Fibonacci analysis is the study of identifying potential support and resistance levels in the future based on past price trends and reversals. Fibonacci analysis is based on the mathematical discoveries of Leonardo Pisano—also known as Fibonacci. He is credited with discovering a sequence of numbers that now bears his name: the Fibonacci sequence.

The Fibonacci sequence is a series of numbers that progresses as follows, 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55…. To arrive at each subsequent number in the sequence, you simply sum the two preceding numbers in the sequence. For example, to find the number that follows 55 in the sequence, you add 55 + 34 (the two preceding numbers in the sequence). The sum of 55 + 34 is 89. This is the next number in the sequence.

What intrigued Fibonacci about this sequence was not the numbers themselves but rather the relationships among the numbers, or the ratios created by various numbers in the sequence. Perhaps the most important ratio is 1.618—also known as the golden ratio, or golden mean. This number can be found throughout nature (in sea shells, growth rings, etc.) and throughout the Fibonacci sequence. Each number in the Fibonacci sequence is 1.618 times larger than the preceding number. For example, 89 is 1.618 times larger than 55 (89 ÷ 55 = 1.618). The golden ratio and the other ratios that exist within the Fibonacci sequence represent the natural ebb and flow of life. They also apply to the natural ebb and flow of the forex market.

In this section, you will learn how Fibonacci ratios can be applied to the forex market using the following analysis tools:

- Fibonacci retracements
- Fibonacci fan

When a currency pair reverses trend, forex traders naturally want to know how far the pair is most likely to move in its new direction. Fibonacci retracement levels can help. Certain Fibonacci ratios are useful when you are trying to determine how far a currency pair is going to retrace, or move against, a previous trend.

The ratios you will be using in your forex trading will help you find the following retracement levels

- **61.8%** - This level is found by dividing a number in the Fibonacci sequence by thenumber immediately following it in the sequence (55 ÷ 89 =61.8%).

- **38.2%** - This level is found by dividing a number in the Fibonacci sequence by the second number following it in the sequence (34 ÷ 89 = 38.2%).

- **23.6%** - This level is found by dividing a number in the Fibonacci sequence by the third number following it in the sequence (21 ÷ 89 = 23.6%).

You will also use three other levels in your retracement analysis. While the following levels are not calculated using numbers within the Fibonacci sequence, they are based on the Fibonacci levels above:

- **50%** - This level is determined by finding the middle between 61.8 percent and 38.2 percent ((61.8% + 38.2%) ÷ 2 = 50%).

- **100%** - This level is determined simply by finding where the previous trend began.

Determining all Fibonacci retracement levels provides you with potential support and resistance levels you can use in your forex trading. You can see these Fibonacci levels on the daily EUR/USD chart below. Each of the illustrated levels was calculated based on the trend highlighted by the red arrow. You could have used each level to help you determine when to enter and exit your trades as the currency pair began to turn around and move lower.

Fibonacci fans are based on three Fibonacci retracement levels-61.8 percent, 50 percent and 38.2 percent. To construct a Fibonacci fan, you have to do the following:

- Identify a trend.
- Identify the three horizontal Fibonacci levels (61.8%, 50% и 38.2%), as they relate to that trend.
- Draw a vertical line that crosses through these levels at the point where the trend ended.
- Draw three lines, each one beginning where the trend began and crossing through a separate poin where the vertical line intersects one of the Fibonacci levels.

You can see a Fibonacci fan on the daily EUR/USD chart below. Each of the illustrated levels was calculated based on the trend highlighted by the red arrow. You could have used the rays from the fan to help you determine when to enter and exit your trades as the currency pair began to turn around and move lower.

From the above chart we can see that the lines built with Fibonacci Fan, provide multiple points of resistance. The analysis is used to detect new levels of support and resistance as the current lines continue to be valid in the future.