# Fibonacci Ratio

Elliott Wave Theory is based on Fibonacci Ratios. We have thoroughly learned Fibonacci ratios and their importance in technical analysis in one of our modules from ELM School, known as "**The World of Fibonacci.**" In this section, we will quickly revisit the Fibonacci ratios and understand their relationship with Elliott Wave Theory. So, let us start.

### What is a Fibonacci Series?

Leonardo Fibonacci da Pisa is a thirteenth-century mathematician. He was one of the most illustrious scientists of his time. Among his great achievements was the introduction of Arabic numerals to supersede the Roman figure. He developed the Fibonacci Summation series: This series takes 0 and adds 1 as the first two numbers. The follow up numbers in the series adds the previous two numbers and thus we have 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89 to infinity.

0,1,1,2,3,5,8,13,21,34,55,89,144 …….

The beauty of the series is that the ratio of any two consecutive numbers in the sequence approximates 1.618, or its inverse, 0.618, after the first few numbers.

The Golden Ratio (1.618) is derived by dividing a Fibonacci number with another previous Fibonacci number in the series. As an example, 144 divided by 89 would result in 1.618.

Another important fact is that the square of any Fibonacci number is equal to the number in the series before it, multiplied by the number after it, plus or minus 1.

5^{2 }= (3 x 8) +1

8^{2} =(5 x 13) -1

13^{2} =(8 x 21)+1

This is an implicit part of the Elliott Wave Principle called Rule of alteration. It states that Complex corrective waves alternate with simple ones, strong impulse waves with weak impulse waves and so on. The Rule of alteration can be either with respect to time price or pattern.

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### Fibonacci Retracement and Extension

Fibonacci Retracement in technical analysis and Elliott Wave Theory refers to a market correction (counter trend) which is expected to end at the areas of support or resistance denoted by key Fibonacci levels. The market is then expected to turn and resume the trend again in the primary direction.

Fibonacci Extension refers to the market moving with the primary trend into an area of support and resistance at key Fibonacci levels where target profit is measured. Traders use the Fibonacci Extension to determine their target profit.

Some Important Fibonacci Levels are given below:

The image below shows the example of both Fibonacci Retracement and Fibonacci Extension.

Here we can see the example of Axis Bank on Daily Time frame, how prices are taking support at the 61.8% retracement levels and how prices are showing resistance at 141.40% extension levels

### What is the relation between Fibonacci Ratio and Elliott Wave Theory?

Fibonacci Ratio is useful to measure the target of a wave’s move within an Elliott Wave structure. Different waves in an Elliott Wave structure relate to one another with Fibonacci Ratio. For example, in an impulse wave.

- Wave 2 is typically 50%, 61.8%, 78.6%, or 88.2% of wave 1
- Wave 3 is typically 161.8% of wave 1
- Wave 4 is typically 14.6%, 23.6%, or 38.2% of wave 3
- Wave 5 is typically inverse 1.236 – 1.618% of wave 4, equal to wave 1 or 61.8% of wave 1+3

Traders can thus use the information above to determine the point of entry and profit target when entering into a trade.

Below is the image of default Fibonacci Retracement and Fibonacci Extension levels for the financial market that we can be found in any charting tool for the financial market: