Leonardo Fibonacci was a mathematician born in 1170 AD. From his work, we get the Fibonacci sequence of numbers, and also the well-known Fibonacci golden ratio. The Fibonacci sequence is a series of numbers where the next number is simply the sum of the two preceding numbers. So for example, it would run 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 and so on, with the sequence continuing indefinitely.

It is based on the rate of reproduction of two theoretical rabbits and the subsequent population growth if the following generations continued to reproduce. At first glance, it may seem somewhat confusing to find that there is a connection between a 12th century mathematician, the rate at which rabbits reproduce and predicting the future direction of the financial markets using technical analysis.

**KEY TAKEAWAYS**

- In the Fibonacci sequence of numbers, after 0 and 1, each number is the sum of the two prior numbers.
- In the context of trading, the numbers used in Fibonacci retracements are not numbers in Fibonacci’s sequence; instead, they are derived from mathematical relationships between numbers in the sequence.
- Fibonacci retracement levels are depicted by taking high and low points on a chart and marking the key Fibonacci ratios horizontally to produce a grid; these horizontal lines are used to identify possible price reversal points.

**Fibonacci Sequence**

A **Fibonacci sequence** is formed by taking 2 numbers, any 2 numbers, and adding them together to form a third number.

Then the second and third numbers are added again to form the fourth number.

And you can continue this until it’s not fun anymore.

The ratio of the last number over the second-to-the-last number is approximately equal to** 1.618**.

This ratio can be found in many natural objects, so this ratio is called the **golden ratio**.

It appears many times in geometry, art, architecture, and even on Sonic the Hedgehog.

The golden ratio is actually an irrational number, like pi, and is often denoted by the Greek letter, **phi** (**φ**).

Okay, that’s enough mumbo jumbo.

With all those numbers, you could put an elephant to sleep. We’ll just cut to the chase; these are the ratios you HAVE to know:

**Fibonacci retracement levels**

The argument of Fibonacci followers is: if so much of nature and the world is made up of these Fibonacci ratios, surely the same would apply to the markets too? Analysts can use this approach when learning to trade Fibonacci through its retracements. Let’s say for example that a market has risen and, similar to all markets, it doesn’t move in a straight line and starts to fall back. Traders will look at Fibonacci ratios to try and figure out where the fall may stop and the market will resume its previous rise.

Fibonacci retracement levels often mark retracement reversal points with surprising accuracy. The retracement levels are a powerful tool that can be applied to all timeframes, including day trading and long-term investing. Fibonacci numbers also play a crucial role in the Elliott Wave principle, a technical analysis tool used to identify market cycles. The tool can be used across many different asset classes, such as foreign exchange, shares, commodities and indices.

**Fibonacci Extension Levels**

0, 0.382, 0.618, 1.000, 1.382, 1.618

You won’t really need to know how to calculate all of this. Your charting software will do all the work for you.

However, it’s always good to be familiar with the basic theory behind the indicator so you’ll have the knowledge to impress your date.

Fibonacci retracement levels work on the theory that after a big price moves in one direction, the price will *retrace* or return partway back to a previous price level before resuming in the original direction.

Traders use the Fibonacci retracement levels as potential **support and resistance areas**.

Since so many traders watch these same levels and place buy and sell orders on them to enter trades or place stops, the support and resistance levels tend to become a self-fulfilling prophecy.

Traders use the Fibonacci extension levels as **profit-taking levels**.

Again, since so many traders are watching these levels to place buy and sell orders to take profits, this tool tends to work more often than not due to self-fulfilling expectations.

Most charting software includes both Fibonacci retracement levels and extension level tools.

In order to apply Fibonacci levels to your charts, you’ll need to identify Swing High and Swing Low points.

A **Swing High** is a candlestick with at least *two lower highs* on both the left and right of itself.

A **Swing Low** is a candlestick with at least *two higher lows* on both the left and right of itself.