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

`1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 u.s.w.`

Use Fibonacci Retracements with our Live Charts

Fibonacci retracements 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, a 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 in-depth 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 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:

`13/55  = 0.23636   34/89  = 0.38202`
`89/144 = 0.61806   55/13  = 4.23076`
`89/34  = 2.61764   144/89 = 1.61797`

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.

Fibonacci Retracements on Charts
When drawn on a chart, Fibonacci levels divide a trend into segments. Each of these segments becomes a likely support or resistance level. In the chart that follows, you can see a Fibonacci retracement applied from the bottom to the top of a recent trend on the EUR/USD. You can see that the market has been bouncing up from the 23.6 percent and 38.2 percent retracement levels for a few months. The interesting thing is, these were identified in advance—which enabled them to serve as excellent guides for placing stops or entry orders.

What Fibonacci Retracements Measure

Market trends seldom take place in straight lines. Most trend pictures show a series of zig-zags with several corrections against the existing trend. These corrections usually fall into certain predictable percentage parameters. The best-known example of this is the fifty-percent retracement. That is to say, a secondary, or intermediate, correction against a major uptrend often retraces about half of the prior uptrend before the bull trend is again resumed.

Fibonacci Retracements provide technical analysts with a very useful tool to measure the strength or the weakness in a trend. Strong uptrends would typically not retrace more than fifty-percent of its prior uptrend. Likewise strong downtrends would typically not retrace more than fifty-percent of its prior downtrend.

A minimum retracement is usually about a third of the prior trend. The two-thirds point is considered the maximum retracement that is allowed if the prior trend is going to resume. A retracement beyond the two-thirds point usually warns of a trend reversal in progress.