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!


  • […] the second wave corrects the first wave only by 61.8%, which is a highly regarded Fibonacci ratio. See here for a discussion about Fibonacci numbers and its application in Elliott Wave […]

  • […] It is interesting to note that the second wave dipped to exactly the 50% retracement level of the first wave. Elliott Wave analysts place a great deal of importance on the use of the Fibonacci number series. […]

  • Steve Bukosky

    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.

    • 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.

  • mahdi

    hi dear Ramki!

    Why do not use 78.6 ratio in your book?

  • Sumit Jain

    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.


    • 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

  • Anil

    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

  • Hadeer

    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.

  • C. Ghaith

    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.

  • krishna

    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).

    • Ramki Ramakrishnan

      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.

Leave a Reply