A Fibonacci retracement is a charting tool. It takes a completed price move, from a swing low to a swing high or the reverse, and marks horizontal lines at fixed percentages of that move: usually 23.6%, 38.2%, 50%, 61.8% and 78.6%. Traders watch these lines as possible support or resistance when price pulls back. The levels are watch zones, not reversal points. A 2022 peer-reviewed study found that price does not behave differently at Fibonacci levels than at other price zones.
Where the numbers come from
The sequence
The sequence is named after Leonardo Pisano, better known as Fibonacci (c. 1170 to c. 1240). In his book Liber abaci, published in 1202, he posed a problem about breeding rabbits. Its answer is the sequence 1, 1, 2, 3, 5, 8, 13, 21, 34, 55…, where each number is the sum of the two before it. Liber abaci is better known for bringing Hindu-Arabic numerals and the decimal place-value system into Europe. Fibonacci released a second edition in 1228.
The ratios
Divide any Fibonacci number by the one before it and the result gets closer to 1.618 as the numbers grow. This value is the golden ratio, φ = (1+√5)/2 ≈ 1.6180339887. The retracement percentages come from related ratios:
| Level | How it is derived | Example from the sequence |
|---|---|---|
| 61.8% | A number divided by the next one (1/φ) | 34 / 55 ≈ 0.618 |
| 38.2% | A number divided by the one two places higher (also 1 − 0.618) | 34 / 89 ≈ 0.382 |
| 23.6% | A number divided by the one three places higher | 34 / 144 ≈ 0.236 |
| 50% | Not a Fibonacci ratio. It comes from Dow Theory's observation that the market averages often retrace half of their prior move | — |
| 78.6% | Not a direct sequence ratio. It is the square root of 0.618 | √0.618 ≈ 0.786 |
Charting software usually also draws 0% and 100%, the two ends of the move.
How to calculate the levels
You need two prices: the swing low (L) and the swing high (H) of the move you are measuring.
- After an advance (price went from L up to H and is now pulling back): level = H − (H − L) × ratio
- After a decline (price fell from H down to L and is now bouncing): level = L + (H − L) × ratio
Worked example
These are made-up numbers, not a real chart. An asset rises from 2,000 to 3,000, a move of 1,000.
| Level | Calculation | Price |
|---|---|---|
| 23.6% | 3,000 − 236 | 2,764 |
| 38.2% | 3,000 − 382 | 2,618 |
| 50% | 3,000 − 500 | 2,500 |
| 61.8% | 3,000 − 618 | 2,382 |
| 78.6% | 3,000 − 786 | 2,214 |
If the same asset had fallen from 3,000 to 2,000, the 38.2% retracement of the bounce would be 2,000 + 382 = 2,382.
How to draw it on a chart
- Pick a clear move. The tool measures one completed swing. A swing high is a peak with lower highs on both sides. A swing low is a trough with higher lows on both sides.
- Anchor it in the direction of the move. After an advance, drag from the swing low to the swing high. After a decline, drag from the swing high to the swing low. The software places the levels.
- Use the same timeframe. A swing chosen on a daily chart produces daily-chart levels. Different anchor points give different levels, and choosing them is the most subjective part of the method.
- Read the depth of the pullback. StockCharts' ChartSchool calls 23.6% a shallow retracement and 38.2% to 50% a moderate one. Its examples focus on the zone between 38.2% and 61.8%, and it calls 61.8% the "golden retracement".
Where do the retracement levels sit?
Enter the swing low and swing high of a completed advance and a retracement level to see the price where that level is drawn.
| Swing low (L), where the advance started | Swing high (H), where the advance ended | Retracement level (23.6, 38.2, 50, 61.8 or 78.6) | Price at that retracement level |
|---|---|---|---|
| 2,000 | 3,000 | 38.2 % | 2,618 |
| 2,000 | 3,000 | 61.8 % | 2,382 |
| 2,000 | 3,000 | 23.6 % | 2,764 |
| 2,000 | 3,000 | 78.6 % | 2,214 |
- The swing low and swing high are your own anchor points; choosing them is the most subjective part of the method, and different anchors give different levels.
- The levels are alert zones to watch, not reversal points: a 2022 study found price behaviour at Fibonacci zones did not differ statistically from other price zones.
This covers a pullback after an advance only (for a bounce after a decline, the level is L + (H − L) × ratio); it does not pick the swing for you or say whether price will react at any level.
Confirmation
ChartSchool describes retracement levels as "alert zones", not "hard reversal points". It recommends confirming a reversal with other evidence:
- candlestick patterns, such as a hammer at the level
- price patterns and gaps
- momentum oscillators, such as Williams %R or MACD
- volume or money-flow indicators, such as Chaikin Money Flow
- moving averages
Its summary: "The more confirming factors, the more robust the signal." Its own examples include reversal attempts at a level that failed before a later one worked.
What the evidence says
- Tsinaslanidis, Guijarro and Voukelatos (2022), Expert Systems with Applications, vol. 187, article 115893. The authors identified retracements with an algorithm across three equity markets and built price zones around the levels. They report a positive link between the zones and the probability of a price bounce. They also report that price behaviour at Fibonacci zones and at non-Fibonacci zones "did not differ statistically". The bounces happened, but the Fibonacci levels showed no edge over other price zones.
- Subjectivity. The result depends on which swing high and low you choose. Two people can draw different levels on the same chart.
Common mistakes
- Treating a level as a guaranteed turning point. Price often trades straight through levels.
- Drawing the tool on a sideways market with no clear swing.
- Choosing anchor points after the fact so the levels match where price already turned.
- Treating 50% and 78.6% as Fibonacci ratios. They are conventions.
