Learn Forex: Fibonacci Retracements

Technical analysis can be a helpful, albeit involved, method of determining price trends in foreign exchange trading. How can a trader know, for example, where a price trend is going and what are good price levels at which to buy and sell? One of the more widely utilised methods of making predictions of the movements of forex trends is using Fibonacci levels.

What Are Fibonacci Levels?

Fibonacci levels come in a multitude of forms, each with a unique purpose. Among the most common are Fibonacci retracement levels, Fibonacci extensions and the Fibonacci fan. These tools are useful in crafting trading decisions with respect to trend, reversal and range strategies.

Fibonacci levels are trading levels based on mathematical ratios from what are known as Fibonacci numbers. In simpler terms, the expression says that certain significant numbers are found by adding integers. Each term in the Fibonacci sequence is the sum of the two terms before it, for example: 1+1=2, 1+2=3, 2+3=5, 3+5=8, etc.

With this, the numbers in the sequence turn out to be 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 and onward to infinity. Although the Fibonacci sequence is integer-based, these mathematical relationships are often expressed visually. In fact, the sequence is a key element of fractal geometry, which may be used to study the symmetric qualities of figures that occur in nature.

History Of Fibonacci Sequence And Numbers

Fibonacci numbers date back to the origins of modern mathematics in renaissance Europe. They were discovered by Renaissance era Italian mathematician Leonardo Pisano Bigollo early in the 13th century. His family name was Bonacci and his pen name was Filius (son) Bonacci, thus the contraction "Fibonacci."

Why Trade with FXCM

Commission free with fast, efficient execution.

In a treatise on mathematics published in 1202, Bonacci revealed what has come to be known as the "Fibonacci sequence" of numbers. It is determined by the following mathematical expression: ƒ1= f2=1; ƒn+2=ƒn + ƒn+1, where ƒ is a term in the sequence and n is an integer.[1]

As the sequence of preceding numbers moves toward infinity, the mathematical relationships between each number to the previous number tends toward 1.618. This ratio has been found to be especially significant over time, describing many patterns found in nature such as the growth patterns of tree branches and leaves, the shapes of flowers, shells, DNA molecules, etc.

Because of its significance within the Fibonacci sequence, the ratio has come to be known as the "golden ratio," and it is represented by the greek letter Phi φ. The golden ratio has also been found to be significant in patterns found in financial calculations, including applications in accounting, corporate income, calculations of loans with interest, technical analysis and the charting of asset prices.

How To Use Fibonacci Retracement Levels In Forex Trading

Beginning in the 20th century, Fibonacci numbers have been used to identify successful trading entrance and exit levels for numerous asset classes, including currencies. Since the early days of financial charting pioneered by Charles Dow and other proponents of the Dow Theory, analysts have noted that when prices reverse trajectory they tend to "retrace" a portion of their previous movements. Mr. Dow himself suggested that the retracement was between 33% and 66%.[2]

Dow's proposal was refined further several years later by Ralph Nelson Elliott, the author of the Elliott Wave Theory, who found that more accurate retracement levels occurred at 38.2% and 61.8% based on the Fibonacci sequence. In addition, Elliott found that 50% was a common retracement level.[3]

As they pertain to the Elliott Wave Theory, Fibonacci retracement levels serve as important support and resistance levels. The most common of which are the 38.2%, 50%, 61.8% and 78.6% retracements of data sets comprising previous numbers. However, it's important to note that 50% isn't an official part of the Fibonacci sequence, but is still viewed as being a valuable measurement device.

In practice, Fibonacci retracement levels are used to determine market state. For instance, a market is thought to be trending if price action remains condensed above (or below) the 38.2% or 61.8%. To illustrate how to use Fibonacci retracement, assume the following scenario:

  • The stock price of Company A rises from US$10.00 to US$20.00 in a steep intraday uptrend.
  • To apply Fibonacci retracements to a data set, one works in concert with the prevailing uptrend or downtrend. In this case, one addresses the bullish trend by beginning at the directional move's high point (US$20.00) and concluding with the low point (US$10.00). Upon doing so, specific price levels will be identified, breaking down potential support levels and pullback strength.

In the case of Company A's stock price, the retracement lines will fall at the following levels:

  • 38.2% retracement @ US$16.18
  • 50% retracement @ US$15.00
  • 61.8% retracement @ US$13.82
  • 78.6% retracement @ US$12.14

When interpreting the above data set, it is safe to say that Company A's stock is trending if prices remain above US$16.18 or US$13.82. Of course, stock market participants are likely to view the bullish trend as stronger if prices remain above US$16.18; if the market falls beneath US$13.82, then a short-term corrective or consolidation phase will become more likely. Also, it's important to realise Fibonacci retracements produce support levels for pullbacks in an uptrend and resistance levels for pullbacks in a downtrend.

One of the great things about using Fibonacci retracements in technical analysis is their ease of application. Most trading and charting software suites offer a Fibonacci retracement tool that features point-and-click functionality. Really, all one has to do is click on the appropriate high and low levels; the calculations are done automatically.

Over the course of history, Dow, Elliott and countless other analysts applied Fibonacci retracements to many price charts. They found that the trend lines described by the percentages frequently predicted where and when on the charts that price support or resistance levels would be reached, and where price reversals would occur. Thus, it was determined that they're reliable constants for predicting when assets should be bought or sold.

To make the forecast, a trader, for example, could start to plot a hypothetical price trend line at a particular peak or trough on a chart for a buy or sell order. Then, they could trace a line to one of the percentage price increases or decreases suggested by the Fibonacci numbers to determine when the next likely best price move would occur for buying or selling. Of course, there are many viable Fibonacci trading strategies. And, as always, a disclaimer of "past performance is not indicative of future results" certainly applies.

How Do You Calculate Fibonacci Retracement Levels?

As technology has evolved, calculating Fibonacci retracement levels has become exponentially easier. Long gone are the days of cumbersome arithmetic; in the modern financial markets, the software trading suite does a lionshare of the work. To derive price targets with Fibonacci retracements, the progression is straightforward:

  1. Build an appropriate price chart. To do so, select the desired products, analysis tools and timeframes. One of the most common pricing chart types is the Japanese candlestick chart.
  2. Identify a pronounced directional move in pricing, or "wave." This task may be accomplished on any timeframe or type of chart. Remember "waves" are typically viewed as consisting of peaks and troughs.
  3. To apply the Fibonacci retracement tool, simply click on the appropriate peaks and troughs in concert with the prevailing trend. For uptrends, first click on the periodic low and then the high; for downtrends, click on the periodic high and then the low. In doing so, the proper sequencing will correctly identify possible support and resistance levels.
  4. After following these three steps, the Fibonacci ratios will be applied to the historical price movements, producing a sequence of numbers akin to retracement values. The 38.2%, 50%, 61.8%, and 78.6% values are then automatically added to the pricing chart as labelled horizontal lines.

Fibonacci retracements, as well as Fibonacci numbers in general, are considered to be public-domain indicators. Like moving averages, MACD and Stochastics, Fibonacci tools are included in most trading platforms' functionality. So, no matter if one is trading shares, futures, or forex, applying Fibonacci retracements to evolving price action is routine.

As a general rule of thumb, technical indicators work best when combined with other analytical devices. In the case of Fibonacci retracements, moving averages and momentum oscillators are often added to enhance accuracy. Although retracements are a solid device for identifying levels of support and resistance, they aren't infallible. So, when developing a comprehensive trading strategy, it is a good idea to integrate at least two technical indicators to help place evolving price action into a manageable context.

What Is The Difference Between Fibonacci Retracement And Extension?

Although Fibonacci retracements and extensions are both based on Fibonacci numbers, they are very different technical tools. First and foremost, retracements are predicated on the concept of price action pulling back (retrace) from a periodic high or low; extensions are based on the inverse idea of trend extension or a market breakout. In this way, the two indicators are fundamentally different.

From a tactical standpoint, Fibonacci retracements and extensions are commonly used in opposing fashions. For instance, Fibonacci retracement levels are often used as stop-loss or market entry locations in trend-following day trading strategies. Conversely, within the context of trend-following day trading strategies, Fibonacci extensions are frequently used to locate bullish or bearish profit targets outside of the trend's established extremes.

However, both technical tools are inherently versatile. In fact, many traders incorporate the two into their trade management gameplans. While each is a unique indicator, they can be complementary to one another when identifying a trade's ideal stop-loss and profit target locations.

Other Fibonacci Level Charting Techniques

In addition to simple charting retracement or trend line, other techniques using Fibonacci numbers have also been found to be useful. Among these are Fibonacci Arcs, Fibonacci Fans, Fibonacci Expansions, Fibonacci Channels and Fibonacci Time Zones.


With arcs, analysts choose a trend line between two extreme points in a price movement between a low and a high, and draw arcs across the chart at the levels of 38.2%, 50% and 61.8%. As a result, they plot all the potential support or resistance levels that are likely to occur over time in the future period that is graphed on the chart.


With fans, an invisible vertical line is drawn through the second extreme point in a price movement and trend lines are drawn from the first extreme point to intersect the invisible vertical line at the levels of 38.2%, 50% and 61.8%. As with arcs, the trend lines from the "fan" of three new trend lines will project into future points on the graph where support or resistance levels will likely appear.


Expansion is a technique for determining the likely second and third "waves" of a longer price movement trend. The height of a movement between two price extremes is used as a reference unit interval, and it is considered to be 61.8% of the three wave movement. When the price rebounds to a new peak or trough, an invisible vertical line is drawn. From there, the new price reversal will be expected to move to support or resistance levels of 100% and 161.8% of the distance described by the reference unit interval.


For channels, a peak and trough of a price movement are chosen to represent a unit width. Then, a series of parallel lines is drawn on the chart based on multiples to the unit width of 0.618, 1.00, 1.618, 2.618, 4.236, etc. The multiples represent the likely points of future support or resistance levels.

Time Zones

Unlike the other charting techniques, Time Zones focus on the timing, rather than the price component of price movements. With this technique, a unit time interval is chosen as a reference, and vertical lines are plotted at Fibonacci intervals of 1, 2, 3, 5, 8, 13, 21, 34, etc., where new support or resistance levels can be expected.

Key Takeaways

Fibonacci retracements are horizontal lines that represent the application of the Fibonacci ratio to a forex pair's trading range. The retracement sequence is 0.0%, 23.6%, 38.2%, 50.0%, 61.8% and 100.0%. Upon the calculation of specific price points, you may be able to identify levels of support and resistance for the trading range.

In the contemporary financial markets, Fibonacci tools are exceedingly popular analytical devices. Users of Fibonacci retracements, arcs, fans, or extensions enjoy strategic freedom and flexible functionality. Generally, the most popular indicator in the Fibonacci family are Fibonacci retracements. Below are the important facets of this technical tool to remember:

  • Key retracement levels are 38.2%, 50%, 61.8%, and 78.6%.
  • Always apply Fibonacci retracements with the trend; trough to peak for bullish trends, peak to trough for bearish.
  • As long as price action is above (or below) the 38.2% and 61.8% levels of a bullish (or bearish) periodic move in pricing, the uptrend (or downtrend) is valid. If price retraces past the 61.8% level, consolidation or reversal becomes increasingly probable.

The basis of all Fibonacci tools is the Fibonacci sequence and golden ratio. Fortunately for active traders, modern software platforms execute all calculations automatically. Given this automated functionality, Fibonacci tools are a fast, efficient means of studying price action in live market conditions.

FXCM Research Team

FXCM Research Team consists of a number of FXCM's Market and Product Specialists.

Articles published by FXCM Research Team generally have numerous contributors and aim to provide general Educational and Informative content on Market News and Products.



Retrieved 30 Nov 2015 https://www.fq.math.ca/Books/Primer/basin2.pdf


Retrieved 13 Nov 2015 http://www.jstor.org/stable/pdf/40981862.pdf

${getInstrumentData.name} / ${getInstrumentData.ticker} /

Exchange: ${getInstrumentData.exchange}

${getInstrumentData.bid} ${getInstrumentData.divCcy} ${getInstrumentData.priceChange} (${getInstrumentData.percentChange}%) ${getInstrumentData.priceChange} (${getInstrumentData.percentChange}%)

${getInstrumentData.oneYearLow} 52/wk Range ${getInstrumentData.oneYearHigh}

Any opinions, news, research, analyses, prices, other information, or links to third-party sites contained on this website are provided on an "as-is" basis, as general market commentary and do not constitute investment advice. The market commentary has not been prepared in accordance with legal requirements designed to promote the independence of investment research, and it is therefore not subject to any prohibition on dealing ahead of dissemination. Although this commentary is not produced by an independent source, FXCM takes all sufficient steps to eliminate or prevent any conflicts of interests arising out of the production and dissemination of this communication. The employees of FXCM commit to acting in the clients' best interests and represent their views without misleading, deceiving, or otherwise impairing the clients' ability to make informed investment decisions. For more information about the FXCM's internal organizational and administrative arrangements for the prevention of conflicts, please refer to the Firms' Managing Conflicts Policy. Please ensure that you read and understand our Full Disclaimer and Liability provision concerning the foregoing Information, which can be accessed here.

Past Performance: Past Performance is not an indicator of future results.

Spreads Widget: When static spreads are displayed, the figures reflect a time-stamped snapshot as of when the market closes. Spreads are variable and are subject to delay. Single Share prices are subject to a 15 minute delay. The spread figures are for informational purposes only. FXCM is not liable for errors, omissions or delays, or for actions relying on this information.