The Fibonacci series is the infinite sequence of numbers (0, 1, 1, 2, 3, 5, 8, 13 ..) in which each item is the sum of the preceding two. For example, 2= 1+1, 5 = 3+2, and so on. This sequence has been recognized and examined in Europe since the 14^{th} century, but Arabs and Indians were aware of its existence even before that time. The series is widely encountered in countless natural phenomena, from the arrangement of tree leaves to various properties of the sub-atomic world, and it is studied by mathematicians with great interest as a fertile field for new discoveries.

It should not be that surprising that the series, as commonly encountered in many natural processes and patterns, is also useful in the study of the price action and the markets. We concern ourselves with the forex trading aspect of indicators: the way in which the market action seems to follow certain suggestions of the Fibonacci Series when it is applied to various trends and range patterns.

### The Golden Ratio

Many traders use the Fibonacci Series for trading decisions, but most of time, the raw numbers themselves find little use. Instead, to make analysis easier, traders use the ratios between the numbers in the Fibonacci Series to determine various factors like retracement levels, extensions of trends, and resistance levels inside a price range. All these ratios are essentially derived from the Golden Ratio which is the limit of the ratio of two successive numbers in the Fibonacci Series. For example, 5/8 is approximately 0.62. while 8/13 is approximately 0.61. If we subtract this number from one, we get 0.38, which is also the ratio of two numbers in the series with one number in between. For example, 3/8 is equal to 0.375, while 5/13 is approximately 0.38. The ratio between Fibonacci numbers converges on ideal values as the series progresses.

To summarize, in the infinite series

0, 0, 1, 1, 2, 3, 5, 8, 13 ..

8/13 = 5/8 = 3/5 =2/3 = 0.61 with the equality being an approximation, and the ratio approaching the ideal Golden Ratio (0.6180339887) as the series progresses.

1/3=2/5=3/8=5/13 = 0.38. Similar to the above, this ratio is simply the subtraction of the Golden Ratio from one.

### Overview of Fibonacci Indicators

So how are the Fibonacci numbers (rather the ratios) used in technical analysis, and forex? It has been observed countless times in the market that the resistance support levels in the context of a developing range or trend pattern are determined by the Fibonacci ratios. So for example, if the first leg of a trend has the length of 3x, the retracement is expected to be 0.38*3x, or 0.61*3x. Similarly, the extension of the trend will be at 5x, or 8x, as we would expect in the series. (Remember that the series runs (…3,5,8…)). All Fibonacci indicators are built on this principle. Let’s see a few examples

**Fibonacci Retracement**

This indicator is used for determining retracement levels in an ongoing trend. The two most important ratios are 0.38, and 0.61, but 0.50 is also used. When using this indicator, the trader simply notes the levels that correspond to the multiplication of the size of the main price movement with the ratios, and notes them as potential support levels. For example, if the price moved from 1 to 1,3 in its main leg, the retracement levels would be at (0.3*0.61= 0.183) and (0.3*0.38=0.11), that is, at 1.18, and 1.11. Here 0.3 is (1.3-1), that’s the length of the main movement, and the factors are the Fibonacci Ratios. Read more about the application of Fibonacci retracement levels and extensions.

**Fibonacci Extension**

Fibonacci Extension serves the same purpose, and is calculated in the same manner as the previous item, only it is used to calculate extension levels, the resistance levels where the trend may reverse after an initial leg. For example, in our previous example, to calculate the next possible leg of the trend (and the resistance level) we need to multiply the length of the first leg at 0.3 with the Fibonacci Ratios of 1.38 and 1.61.

**Fibonacci Time Series**

The Fibonacci Time Series is the Fibonacci Series applied to the timeframe of trading. Thus, we first choose a developed pattern from the past, preferably at the beginning of some long term trend. For example, we pick a head and shoulders pattern which is the first leg of a long term uptrend, and apply the time series to it. If the H&S pattern developed over a period of 2x days, we expect the subsequent triangle to develop over a period of 3x days, and the correction after that to last 5x days with the number picked up from the sequence discussed above (0, 1, 1, 2, 3, 5, 8, 13 ..). The principle is that each complete phase of the trend should develop in a time period determined by the Fibonacci Sequence.

### Conclusion

The trading software will do all of the calculations above and provide them for you without you having to crunch a single number. So don’t be discouraged if you find the topic a bit too complicated. It is very easy to get the hang of this subject after drawing a couple of Fibonacci levels on a forex chart.

Fibonacci Series is a mathematical concept, but since the market action is a chaotic process, it would not be sensible to expect the prognostications based on this series to be correct at all times. However, it is very useful in determining potential reversal, or reaction points, as well as points where we can leave or join a trend, based on the Fibonacci Ratios. It is easy to use the Fibonacci Indicators, and they are very popular among traders of all experience levels. As long as you don’t regard them as infallible, they will be very useful in your trading decisions.