# Definition and uses of Fibonacci number lines

By Mark Holland / 5 days ago ## What are Fibonacci Lines and Numbers?

Fibonacci numbers are used to create technical indicators using a mathematical sequence developed by the Italian mathematician, commonly known as “Fibonacci”, in the 13th century. The sequence of numbers, starting with zero and one, is created by adding the previous two numbers. For example, the first part of the sequence is 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89,144, 233, 377, etc.

This sequence can be broken down into ratios that some believe provide clues as to where a given financial market will move.

The Fibonacci sequence is significant due to the so-called golden ratio of 1.618, or its inverse 0.618. In the Fibonacci sequence, any given number is approximately 1,618 times the previous number, ignoring the first few numbers. Each number is also 0.618 of the number to its right, again ignoring the first few numbers in the sequence. The golden ratio is ubiquitous in nature, where it describes everything from the number of veins in a leaf to MRI of the spins in cobalt niobate crystals.

### Key takeaways

• Fibonacci lines and numbers are created using the proportions found in the Fibonacci sequence.
• Common Fibonacci numbers in financial markets are 0.236, 0.382, 0.618, 1.618, 2.618, 4.236. These proportions or percentages can be found by dividing certain numbers in the sequence by other numbers.
• While they are not officially Fibonacci numbers, many traders also use 0.5, 1.0, and 2.0.
• The numbers reflect how far the price could go after another price move. For example, if a stock moves from \$ 1 to \$ 2, the Fibonacci numbers can be applied to that. A drop to \$ 1.76 is a 23.6% retracement of the \$ 1 price movement (rounded).
• Two common Fibonacci tools are retracements and extensions. Fibonacci retracements measure how far a retracement could go. Fibonacci extensions measure how far an impulse wave could go.

## Formulas for Fibonacci numbers and levels

Fibonacci numbers do not have a specific formula, rather it is a number sequence where the numbers tend to have certain relationships with each other.

## How to calculate Fibonacci retracement levels

The Fibonacci number sequence can be used in different ways to obtain Fibonacci retracement levels or Fibonacci extension levels. Here’s how to find them. How to use them is discussed in the next section.

Fibonacci retracements require two price points to be chosen on a chart, usually a high swing and a low swing. Once those two points are chosen, the Fibonacci numbers / lines are drawn at percentages of that move.

If a stock rises from \$ 15 to \$ 20, then the 23.6% level is \$ 18.82, or \$ 20 – (\$ 5 x 0.236) = \$ 18.82. The 50% level is \$ 17.50, or \$ 15 – (\$ 5 x 0.5) = \$ 17.50.

Fibonacci extension levels are also derived from the number sequence. As the sequence progresses, divide a number by the number above to get a ratio of 1.618. Divide a number by two places to the left and the ratio is 2,618. Divide a number by three on the left and the ratio is 4,236.

A Fibonacci extension requires three price points. The beginning of a movement, the end of a movement and then a point in between (the retracement).

If the price rises from \$ 30 to \$ 40, and these two price levels are points one and two, then the 161.8% level will be \$ 16.18 (1.618 x \$ 10) above the price chosen for point three. If point three is \$ 35, the 161.8% extension level is \$ 51.18 (\$ 35 + \$ 16.18).

The 100% and 200% levels are not official Fibonacci numbers, but they are useful as they project a similar movement (or a multiple) to what just happened on the price chart.

## What do the numbers and Fibonacci lines tell you?

Some traders believe that Fibonacci numbers play an important role in finance. As discussed above, the Fibonacci number sequence can be used to create ratios or percentages that traders use.

These include: 23.6%, 38.2%, 50%, 61.8%, 78.6%, 100%, 161.8%, 261.8%, 423.6%.

These percentages are applied using many different techniques:

1. Fibonacci retracements. These are horizontal lines on a chart that indicate areas of support and resistance.
2. Fibonacci extensions. These are horizontal lines on a chart that indicate where a strong price wave can go.
3. Fibonacci arcs. These are compass-shaped movements arising from a high or low that represent areas of support and resistance.
4. Fibonacci fans. These are diagonal lines created using a high and a low that represent areas of support and resistance.
5. Fibonacci time zones. These are vertical lines into the future designed to predict when the major price movements will occur.

Fibonacci retracements are the most common form of technical analysis based on the Fibonacci sequence. During a trend, Fibonacci retracements can be used to determine how deep a retracement might go. Impulse waves are the largest waves in the direction of the trend, while retracements are the smallest waves in between. Since they are smaller waves, they will be a percentage of the larger wave. Traders will watch Fibonacci ratios between 23.6% and 78.6% during these times. If the price stops near one of the Fibonacci levels and then begins to move back in the direction of the trend, a trader can place a trade in the direction of the trend.

Fibonacci levels are used as guides, possible areas where a trade could develop. The price must be confirmed before acting on the Fibonacci level. Traders don’t know what level will be significant beforehand, so they have to wait and see what level the price respects before placing a trade.

Arcs, fans, extents, and time zones are similar concepts, but they apply to charts in different ways. Each shows potential areas of support or resistance, based on Fibonacci numbers applied to previous price movements. These support or resistance levels can be used to forecast where the price May stop falling or going up in the future.

## The difference between Fibonacci numbers and Gann numbers

WD Gann was a famous trader who developed various number-based trading approaches. Indicators based on his work include the Gann Fan and the Gann Square. Gann’s fan, for example, uses 45-degree angles, as Gann found them especially important. Gann’s work largely revolved around cycles and angles. Fibonacci numbers, on the other hand, are primarily concerned with proportions derived from the Fibonacci number sequence. Gann was a trader, so his methods were created for the financial markets. Fibonacci methods were not created for trading, but were adapted to the markets by traders and analysts.

## Limitations of using Fibonacci numbers and levels

The use of Fibonacci studies is subjective, as the trader must use the highs and lows of his choice. The highs and lows that are chosen will affect the results a trader achieves.

Another argument against Fibonacci number trading methods is that there are so many of these levels that the market is bound to bounce or change direction near one of them, making the indicator appear significant in hindsight. The problem is that it is difficult to know which number or level will be important in real time or in the future.

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