
Leonardo Fibonacci was an Italian mathematician who helped popularize the study of what is now known as the Fibonacci sequence. The sequence is tied to the golden ratio, which shows up repeatedly in the natural world in the shape of snail shells, pinecones, and the spin of hurricanes. So, what does the ratio for the spiral on a pinecone have to do with stock prices?
Many technical traders guide their trading by using chart drawing tools like Fibonacci retracements and Fibonacci extensions, which are based on ratios from the Fibonacci sequence. They “follow the Fib” to predict potential price movements, looking for buy and sell opportunities.
What is the Fibonacci sequence?
The Fibonacci sequence represents a series of numbers in which a given number is equal to the sum of the two preceding numbers:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, etc.
The numbers were used long before Fibonacci's time, and the sequence is ultimately less significant than the ratios derived from dividing the numbers into one another. For example, 13/8 = 1.625. As you move up the sequence, to say 55/34, the ratio approaches the number 1.618—what is famously known as the golden ratio and observed by people as far back as the Greek mathematician Euclid.
For traders, other ratios from dividing the number have potential value, like the inverse of the calculation for the golden ratio: 34/55, or 0.618. Studies about how the ratios may relate to markets began being developed decades ago.
How Fibonacci applies to trading and technical analysis
In the 1930s, Ralph Nelson Elliott developed his Elliott Wave Theory, which looked at long-term market trends based on the Fibonacci sequence. His analysis found that market trends tend to follow a pattern of five waves on the direction of the trend, followed by three corrective waves. It looked at price movements along ratios found in the Fibonacci sequence, including 23.6%, 38.2%, 61.8%, and 161.8%. The 38.2% comes from dividing any number in the Fibonacci series by the number found two places to the right, and 23.6% comes from dividing a number by the number found three places to the right.
The 50% and 100% levels aren’t derived from the Fibonacci numbers, but many traders consider these significant levels. Some traders use additional numbers that come from the midpoint of two of these numbers.
Fibonacci ratios can help technical traders identify areas of support, resistance, and retracement. When a stock moves off its peak or trough levels, traders want to know where it might go next. Tools on the thinkorswim® platform apply the Fibonacci numbers to a chart to show where the support and resistance levels may be.
A retracement is a temporary reversal in the direction a stock is trending, and it often occurs between support and resistance levels. If a stock sells off during a rally, at a certain point, the price sometimes goes so low that it attracts new buyers, ending the price decline. That is the support level, and it’s a place where some short sellers may want to cover and some long buyers may want to jump in. The resistance level indicates the point where the stock may seem overpriced. It’s the point where some long traders take profits, so the price starts to decline until it hits support.
Finding Fibonacci retracement levels
Because the Fibonacci retracement tool can help traders find those support and resistance levels, it may provide insight into when to place a trade, depending on how the security is trending.
How to use the Fibonacci retracement drawing tool on thinkorswim:
- Select Charts.
- Enter a ticker symbol and select a time frame.
- You can analyze from either a high or low price point. For this example, place your cursor at a high price point you want to analyze, then right-click and select Add a drawing.
- From the Active Tool menu, select % (Fibonacci Retracements).
- Place the cursor on the high or low point, click once, move to the next high or low point to the right, and click again. The tool automatically calculates the corresponding Fibonacci percentage and price levels.

Source: thinkorswim platform
For illustrative purposes only. Past performance is no guarantee of future results.
The chart of the S&P 500® index (SPX) above shows the range of retracement levels where traders can watch for potential technical support or resistance levels. In this scenario, retracing a move higher, the Fibonacci series indicates key points of support in the pullback or correction. When the SPX started to move above the March low, it met slight resistance at the 23.6% level. Even though it broke above it, the close was right around that level. The SPX then continued moving toward the 38.2% level, hesitated there for a few days, and then went back toward the 23.6% level. When reviewing the price chart, it's possible to see how the different retracement levels revealed support and resistance levels, which could have served as entry or exit points.
Given the simplicity of the Fibonacci retracement tool, traders can try applying it to individual stocks as well as market indexes. It's also possible to combine Fibonacci levels with other indicators to get more trading signals.
There's no guarantee that using Fibonacci retracements will work effectively as part of a trading strategy, but they can provide some levels to watch when engaging in technical analysis.
Using Fibonacci extensions
Another Fibonacci tool is the extension. While Fibonacci retracements help traders track moves within the current trading range, Fibonacci extensions help traders find new support and resistance levels when the underlying security rallies to a new all-time high or unprecedented low. At these new price levels, historical support and resistance levels no longer hold because the stock is trading outside former ranges. The extensions tool can help a trader determine what the new support and resistance could be. One approach is to use Fibonacci extensions for guidance on where to take profits by extending the series of price movement amounts above 100% or below 50%—including 23.6%, 38.2%, 138.2%, 161.8%, and 261.8%.
Creating Fibonacci extensions begins by selecting three very recent prices. The first is a recent significant high, the second is a recent significant low, and the third is the end of the retracement against a recent move. Then using the tool, you can begin to find potential support, resistance, and price target levels at these new price levels.
Here's how to use the tool on the thinkorswim platform:
- Select Charts.
- Enter a ticker symbol.
- Place your cursor at the first price point you want to analyze, then right-click and select Add a drawing.
- From the Active Tool menu, select the Fibonacci extensions tool, which is represented by a percentage mark with two lines zagging from it. The tool will allow you to select the next two price points. Select the Fibonacci extensions tool at those particular points—all will turn red once they're selected.

Source: thinkorswim platform
For illustrative purposes only. Past performance is no guarantee of future results.
Once the extensions are set, that chart will look something like this:

Source: thinkorswim platform
For illustrative purposes only. Past performance is no guarantee of future results.
The right side of the chart shows the Fibonacci extensions calculated by the selection of price points 1, 2, and 3. Three extensions with circles around them (yellow at the 23.6% level, light blue at the 38.2% level, and blue at the 50% level) show areas of potential support and resistance. The trader will use these to analyze the price action.
In this example, the security's price tests above and below the 23.6% level (yellow circle) following the new high at point 3. The candle after point 3 shows a closing low near the same extension level (again, yellow circle). The next candlestick moves further downward to test the 38.2% extension level (light blue circle), which held on the day and closed higher at the 23.6% level. This means the 23.6% level appears to be a new resistance level. The last candle opens with a gap below the 38.2% level, becoming the new support level just short of the 50% extension level (dark blue circle) before closing largely unchanged. This indicates the stock is unlikely to fall further because a new support and resistance range is forming beyond the range of previous retracements.
Fibonacci extensions highlight potential points of support and resistance, which a trader can use to adjust orders as necessary. In this example, the trader would likely consider trading between the new support and resistance until a breakout occurs. Of course, the markets don't always heed the golden ratio as well as snails and pinecones do.
Bottom line
Fibonacci retracements and extensions give traders a potential idea of where a security's price may be moving next. Traders can use the Fibonacci tools in thinkorswim to help plan and evaluate their trading strategy.