Lesson T4.6 · 6 of 7 · Trend, support and resistance
Fibonacci retracements and extensions: how to calculate them
Fibonacci retracements show how much of a move the price gives back: 23.6%, 38.2%, 50%, 61.8% or 78.6%. Extensions (127.2%, 161.8%) estimate how far the next move might go. They are hugely popular, but tests have not found that prices stop at them more often than at any other percentage.
Terms in this lesson
- Support and resistance
- Prices at which a stock has often stopped falling or stopped rising.
- Stop-loss
- An order that sells automatically if the price falls to a level you choose.
Fibonacci retracement levels: 23.6, 38.2, 50, 61.8 and 78.6%
Definition
What is a Fibonacci retracement?
The share of a move that the price gives back before carrying on.
You pick the start and the end of the move, say a low of 100 and a high of 120. Each level is end - move × percentage. For 38.2%: 120 - 20 × 0.382 = 112.36. Traders watch these levels as areas where a pullback might stop. The chart below is built to show the calculation; how often prices really stop at these levels comes at the end of the lesson.
The price rises from a low of 100 to a high of 120, then falls to 107.80 and turns up again. The retracement levels: 23.6% at 115.28, 38.2% at 112.36, 50% at 110, 61.8% at 107.64 and 78.6% at 104.28.
For a fall, you work the other way: start at the low and go up. If the price dropped from 80 to 60, the 50% retracement is at 60 + 20 × 0.5 = 70.
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Create a free accountFibonacci extensions: 127.2% and 161.8%
Definition
What is a Fibonacci extension?
A level beyond the end of the move, used as a possible target.
Once the price breaks the old high, some traders look for targets at 127.2% or 161.8% of the move, measured from its start: start + move × percentage. For the move from 100 to 120: 100 + 20 × 1.272 = 125.44. Some platforms measure extensions differently, from the low of the pullback, so check what yours uses.
The same move from 100 to 120, with the pullback to 107.80. The price then breaks above 120 and climbs to 125.60, close to the 127.2% extension (125.44). The 161.8% extension is higher, at 132.36, and is not reached.
Why 50% is not a Fibonacci ratio
The 50% level sits alongside the Fibonacci levels on almost every platform, but it does not come from the Fibonacci sequence. It comes from Dow Theory, which holds that the stock market averages often retrace about half of their previous move.
Do Fibonacci levels work? What the tests show
If Fibonacci levels had some special power, pullbacks would stop at 38%, 50% and 62% more often than at other percentages. That has been checked:
- Bulkowski, 1995-2009More than 23,900 retracements from 576 US shares, with no spikes at 38%, 50% or 62%. An earlier test, done differently, had shown small peaks at 50% and 61%; in the automated test they disappeared.
- Bulkowski, 2009-2020489 shares in a rising market, from about 10,000 to more than 65,000 cases depending on the method. Retracements of 38%, 50% and 62% were no more common than any other number from 1% to 100%.
- Tsinaslanidis, Guijarro and Voukelatos, 2022A study in Expert Systems with Applications covering three equity markets: price behaviour in Fibonacci zones did not differ statistically from that in non-Fibonacci zones.
Lessons are educational. They are not a recommendation to buy or sell. Investing involves risk and you can lose money. Sources: StockCharts ChartSchool (Fibonacci Retracements); Thomas N. Bulkowski, thepatternsite.com (Swing Setup, Fibonacci retracement tests), accessed 29 October 2026; P. Tsinaslanidis, F. Guijarro and N. Voukelatos, “Automatic identification and evaluation of Fibonacci retracements: Empirical evidence from three equity markets”, Expert Systems with Applications 187 (2022). The charts are teaching diagrams, not real prices.