Fibonacci Retracement Ratios
Fibonacci ratios can be used in trading, and they’re used to describe the proportions of everything, from the smallest things in nature, such as atoms, to the largest structures in the universe, such as celestial bodies too vast to picture.
Nature relies on this innate ratio to maintain balance, and financial markets appear to follow Fibonacci ratios too. Here we look at some of the technical analysis tools built around them.
Who Is Leonardo Fibonacci?
Mathematicians, scientists, and naturalists have known this ratio for centuries. It comes from what is known as the Fibonacci sequence, named after its founder Leonardo Fibonacci, an Italian mathematician. Nature uses this ratio to maintain balance, and financial markets appear to as well.
Read also: What Are Fibonacci Levels?
The Fibonacci Ratio Sequence
In Fibonacci ratios, the sequence of Fibonacci numbers runs as follows: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, and so on. Each number in this sequence is simply the sum of the two numbers before it, and that’s how we get the Fibonacci sequence.
Calculating the sequence
1+0=1
1+1=2
2+1=3
5+3=8
13+8=21
34+21=55
89+55=144, and so on — the series of numbers extends to infinity this way, and it carries many unique mathematical properties.
One of the distinctive properties of the Fibonacci sequence is that each number is roughly 1.618 times larger than the number before it.
Examples From the Fibonacci Sequence
Example: the number 34 in the series is roughly 1.618 times the number that comes before it in the sequence, which is 21, and this holds true across the whole sequence.
This shared relationship between each number in the series is the basis of the common ratios used in Fibonacci retracements in the markets.
The main Fibonacci ratio of 61.8% is found by dividing one number in the series by the number that follows it.
For example, 21 divided by 34 equals 0.618, and 55 divided by 89 equals 0.618.
The 38.2% ratio is found by dividing one number in the series by the number two places to its right.
For example, 55 divided by 144 equals 0.38.
The 23.6% ratio is found by dividing one number in the series by the number three places to its right.
For example, 8 divided by 34 equals 0.23.
The ratio of 1.618 refers to the golden ratio, or golden mean, also called phi (PHI). There is also what is known as the Fibonacci 88 ratio, meaning “wealth ratios.”
For example, the inverse of 1.618 is 0.618. These ratios can be found throughout nature, architecture, art, and biology.
The ratio 0.618 to 1 is the mathematical basis for the shape of playing-card leaves, sunflowers, spiral shells, Greek vases, and spiral galaxies in outer space. The Greeks built much of their art and architecture around this ratio and called it the golden ratio.
For reasons that aren’t entirely clear, these ratios appear to play an important role in the stock market, much as they do in nature, and can be used to identify critical points where price is likely to reverse, through the Fibonacci tool.
Using Fibonacci level ratios on the price wave helps a trader anticipate future corrective price levels.
The ratio describes proportions found in everything from atoms to the massive stars in the sky. The Fibonacci sequence can be applied to the market using four main techniques: retracements, arcs, fans, and time zones.
Read also: How to Use the Fibonacci Tool With a Trend Line
Fibonacci Retracement Ratios
Fibonacci ratios are ratios used to identify potential reversal levels based on the market’s price direction, and they’re among the most widely used tools in the forex market. These ratios come from the Fibonacci sequence.
The most popular and widely used ratios are 61.8% and 38.2%. Note that 38.2% is rounded to 38% and 61.8% is rounded to 62%, alongside the Fibonacci 88 ratio and the Fibonacci 23 ratio.
They can be used to identify support and resistance levels, to place stop-loss orders or target prices, and even as a core mechanism within a counter-trend strategy for the price’s expected move afterward, marking entry and exit points with precision.
Most modern trading platforms include a tool that automatically draws Fibonacci retracement ratios and displays horizontal lines at these key market levels.
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Fibonacci retracement ratios are a very popular technical indicator and one of the valuable tools that can become even more powerful when used alongside other indicators.
The chart below shows how Fibonacci ratios can be used in a downtrend (from the top down to the bottom): the zero level sits at the bottom and the 100 level at the top. The tool is drawn from the top down to the bottom, and you can then see the horizontal lines.
Notice how price tends to change direction as it approaches the Fibonacci retracement levels of 0.38, 0.61, and 0.5.
The chart below shows how Fibonacci ratios can be used in an uptrend (from the bottom up to the top): the 0 level sits at the top and the 100 level at the bottom. The tool is drawn from the bottom up to the top.
In addition to the ratios shown above, many traders also like to use the 50% level line alongside 61.8%. The 50% retracement level isn’t technically a Fibonacci ratio, but it gets used because price tends to respect this level, and it forms a strong horizontal level that traders end up relying on often.
Should You Rely on This Tool When Trading?
When using the golden Fibonacci ratios in technical analysis, the golden ratio is usually translated into three ratios: 38.2%, 50%, and 61.8% (the price zones on the chart). That said, more multiples can be used when needed, such as 23.6%, 78.6%, 123%, 127%, 161.8%, 423%, and so on.
This makes the Fibonacci sequence one of the most widely used tools across trading instruments in the market, especially for support and resistance, and it underpins Elliott Wave analysis. This is partly due to its relative simplicity, combined with the fact that it can be applied to almost any trading instrument. Here it’s worth distinguishing between Fibonacci extension and retracement.
In the end, Fibonacci ratios are used as one of the most common technical trading strategies, and a trader can use a Fibonacci retracement level to flag where they might enter a trade or position. If a trader notices that price has dropped 38.2% after a strong move, they may decide to enter the trade once price starts moving upward again.
Because price has reached a Fibonacci level, it’s considered a favorable time to buy, since the trader expects price to pull back or recover its recent losses from there.
Read also: What Is the Fibonacci Sequence? An Explanation With a Practical Example
Frequently Asked Questions About Fibonacci Ratios
What are Fibonacci ratios?
It’s a mathematical ratio — a numerical sequence in which each term is the sum of the two preceding terms. It’s also called the harmonic pattern, and the Fibonacci sequence is used to identify support and resistance zones for a stock.
Who invented the sequence?
The sequence is attributed to the Italian mathematician Leonardo Fibonacci, one of the most important mathematicians in history, who belonged to the medieval era. He was born in 1175 and died in 1250.
Is the Fibonacci sequence arithmetic?
Yes, it’s a numerical sequence, and this sequence is used to build technical indicators through a sequential numerical pattern. It’s also linked to nature, since the proportions of natural things, such as galaxies and planets, follow it.
What does the golden ratio equal, and who discovered this sequence?
The golden ratio, or golden number, equals approximately 1.618. It’s a ratio between two numbers linked to the Fibonacci sequence, where dividing each term by the term before it in the sequence approaches the golden number 1.618. The sequence was discovered by the Italian mathematician Leonardo Fibonacci.
How is Fibonacci drawn?
Fibonacci is drawn from the end of the move at the top down to the bottom, so that the zero level sits at the bottom and the 100 level sits at the top.
What is a Fibonacci projection?
It’s one of the technical analysis tools. Fibonacci projections are used to identify the expected extension once a retracement move ends. The projection is drawn by placing two points on the directional move, plus a point at the end of the corrective move.
Disclaimer: All information in this article is for educational purposes only and does not constitute investment advice or a trading recommendation. Trading forex and CFDs involves a high level of risk due to leverage and may result in the loss of some or all of your invested capital. Fibonacci ratios do not guarantee results, and price does not always react at the levels they show. This article may contain affiliate links through which we may earn a commission at no additional cost to you.
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