# Fibonacci Numbers and Lines Definition and Uses ### What are the Fibonacci numbers and lines?

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 two preceding 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 then be broken down into ratios which, according to some, provide clues to the destination of a given financial market.

The Fibonacci sequence is important because of 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 numbers. Each number also represents 0.618 of the number to its right, again ignoring the first numbers in the sequence. The golden ratio is ubiquitous in nature where it describes everything from the number of veins in a leaf to the magnetic resonance of the spins in cobalt niobate crystals.

### Key points to remember

• Fibonacci numbers and lines are created by ratios found in the Fibonacci sequence.
• The common Fibonacci figures on the financial markets are 0.236, 0.382, 0.618, 1.618, 2.618, 4.236. These ratios or percentages can be found by dividing certain numbers in the sequence by other numbers.
• Although they are not officially Fibonacci numbers, traders can also use 0.5, 1.0 and 2.0.
• The figures reflect how far the price could go following another price movement. For example, if a stock goes from \$ 1 to \$ 2, Fibonacci numbers can be applied to it. A drop to \$ 1.76 is a 23.6% retracement of the \$ 1 price movement (rounded).
• Fibonacci’s tools are retracements and extensions. Fibonacci retracements measure how far a withdrawal could go. Fibonacci extensions measure how far a pulse wave could go.

### The formulas for Fibonacci numbers and levels are

Fibonacci numbers have no specific formula, rather it is a sequence of numbers where numbers tend to have certain relationships with each other.

### How to Calculate Fibonacci Retracement Levels

The sequence of Fibonacci numbers 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 choosing two price levels on a chart, usually a high swing and a low swing. Once these two points have been chosen, the Fibonacci numbers / lines are plotted as percentages of this movement.

If a security goes from \$ 15 to \$ 20, the level of 23.6% is \$ 18.82 (\$ 20 – (\$ 5 x 0.236) = \$ 18.82). The 50% level is \$ 17.50 (\$ 15 – (\$ 5 x 0.5) = \$ 17.50).

The Fibonacci extension levels are also derived from the numerical sequence. As the sequence progresses, divide a number by the previous number 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 prices. The beginning of a movement, the end of a movement, then a point somewhere in between (the withdrawal).

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

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

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

Some traders believe that Fibonacci figures play an important role in finance. As stated 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 graph that indicate areas of support and resistance.
2. Fibonacci Extensions – These are horizontal lines on a graph that indicate where a strong price wave can reach.
3. Fibonacci arcs – These are compass type movements from a high or low level that represent areas of support and resistance.

4. Fibonacci Fans – These are diagonal lines created using a top and a bottom that represent areas of support and resistance.

5. Fibonacci Time Zones – These are vertical lines in the future designed to predict when large 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 the depth of a withdrawal. Pulse waves are the largest waves in the direction of the trend, while the indents are the small waves in between. Since these are smaller waves, they will represent a percentage of the larger wave. Traders will monitor Fibonacci ratios between 23.6% and 78.6% during these periods. If the price stagnates near one of the Fibonacci levels and then begins to fall in the direction of the trends, a trader can trade in the direction of the trends.

Fibonacci levels are used as guides, possible areas where a business could develop. The price should confirm before acting on the Fibonacci level. In advance, traders do not know which level will be significant, so they must wait and see what level the price meets before taking a transaction.

Arcs, fans, extensions, and time zones are similar concepts but are applied to charts in different ways. Each shows potential areas of support or resistance, based on the Fibonacci numbers applied to previous price movements. These support or resistance levels can be used to predict where the price may stop falling or climbing in the future.

### The difference between Fibonacci numbers and Gann numbers

W.D. Gann was a famous trader who developed several number-based approaches to trade. Indicators based on his work include Gann Fan and Gann Square. The Gann Fan, for example, uses 45-degree angles, as Gann found them particularly important. Gann’s work revolved largely around cycles and angles. Fibonacci numbers, on the other hand, have mostly to do with ratios derived from the sequence of Fibonacci numbers. 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.

### Limits on the use of Fibonacci numbers and levels

The use of Fibonacci studies is subjective because the trader must use the ups and downs of his choice. The ups and downs that will be chosen will affect the results a trader gets.

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