What is Fibonacci Retracement? Definition, Formula, and Example
Fibonacci retracement is a technical analysis tool that draws horizontal support and resistance levels at ratios derived from the Fibonacci sequence — 23.6%, 38.2%, 61.8%, and 78.6% — across a defined price swing.
What is Fibonacci Retracement?
Fibonacci retracement is a charting tool that identifies potential support and resistance zones by applying ratios from the Fibonacci sequence to a price swing. A trader anchors the tool at a swing low and a swing high (or vice versa for downtrends), and the tool draws horizontal lines at the key ratios. These levels mark where price commonly stalls, reverses, or accelerates during pullbacks. The underlying thesis is that markets retrace in proportions that mirror the golden ratio — a ratio that appears throughout natural geometry and, by extension, crowd behavior.
How Fibonacci Levels Are Calculated
The ratios come from the mathematical properties of the Fibonacci sequence (1, 1, 2, 3, 5, 8, 13…), specifically the golden ratio φ ≈ 1.618:
| Level | Derivation |
|---|---|
| 23.6% | 1 / φ³ |
| 38.2% | 1 − (1 / φ) |
| 50.0% | Dow Theory addition — no Fibonacci basis |
| 61.8% | 1 / φ (the "golden ratio" retracement) |
| 78.6% | √(1/φ) |
Retracement Price = High − (Swing Range × Ratio)
Extension Price = High + (Swing Range × Extension Ratio) for targets above the swing high
Worked Example: SPY
SPY rallies from a swing low of $480 to a swing high of $565. Swing range = $85.
| Level | Calculation | Price |
|---|---|---|
| 23.6% | $565 − ($85 × 0.236) | $544.94 |
| 38.2% | $565 − ($85 × 0.382) | $532.53 |
| 50.0% | $565 − ($85 × 0.500) | $522.50 |
| 61.8% | $565 − ($85 × 0.618) | $512.47 |
| 78.6% | $565 − ($85 × 0.786) | $498.19 |
If SPY pulls back from $565 and finds buyers at $512–$513 with a bullish RSI divergence, that 61.8% retracement becomes a high-confluence long entry. A stop below $510 and a target back toward the prior high gives a favorable risk/reward.
When Traders Use Fibonacci Retracement
Fibonacci levels are most useful in trending markets with clear swing points — they lose coherence in choppy, range-bound action. Traders use them to set limit orders at pullback zones rather than chasing momentum entries. The 38.2% level catches shallower retracements in strong trends; the 61.8% level is the primary target in moderate pullbacks. Combining Fibonacci levels with volume profile nodes, prior support/resistance, or MACD crossovers creates confluence — a zone where multiple systems agree — making the signal more robust than any single tool.
Limitations and Misconceptions
The most common misconception is that Fibonacci levels predict reversals. They identify *zones of interest*, not guaranteed turning points. With five or more lines on a chart, price is always near a Fibonacci level — the tool can rationalize any outcome after the fact. The 50% level has no mathematical Fibonacci basis and is included by convention. Perhaps most critically, Fibonacci levels work partly because they are self-fulfilling: enough institutional and retail traders place orders there that the levels generate activity. When a market moves fast enough that limit orders get skipped, or when an asset class isn't widely covered, the levels become meaningless.