 # A Crash Course on Fibonacci Calculators: How to Calculate Retracements and Extensions Reading time: 7 minutes

To some, Fibonacci values (often referred to as Fibs) exhibit an air of mystery, an esoteric mathematical approach few understand. To others, Fibonacci is nothing more than percentage ratios applied to charts. Introduced by Italian mathematician Leonardo Pisano Bigollo in the 13th century, or better known as ‘Leonardo of Pisa’ or ‘Leonardo Fibonacci’, Fibonacci studies represent unique mathematical ratios found in everyday structure. This includes nature: geometry of plants, flowers and fruit, for example. Fortunately for technical analysts, this mathematical discovery extends to financial markets.

## Fibonacci Sequence

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1,597, 2,584…

Each number in the Fibonacci sequence represents the sum of the two previous numbers (0+1=1, 1+2=3, 89+144=233).

Ratios between any two successive Fibonacci figures provide what is known as the Golden Ratio hay đồng tiền định giá Phi: 1.618. For example, dividing 233 by 144 is 1.618055… Dividing 55 by 34 is 1.617647. The larger the values, the closer the approximation. The inverse of 1.618 is 0.618, found by dividing a smaller preceding Fibonacci value by its subsequent figure. For example, dividing 34 by 55 is 0.618181 or dividing 1,597 by 2,584 equates to 0.618034.

0.382 is another important Fibonacci figure to be mindful of, identified by dividing a value two places ahead. As an example, dividing 377 by 987 equals 0.381965… Dividing 21 by 55 is 0.381818.

Other notable Fibonacci ratios are 0.236 (divided by three values ahead), 0.786 (represents the square root of 0.618) and 0.886 (derived from the square root of 0.786).

Fibonacci trading strategies focus largely on the aforementioned values, helping to gauge corrections/pullbacks within trending environments, and arrange price targets (profit targets) – horizontal lines which traders believe a favourable position may encounter support or resistance.

## Fibonacci Calculator

Although the Fibonacci trading tool is available on most reputable charting packages, and can be accurately applied to any timeframe, some traders prefer to calculate Fibonacci retracements and extensions.

What is a Fibonacci retracement?

A Fibonacci retracement, as its name implies, is a measurement that defines a correction or pullback. The measurement incorporates two price points: swing highs and lows.

What is a Fibonacci extension?

A Fibonacci extension measures extended moves and utilises three price points: swing highs, swing lows and a retracement swing (this will become clearer in the charts below). It is an extension of the Fibonacci retracement.

Extensions are often used to establish take-profit areas and additional points of extended support and resistance.

What is a Fibonacci projection?

Many confuse extensions and projections. Both measure two different things.

While the extension incorporates three price points, a projection requires only two price points.

A Fibonacci projection works by projecting a move in the direction of the original price move (before a retracement), projecting probable price levels should a continuation develop.

Fibonacci Calculator

Freely available on Myfxbook.com, a Fibonacci calculator (one of the many Forex calculators) is a basic tool in place to calculate Fibonacci ratios in any financial asset, including Forex (currency markets – FX trading), commodities, stocks, bonds, cryptocurrencies (think Bitcoin) and other derivatives markets, such as CFDs (contracts for difference).

To use the calculator, select the financial instrument’s trend: uptrend or downtrend, and subsequently input the high and low values to derive the Fibonacci ratios. The custom value is for extension levels (third price point). (Source: Myfxbook Fibonacci Calculator)

## Fibonacci in Action: Support and Resistance

Figure 1.A and 1.B (EUR/USD daily chart) demonstrate a common Fibonacci retracement level (correction and pullback) using the Fibonacci retracement tool. The 38.2% value is considered a shallow retracement whereas a 61.8% move represents deeper price retracement. (Figure 1.A Source: TradingView.com – EUR/USD Daily Chart) (Figure 1.B Source: TradingView.com – EUR/USD Daily Chart)

Figure 1.C (EUR/USD daily chart) displays a Fibonacci extension measurement, using three price points. Readers will note the currency pair extended 100% in this example, consequently shaping a basic harmonic configuration: AB=CD. In this case, the 100% level served well as a take-profit level.

Figure 1.D (EUR/USD daily chart) demonstrates the difference between Fibonacci extension and projection. The projection, measured using two price points, shows price action modestly rebounded from the 127.2% level, yet found substantial support off the 161.8% projection, which happened to unite closely with the 100% Fibonacci extension. (Figure 1.C Source: TradingView.com – EUR/USD Daily Chart) (Figure 1.D Source: TradingView.com – EUR/USD Daily Chart)

## Fibonacci Strategies

Technical analysis remains a popular vehicle to analyse financial markets.

Included within this field are Fibonacci studies.

Though like all technical analysis tools, trading only individual Fibonacci levels may lead to underperformance. A concept known as Fibonacci clusters, however, helps traders assemble Fibonacci confluence: a collection of Fibonacci retracements and extension levels, based on various price swings, convening around a price area. The 100% Fibonacci extension and 161.8% Fibonacci projection in figure 1.D is an example of a Fibonacci cluster (the more Fibonacci levels present the better).

Fibonacci studies are found in harmonic patterns and Elliot wave theory.

Combining Fibonacci studies with other technical tools also helps shape confluence. An example may be converging support and resistance levels, relative strength index (RSI) overbought/oversold signals or volume studies.

Disclaimer: The information contained in this material is intended for general advice only. It does not take into account your investment objectives, financial situation or particular needs. FP Markets has made every effort to ensure the accuracy of the information as at the date of publication. FP Markets does not give any warranty or representation as to the material. Examples included in this material are for illustrative purposes only. To the extent permitted by law, FP Markets and its employees shall not be liable for any loss or damage arising in any way (including by way of negligence) from or in connection with any information provided in or omitted from this material. Features of the FP Markets products including applicable fees and charges are outlined in the Product Disclosure Statements available from FP Markets website, www.fpmarkets.com and should be considered before deciding to deal in those products. Derivatives can be risky; losses can exceed your initial payment. FP Markets recommends that you seek independent advice. First Prudential Markets Pty Ltd trading as FP Markets ABN 16 112 600 281, Australian Financial Services License Number 286354.

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