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Trading with Fibonacci Numbers

Utility: Evaluating the Master Trend, Calculating Trend Reversals

Leonardo Pisano or else Fibonacci was a famous Italian mathematician of the 12th century who introduced a revolutionary sequence of numbers that are called the Fibonacci numbers.


The Fibonacci Sequence of Numbers

The Fibonacci series of numbers is an infinite sequence of numbers with some unique characteristics. First of all each number is the sum of the previous two numbers:

The General Rule is:

■ X(n) = X(n-1) + X(n-2)

0 | 1 | 1 | 2 | 3 | 5 | 8 | 13 | 21 | 34 | 55 | 89 | 144 | 233 etc

Where 3 = 2+1, 5=3+2, 8=5+3, 13=8+5, 21=13+8 etc

The 0.618 and 0.382 Levels

■ The quotient of the adjacent numbers (after the first few numbers) is always constant at 1.618 or its inverse .618.

This number 1.618 is called the Golden Ratio and can be found everywhere in our body, in our earth’s nature and even in our universe.

■ Subtracting .618. from 1 equals .382. 0.382 can be found in the sequence of Fibonacci numbers as 8/21 = .382, 13/34 = .382, 21/55 = .382 etc


Using Fibonacci Series for trading Financial Markets

A great number of traders are using the Fibonacci series for their trading decisions. Furthermore, there are hundreds of manual and automated trading systems that incorporate algorithms based on the Fibonacci numbers. The most important technical analysis tools based on Fibonacci are:

  1. Fibonacci Fans

  2. Fibonacci Retracements

  3. Fibonacci Expansions

  4. Fibonacci Time Zones

  5. Fibonacci Pivot Points

Hotforex Benefits



Fibonacci Fans are lines based on the Fibonacci numbers drawn on any price chart. The Fibonacci Fans are used for the determination of important support and resistance levels.

Each line is created between two key points that are representing an important High and an important Low. After placing these two dots, the Fibonacci fan calculates the vertical distance by the key ratios 0.382, 0.50 and 0.618.



Fibonacci retracements are widely used by all traders who are trying to estimate potential reversals during strong trends.

□ Traders who wish to buy the market will try to buy on retracements at a Fibonacci support level (bullish trends)

□ Traders who wish to sell the market will try to sell on a retracement at a Fibonacci resistance level (bearish markets)

Based on the Fibonacci series of numbers these are the important ratios used by the Fibonacci retracements:

i) 23.6% Ratio

ii) 38.2% Ratio

iii) 61.8% Ratio

Some traders are also using:

iv) 50% Ratio

v) 78.6% Ratio


Fibonacci expansions can serve the role of forecasting price targets. As in the case of the other Fibonacci tools, the expansion levels are calculated according to the Fibonacci numbers. The expansion levels are found as horizontal lines placed up and down of the previous trend move. These expansion levels can be used also as support/resistance levels.



The time zones are vertical lines placed in increments on the price chart. These vertical lines can identify important areas in which significant volatility may take place. The Fibonacci time zone lines can also identify the time periods when price patterns first develop and then complete.

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The Fibonacci Pivot Points are price levels of significance. These points can be used for identifying strong trends or major support and resistance levels. These Pivot Points are calculated on daily periods. The Pivot Points can highlight the general conditions of the price action.

■ Fibonacci Pivot Point (P) = (High Price + Low Price + Close Price)/3

■ Fibonacci Support 1 (S1) = (P x 2) - High Price

■ Fibonacci Support 2 (S2) = P - (High Price - Low Price)

■ Fibonacci Support 3 (S3) = P - 2 * (High Price - Low Price)

■ Fibonacci Resistance 1 (R1) = (P x 2) - Low Price

■ Fibonacci Resistance 2 (R2) = P + (High Price - Low Price)

■ Fibonacci Resistance 3 (R3) = P + 2 X (High Price - Low Price)




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Fibonacci Trading

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