Fibonacci Retracement

In finance, Fibonacci retracements is a method of technical analysis for determining support and resistance levels. They are named after their use of the Fibonacci sequence. Fibonacci retracement is based on the idea that markets will retrace a predictable portion of a move, after which they will continue to move in the original direction.

Fibonacci retracement is created by taking two extreme points on a chart and dividing the vertical distance by the key Fibonacci ratios. 0.0% is considered to be the start of the retracement, while 100.0% is a complete reversal to the original part of the move. Once these levels are identified, horizontal lines are drawn and used to identify possible support and resistance levels.
Fibonacci ratios

The key Fibonacci ratio of 0.618 is derived by dividing any number in the sequence by the number that immediately follows it. For example: 8/13 is approximately 0.6154, and 55/89 is approximately 0.6180.

 The 0.382 ratio is found by dividing any number in the sequence by the number that is found two places to the right. For example: 34/89 is approximately 0.3820.

The 0.236 ratio is found by dividing any number in the sequence by the number that is three places to the right. For example: 55/233 is approximately 0.2361.

Other important ratios are: 50%, 76.3%, 78.6%

* If you really want to understand the importance of fibonacci in trading read this post until the end. Fibonacci numbers and golden ratios are everywhere.

The mathematician Fibonacci

Leonardo Pisano Bigollo (c. 1170 – c. 1250) also known as Leonardo of Pisa, Leonardo Pisano, Leonardo Bonacci, Leonardo Fibonacci, or, most commonly, simply Fibonacci, was an Italian mathematician, considered by some "the most talented western mathematician of the Middle Ages."

Fibonacci is best known to the modern world for the spreading of the Hindu-Arabic numeral system in Europe, primarily through the publication in the early 13th century of his Book of Calculation, the Liber Abaci; and for a number sequence named after him known as the Fibonacci numbers, which he did not discover but used as an example in the Liber Abaci.

Fibonacci numbers

In mathematics, the Fibonacci numbers are the numbers in the following integer sequence:

0,\;1,\;1,\;2,\;3,\;5,\;8,\;13,\;21,\;34,\;55,\;89,\;144,\; \....\; (sequence A000045 in OEIS).

By definition, the first two numbers in the Fibonacci sequence are 0 and 1, and each subsequent number is the sum of the previous two.



Golden ratio

In mathematics and the arts, two quantities are in the golden ratio if the ratio of the sum of the quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller one. The golden ratio is an irrational mathematical constant, approximately 1.61803398874989.[1] Other names frequently used for the golden ratio are the golden section (Latin: sectio aurea) and golden mean.[2][3][4] Other terms encountered include extreme and mean ratio,[5] medial section, divine proportion, divine section (Latin: sectio divina), golden proportion, golden cut,[6] golden number, and mean of Phidias.[7][8][9] In this article the golden ratio is denoted by the Greek lowercase letter phi (φ), while its reciprocal, \frac{1}{\varphi} or φ − 1, is denoted by the uppercase variant Phi (Φ).

The figure on the right illustrates the geometric relationship that defines this constant. Expressed algebraically:




This equation has one positive solution in the set of algebraic irrational numbers:





Fibonacci and Golden Ratio in nature, architecture and art:


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