Fibonacci retracements: levels, extensions and real evidence

Fibonacci retracements are horizontal lines drawn at fixed percentages of a price swing: 23.6%, 38.2%, 50%, 61.8% and 78.6%. The idea is that after a strong move, price often pulls back by a predictable fraction of it before the move resumes, and that those fractions come from the Fibonacci sequence and the golden ratio. Nearly every charting platform ships a Fibonacci tool, and the levels show up in broker research, trading forums and financial television.

They are also one of the least proven tools in technical analysis. This guide shows exactly how the levels are calculated and drawn, how extensions project targets beyond the swing, and how one real swing in the S&P 500 played out level by level. Then it looks honestly at why the levels sometimes seem to work, and why that is weaker evidence than it looks.

Where the numbers come from

The Fibonacci sequence starts 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, and each number is the sum of the two before it. Leonardo of Pisa used it in 1202 to model a rabbit population. As the numbers grow, the ratio of one number to the next settles toward a constant, about 0.618, and the ratio of a number to the previous one settles toward about 1.618. That second figure is the golden ratio, usually written φ.

Technicians derive the standard levels from it:

The 50% level is not Fibonacci at all. It was in common use long before anyone attached the golden ratio to markets, as the rule of thumb that a strong move often gives back about half its gain. Most tools include it anyway.

Markets met Fibonacci mainly through Ralph Nelson Elliott. His 1938 book The Wave Principle described price as alternating waves, and his later writing tied the relative sizes of those waves to Fibonacci ratios. A. J. Frost and Robert Prechter popularized the approach in 1978. Many traders who use Fibonacci levels today ignore wave counting entirely and keep only the ratios.

How to calculate and draw the levels

You need one completed swing: a clear swing high and a clear swing low. The levels then measure how much of that move price has given back.

A worked example

Suppose a stock rallies from $80 to $120. The range is $40. A pullback is measured down from the high:

A shallow pullback that holds above $110 suggests strong demand. One that falls past $88.56 has given back nearly the whole advance, and most Fibonacci users would treat the original move as failed.

Choosing the anchors

The arithmetic is trivial. Choosing the two anchor points is where the judgment, and most of the trouble, lies.

• Use a swing that matters on the timeframe you trade. A swing that took three days on a daily chart produces levels a few dollars apart, which noise will cross constantly.
• Decide between wicks and closes and stay consistent. Intraday highs and lows are the convention. Closing prices give slightly different levels.
• Anchor only after the swing is complete. A low is a swing low only once price has moved away from it. Redrawing the tool every time a new low prints is how traders end up fitting levels to whatever happened.

An objective way to find swings is the ZigZag indicator: filtering swings, and why the last leg repaints indicator, which marks every move larger than a chosen percentage. It removes some of the temptation to pick the anchor that makes the levels look best.

A real swing: SPY in 2025

From its intraday high of $613.23 on February 19, 2025, the SPDR S&P 500 ETF (SPY) fell to an intraday low of $481.80 on April 7, a decline of 21.4% in seven weeks. The slide began on growth and tariff worries and deepened sharply after the US tariff announcements of April 2. The range is $131.43. Measured up from the low, the recovery levels were:

A Fibonacci enthusiast would point to several of these. On April 9, the day the administration paused most of the new "reciprocal" tariffs for 90 days, SPY jumped 10.5% and finished the session almost exactly on the 50% line. The 61.8% level marked a week-long pause in early May, until news of a US–China tariff truce gapped the market past it on May 12. And the 161.8% extension, $694.45, capped SPY for three months in early 2026: the highest close from January 9 to mid-April was $695.49, and in between the index fell about 9% to $631.97 on March 30. SPY only closed decisively above that level on April 15, 2026.

A skeptic would point to the rest. The 23.6% and 38.2% levels were crossed in a day. The big turns that mattered, April 9 and May 12, were caused by policy news that no ratio could anticipate. The $694–$700 area that held in 2026 is also the round $700 mark, which attracts orders for reasons that have nothing to do with φ. And every level here depends on one choice of swing. Anchor on closing prices, or on the December 2024 high instead of February's, and every line moves.

Why the levels sometimes seem to work

They are easy to confirm after the fact

Five retracement levels spread across a swing leave little room between them. In the SPY example, a band of ±1% of price around each of the five levels covers about 42% of the whole $481.80–$613.23 range. Even a ±0.5% band covers about 21%. Price wandering anywhere in that space will often "react near a Fibonacci level" simply because there is almost always one nearby. Add the 0% and 100% anchors, the extensions, and the choice of several swings, and some line will line up with almost any turn.

That is the core problem: a level that is judged only after price turns cannot fail. A fair test fixes the swing, the levels and the tolerance first, then counts how often price actually turns there compared with arbitrary levels. Rigorous public tests of that kind are scarce, and none we know of establishes that the Fibonacci ratios beat arbitrary percentages.

They may be self-fulfilling

The stronger argument for the levels is behavioral. Millions of traders draw the same tool on the same obvious swings, and many of them place limit orders, stops and profit targets at the resulting prices. Orders that cluster at a price can make it act as Support or Resistance for a while (see Support and resistance: why price levels form and how to use them).

There is research on that mechanism in a different setting. Carol Osler's 2003 study of currency order books found that stop-loss and take-profit orders cluster at round numbers, and that this clustering helps explain why prices tend to reverse or accelerate at those levels. The same logic plausibly applies to widely watched Fibonacci levels. But it predicts only a short-lived effect where crowds look, and it is no reason to believe that markets obey the golden ratio.

How traders use them sensibly

Used as a forecast, the levels are weak. Used as a planning grid, they can be useful, mainly because they force a trader to decide in advance where a pullback is "normal" and where it has gone too far.

• Define zones, not lines. Treat 38.2%–61.8% of a strong move as the area where a pullback is still ordinary, and wait for price itself to show a turn, such as a higher low or a bullish reversal candle, before acting.
• Combine with other evidence. A Fibonacci level that coincides with a prior swing high, a rising 50-day moving average or a gap is more interesting than one sitting in empty space.
• Place stops beyond the next level, not on it. A stop exactly on a popular level is where everyone else's stop sits too. See Stop-loss placement: volatility, structure and time stops.
• Use extensions as targets with humility. A 127.2% or 161.8% projection can frame a reward-to-risk estimate, but the market has no obligation to reach it.

Retracements compared with other level tools

How Finabase draws Fibonacci levels

Every symbol's chart on the Finabase web app has a Fibonacci drawing tool in its toolbar, next to trend lines, horizontal lines, rectangles and text notes. Choose it, then click two points on the chart. Finabase draws seven levels between them: 0%, 23.6%, 38.2%, 50%, 61.8%, 78.6% and 100%. The 0% line sits at the second point you click and 100% at the first, so to measure a bounce after a decline, click the swing high first and the swing low second. The tool does not draw extensions; if you want 127.2% or 161.8%, compute them with the formula above and add a horizontal line.

Drawings are anchored to bar dates and prices, so they stay in place when you zoom or switch ranges. If you are signed in, they are saved to your account and come back the next time you open that symbol on the web. The mobile apps do not have drawing tools.

To reproduce the example on this page, open a two-year SPY chart, choose the Fibonacci tool and click the February 19, 2025 high, then the April 7 low. The Scanner can help you find candidates for a pullback study: stocks crossing moving averages or making new highs. It does not scan for Fibonacci levels.

Frequently asked questions

Which Fibonacci level is the most important?

None is reliably special. Traders talk most about 61.8% and 50%, partly because a pullback of about half a strong move is common, and partly because those are the levels everyone watches. The most watched levels are the most likely to see order clustering, which is a behavioral reason, not a mathematical one.

Should I draw Fibonacci levels on wicks or closing prices?

Intraday highs and lows are the common convention because they capture the full extent of the swing. Closing prices give a slightly tighter set of levels. Either is defensible. What matters is using the same rule every time instead of picking whichever version fits the chart.

Do Fibonacci retracements work on crypto and forex?

The calculation works on any price series. Whether the levels mean anything is the same open question in every market. The best evidence of real level effects comes from currency markets, and it concerns round numbers rather than Fibonacci ratios.

What is the difference between a retracement and an extension?

A retracement measures how much of a completed swing price has given back, so its levels lie inside the swing. An extension projects the swing beyond its starting point, at 127.2%, 161.8% and so on, and is used to estimate targets.

Summary

Fibonacci retracements turn one price swing into a grid of levels at 23.6%, 38.2%, 50%, 61.8% and 78.6%, and extensions project it further. The math is simple and the tool is everywhere, which is the best argument for it: widely watched levels can attract orders. The evidence that the golden ratio itself has predictive power is thin, and with five levels close together, coincidences are easy to find. In SPY's 2025 swing, some levels marked real pauses and others meant nothing. Treat Fibonacci levels as zones for planning entries, stops and targets, decide in advance what would prove you wrong, and let price confirm before you act.