Fibonacci numbers play an huge role in Elliott Wave trading.
Elliott didnâ€™t discover the Fibonacci relationships himself, but this was brought to author's attention by Charles J. Collins who had published Elliott's "The Wave Principle" and helped introduce Elliott's theory to Wall Street.
Using known Fibonacci ratios (38.2%, 50%, 61.8%, 161.8% and so on) traders can project the length of waves, the depth of corrections, move extensions etc.

Wave 1
The first impulsive wave, which Elliott traders don't use for trading, but rather for analysis of the wave 2. 

Wave 2
Wave 2 should not retrace below the beginning of wave 1.
Normally the retracement is from 50% to 61.8% of Wave 1. At times it can go below the 61.8% due to the fact that wave 2 retracement is quite aggressive since many traders don't acknowledge the change in the main trend yet.
The minimum retracement to expect is 38.2%. 

Wave 3
Wave 3 is never be the shortest among waves 1, 3 and 5.
At the very least it should be equal to wave 1 in length.
Wave 3 as the longest wave normally tend to be 161.8% of wave 1.
If goes beyond 161%  the next target is 261.8%, and rarely extended target  425% of wave 1. 

Wave 4
Wave 4 is one of the shallowest waves: at this stage many traders take profits, while there are few others who are willing to trade countertrend.
It often retraces slowly for an extended period of time and reach normally only 38.2% of wave 3.
It rarely retraces to 50% of wave 3. 

Wave 5
Wave 5 should move at least 61.8% of the length of wave 1.
If wave 3 is greater than 161.8% of wave 1 in length, the targets for wave 5 will be 100% of Wave 1,
or 161.8% of wave 1, rarely 261.8% of wave 1.
If wave 3 is less than 161.8% of wave 1 in length, wave 5 will often be extended with targets of:
61.8% of wave 1 + wave 3
100% of wave 1 + wave 3
or 161.8% of wave 1 + wave 3 
Tips: Fibonacci projections  completion of wave 5
As you can see, as soon as wave 1 is completed we can already make a projection of the first possible target for wave 5.
To do so we multiply the height of wave 1 by 161.8% and project the result from the end of wave one.
Later when wave 3 is completed we can add yet another projection of the second possible price target for wave 5. To do so we have to examine wave 3: if wave 3 is greater than 161.8% of wave 1, the targets for wave 5 will be 100% of Wave 1, or 161.8% of wave 1. If wave 3 is less than 161.8% of wave 1 in length, wave 5 will often be extended with targets of at least 61.8% of wave 1 + wave 3.
In the end, the closer are the results for wave 5 targets calculated by different methods the higher will be the chances to see a trend reversal in between those levels.
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Hi, great job!! very helpful. Will you be providing a free harmonic pattern indicator here? thanks..
thanks a lot,i grabbed a very good knowledge from here.
very good job superb
thanks
thanks for your indicator helping in a easier way to understand.....t.rajganesh
very nice,i am trading for years and apply indicators along with elliot wave to trade.my email address is shogh11@yahoo.com.i am very happy if we could share our idea with each other.
Best of Luck,
Manan
3 wave length should be starting from the beginning of 1 wave instead of beginning of 2 wave
TQVM, this very useful