How to Calculate Fibonacci Retracements

Use Fibonacci retracement to determine where a stock may find support.

Use Fibonacci retracement to determine where a stock may find support.

There's at least one thing about Fibonacci retracement levels that separates them from just about any other tool you use to speculate: They were invented in the 13th century.

That's right – Italian mathematician Leonardo Fibonacci's namesake numbers predate the stock market by about 400 years. While just saying "Fibonacci retracement" makes you feel like a genius, the concept is actually fairly straightforward. A Fibonacci retracement is simply a series of numbers that expresses a key relationship via ratios, where each number in the sequence is the sum of its two preceding numbers.

How it Works

The good news is that you don't have to do much calculating to arrive at a Fibonacci retracement. Here's a cheat for you; the Fibonacci sequence starts like this: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144. The sequence continues to infinity (so the next two numbers would be 233 and 377, for example) and reveals patterns that have captivated mathematicians for centuries. Chiefly, each number is about 1.618 times greater than the one before it and results in a ratio of 61.8 percent when you divide any number in the sequence by the one that follows it. This is known as "the golden ratio."

Some other key ratios in the sequence are 38.2 percent – found by dividing any number in the sequence by the number two places to its right – and 23.6, found by dividing a number by the one three places to its right.

Why You Should Know

Here's where things get interesting and a little weird. Those ratios occur consistently throughout nature, appearing in the proportions of snail shells and flowering plants, to name just a few instances. And – you guessed it – they also occur in the stock market.

For traders, Fibonacci retracements are a valuable and time-tested tool for predicting the point at which an asset's price might reverse. Once the price of the asset has retraced to one of those key ratios, it's likely to continue in the direction of the trend. Though they're not a guaranteed prediction method, Fibonacci retracements can be even more effective when used at big swing highs and lows. Shortly, they're another tool in the toolbox that can help you forecast the potential level of correction or pullback when an asset is prime for reversal.


If you want to go old school, you can create a Fibonacci retracement by taking two extreme high and low points on the stock chart of any given asset and dividing the vertical distance by one of those key Fibonacci ratios (23.6, 38.2 or 61.8).

Of course, that's not your only option. For a more detailed analysis that's even easier to obtain, a cornucopia of market-oriented sites, such as and The Pattern Trapper, offer free online calculation tools. All you have to do is input your asset's highs and lows, and these calculators automatically spit out retracement levels for you, helping you project both up trends and down trends.

Items you will need

  • Calculator


  • Fibonacci retracements can be used in a downtrend. Label the high point A and the low point B. Use the formula (A minus B) multiplied by the Fibonacci percentage, and add this to B.
  • Most charting platforms provide a Fibonacci retracement tool. In the platform, select the tool, then click on a price and drag the indicator down to the low price. All the Fibonacci levels will be automatically calculated for you.


  • There is no guarantee that a pullback in price will stop at a Fibonacci retracement level. If the trend reverses it is possible Fibonacci retracement levels will have no effect on stopping the price at all.

About the Author

Dan Ketchum has been a professional writer since 2003, with work appearing online and offline in Word Riot, Bazooka Magazine, Anemone Sidecar, Trails and more. Dan's diverse professional background spans from costume design and screenwriting to mixology, manual labor and video game industry publicity.

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