Fibonacci retracement is a very popular tool among technical traders and is based on the key numbers identified by mathematician Leonardo Fibonacci in the thirteenth century. However, Fibonacci's sequence of numbers is not as important as the mathematical relationships, expressed as ratios, between the numbers in the series.
In technical analysis, Fibonacci retracement is created by taking two extreme points (usually a major peak and trough) on a stock chart and dividing the vertical distance by the key Fibonacci ratios of 23.6%, 38.2%, 50%, 61.8% and 100%. Once these levels are identified, horizontal lines are drawn and used to identify possible support and resistance levels. Before we can understand why these ratios were chosen, we need to have a better understanding of the Fibonacci number series. (For a more indepth discussion of this subject, see Fibonacci And The Golden Ratio.)
The Fibonacci sequence of numbers is as follows: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, etc. Each term in this sequence is simply the sum of the two preceding terms and the sequence continues infinitely. One of the remarkable characteristics of this numerical sequence is that each number is approximately 1.618 times greater than the preceding number. This common relationship between every number in the series is the foundation of the common ratios used in retracement studies.
The key Fibonacci ratio of 61.8%  also referred to as "the golden ratio" or "the golden mean"  is found by dividing one number in the series by the number that follows it. For example: 8/13 = 0.6153, and 55/89 = 0.6179.
The 38.2% ratio is found by dividing one number in the series by the number that is found two places to the right. For example: 55/144 = 0.3819.
The 23.6% ratio is found by dividing one number in the series by the number that is three places to the right. For example: 8/34 = 0.2352.
For reasons that are unclear, these ratios seem to play an important role in the stock market, just as they do in nature, and can be used to determine critical points that cause an asset's price to reverse. The direction of the prior trend is likely to continue once the price of the asset has retraced to one of the ratios listed above. The following chart illustrates how Fibonacci retracement can be used. Notice how the price changes direction as it approaches the support/resistance levels.
In addition to the ratios described above, many traders also like using the 50% and 78.6% levels. The 50% retracement level is not really a Fibonacci ratio, but it is used because of the overwhelming tendency for an asset to continue in a certain direction once it completes a 50% retracement.
To learn more about the various tools used in technical analysis, see our Technical Analysis tutorial.

What are the alert zones in a Fibonacci retracement?
Discover more about the Fibonacci number sequence, and specifically about the key Fibonacci retracement alert levels most ... Read Answer >> 
What are some of the more common Fibonacci retracements?
Examine the basic Fibonacci retracement levels, and learn how key Fibonacci levels are used by traders to identify potential ... Read Answer >> 
What are the main disadvantages of using Fibonacci Retracements for trading strategies?
Learn about the disadvantages inherent to the Fibonacci retracement, an indicator built on the Fibonacci sequence used in ... Read Answer >> 
Why is the Fibonacci Retracement important for traders and analysts?
Find out why traders and analysts in financial markets use Fibonacci retracement to help identify support and resistance ... Read Answer >> 
How reliable is the Fibonacci retracement in predicting stock behavior?
Learn why the reliability of the Fibonacci retracement indicator is debatable, and how the indicator is used to identify ... Read Answer >> 
How can a swing trader use a Fibonacci retracement?
Learn how swing traders can use Fibonacci retracements to identify areas of support and resistance, as well as entry and ... Read Answer >>

Trading
Strategies For Trading Fibonacci Retracements
Investopedia explains Fibonacci retracementsbased on the elegant "golden" ratioand how the levels are derived. 
Trading
Using a Fibonacci Retracement
The Fibonacci retracement is the potential retracement of a financial asset's original move in price. 
Trading
Top 4 Fibonacci Retracement Mistakes To Avoid
There are common mistakes traders make when applying Fibonacci retracements to foreign exchange markets. Here are four wellknown errors to avoid. 
Investing
Taking The Magic Out Of Fibonacci Numbers
Uncover the history and logic behind this popular trading tool. 
Trading
Fibonacci And The Golden Ratio
Discover how this amazing ratio, revealed in countless proportions throughout nature, applies to the financial markets. 
Trading
Top 4 Fibonacci Retracement Mistakes To Avoid
Using Fibonacci incorrectly can have disastrous consequences. Find out which common moves to avoid. 
Trading
Advanced Fibonacci Applications
Extensions, clusters, channels and more! Discover new ways to put the "golden ratio" to work. 
Investing
Using Fibonacci to Analyze Gold (GLD, GC)
Use Fibonacci studies to analyze gold by picking out hidden harmonic levels that can provide major support or resistance. 
Trading
Stocks Trading at the 61.8% Pullback Level (TSLA,NAVI)
Here are stocks trading the 61.8% Fibonacci retracement level, and how to trade them (and this recurring pattern). 
Trading
How To Use Fibonacci To Trade Forex
Fibonacci offers a perfect fit with forex strategies, locating hidden support and resistance levels that translate into high odds entry and exit prices.

Fibonacci Time Zones
An indicator used by technical traders to identify periods in ... 
Fibonacci Numbers/Lines
Leonardo Fibonacci was an Italian mathematician born in the 12th ... 
Fibonacci Retracement
A term used in technical analysis that refers to areas of support ... 
Fibonacci Channel
A variation of the Fibonacci retracement pattern in which the ... 
Fibonacci Extensions
Levels used in Fibonacci retracement to forecast areas of support ... 
Fibonacci Fan
A charting technique consisting of three diagonal lines that ...