Fibonacci Analysis

Elliott referred to three important aspects of price movement in his theory: pattern, ratio and time. As described in previous sections we use Elliott Wave Theory to determine the price pattern of markets at all degrees of a trend.

Elliott's analysis of the mathematical properties of waves and patterns eventually led him to conclude that "The Fibonacci Summation Series is the basis of The Wave Principle”. Numbers from the Fibonacci sequence surface repeatedly in Elliott wave structures. Elliott actually developed his market model before he realised that it reflects the Fibonacci sequence. The Fibonacci sequence is also closely connected to the Golden ratio (1.618).

Fibonacci Series

Fibonacci numbers provide the mathematical foundation for the Elliott Wave Theory.

The Fibonacci number sequence is made by simply starting at 1 and adding the previous number to arrive at the new number:

0+1=1, 1+1=2, 2+1=3, 3+2=5, 5+3=8, 8+5=13, 13+8=21, 21+13=34, 34+21=55, 55+34=89,…

This series has numerous interesting properties:

  • The ratio of any number to the next number in the series approaches 0.618 or 61.8% (the golden ratio) after the first 4 numbers. For example: 34/55 = 0.618
  • The ratio of any number to the number that is found two places to the right approaches 0.382 or 38.2%. For example: 34/89 = 0.382
  • The ratio of any number to the number that is found three places to the right approaches 0.236 or 23.6%. For example: 21/89 = 0.236

These relationships between every number in the series are the foundation of the common ratios used to determine price retracements and price extensions during a trend.

Elliott Wave Fibonacci Levels:

Wave Ratios and Measurements


The price distance of each wave is measured as a vertical distance from the beginning of the wave to the end of the wave. The length is measured in price.

The first wave in an Elliott sequence is Wave 1. The measurement of Wave 1 is used to find ratios for other waves. These ratios are not rules, but guidelines in estimating the lengths of different waves.

Fibonacci Ratios for Wave 2

Wave 2 is always related to Wave 1.
Wave 2: Should commonly retrace between 38.2% and 78.6 % of Wave 1

Fibonacci Ratios for Wave 3

Wave 3 is related to Wave 1 by one of the following:

Wave 3 = either 1.618 x length of Wave 1
or 2.62 x length of Wave 1
or 4.25 x length of Wave 1

We find that the most common multiples are 1.618, 1.764, and 2.00 However, if the 3rd Wave is an extended wave, then 2.62 and 4.25 ratios may be seen.

Fibonacci Ratios for Wave 4

Wave 4 is related to Wave 3 by one of the following:

Wave 4 = either 23.6% of Wave 3, 38.2% of Wave3 or 50% of Wave 3

The 23.6% and 38.2% retracement levels are the most common ratios for Wave 4.

Wave 4 will also terminate within the range of the 76.4 and 1.00 Fibonacci Extension of Wave 1 from the bottom of Wave 2 and reside within the region of the Wave 4 (IV) of one lesser degree (ie Wave IV of Wave III of the Wave 3).

Fibonacci Ratios for Wave 5

Wave 5 has two different relationships:

If Wave 3 is greater than or equal to 1.618 or extended, then Wave 5 ratios are as follows:

Wave 5 either= Wave 1 or = 1.618 x Wave 1 or = 2.62 x Wave 1

When Wave 3 is less than 1.618, the 5th Wave often extends. The ratio of Wave 5 will often then be based on the entire length from the beginning of Wave 1 to the top of Wave 3.

Extended Wave 5 = either 0.62 x length (beginning of Wave 1 to top of Wave 3)

OR = length of(beginning of Wave 1 to top of Wave 3)
OR = 1.62 x length of (beginning of Wave 1 to top of Wave 3)

Corrective Waves

While we have provided expectations for the Fibonacci levels of the corrective waves (Wave 2 & Wave 4), there are also further common Fibonacci relationships between the internal waves (Waves A, B & C) that make up those larger degree correctives.

Wave A is always the first wave in any correction. The measurement of Wave A is used to find ratios for other waves. Again, these ratios are not rules, but guidelines in estimating the lengths of different waves.

Wave B will most commonly retrace 38.2% to 78.6% of Wave A

If Wave B extends beyond the start of Wave A in an expanded corrective wave then Wave B is most commonly 1.272 X or 1.382 X the length of Wave A

Wave C will most commonly be 1.00 X the length of Wave A.

If Wave C extends beyond the length of Wave A the the length of Wave C will most likely be 1.382 or 1.618 X the length of Wave A.

By mapping out all of the above potential Fibonacci levels on our charts in conjunction with the prospective Elliott Wave Structures we are able to provide a potential road map for future market price action together with support, resistance and invalidation levels.

There are a good number of additional Fibonacci levels that we look for when constructing our analysis and these are all covered in detail within the series of Educational Videos on this subject below. Again, members to also watch the series of video tutorials in this section.

For those wanting to study Fibonacci Analysis in greater depth we recommend the following reading:

Fibonacci Analysis Constance Brown
Fibonacci Trading Carolyn Boroden (AKA The Fib Queen)