in stand of going on lower time frame and trying to find sub-waves

    1. Hi Daniel, The sub waves follow exactly the same rules and guidelines as do the main waves. May I recommend that you read the book a third time, not skipping any page, and also visit the various examples in this blog to enhance your comprehension. All the est

  11. Sir
    I was reading ur book about Elliot wave sir I could not interpret “the technique involve calculating the distance traveled from From the start of wave 1 to the end of the wave three and computing a 38.2% and 61.8% measure of this distance and adding the results to the bottom of the wave four, and you will get to potential targets for the wave five. If both the wave one and three are normal then we should expect that the 5 to potentially extend, and reach a possible target of hundred percent of the distance from point zero to point 3
    Kindly elaborate

    1. Kamal, I have corrected your question so that it conveys what you are having difficulty with. May I recommend that you go through the numerous examples in this blog and see how I have computed possible targets for wave 5, and then it might make more sense to you. Good luck.

  12. Hi sir,
    First of all, thanks for your amazing piece of jewel on elliot wave. This will be the guiding pillar for generations to come..
    My question is that
    1. Is it always necessary that if 5 th wave is extended then it will retrace heavily in intraday
    2. If truncation happens then chances of sharp move other side is expected
    3. Can I trade EW in ONE MIN CHART in direction of main swing in bigger chart.

    1. Rakesh, Thank you for writing. 1. Bear in mind that with financial markets, nothing is guaranteed. Yet, the tendency is for a sharp sell off after an extended fifth wave ends. 2. If truncation happens in wave 5, it means the interest to continue in the direction of the trend is evaporating rapidly, and in turn, that means a good correction is likely in the opposite direction. 3. EWP works in all time frames, but if you trade waves in such small time frames,you are likely to make errors, and hence more likely to suffer losses. I would stick to daily charts, with some confirmation from hourly charts.

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