Fibonacci Retracements and Extensions
Fibonacci retracements and extensions provide a framework for identifying potential price levels where trends may pause, reverse, or extend. These levels are derived from mathematical ratios found in the Fibonacci sequence. While not predictive, they help traders establish structured price zones for entries, exits, and risk management rather than relying on arbitrary round numbers.
The Mathematical Foundation
The Fibonacci sequence begins: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144... Each number is the sum of the two preceding numbers.
The ratios used in trading derive from relationships within this sequence:
- 61.8%: Any number divided by the next number (e.g., 89/144 = 0.618)
- 38.2%: Any number divided by the number two places higher (e.g., 89/233 = 0.382)
- 23.6%: Any number divided by the number three places higher (e.g., 89/377 = 0.236)
Additional levels commonly used:
- 50%: Not a Fibonacci ratio, but included due to observed market behavior at half-retracements
- 78.6%: The square root of 61.8% (0.786)
- 161.8%: The inverse of 61.8% (1/0.618 = 1.618), used for extensions
Key Fibonacci Levels
Retracement Levels (measuring pullbacks within trends):
| Level | Use Case |
|---|---|
| 23.6% | Shallow retracement; strong momentum continuation |
| 38.2% | Moderate retracement; common in steady trends |
| 50.0% | Half-retracement; psychological significance |
| 61.8% | Deep retracement; often final support before trend failure |
| 78.6% | Very deep retracement; near trend invalidation |
Extension Levels (projecting price targets beyond previous highs/lows):
| Level | Use Case |
|---|---|
| 100% | Price target equals the prior move length |
| 127.2% | First extension target |
| 161.8% | Primary extension target; most commonly watched |
| 200% | Price target is double the prior move |
| 261.8% | Extended target for strong trends |
Calculating Retracement Levels
Formula for uptrend retracement: Retracement Level = High - [(High - Low) x Fibonacci Ratio]
Formula for downtrend retracement: Retracement Level = Low + [(High - Low) x Fibonacci Ratio]
Worked Example (Uptrend):
A stock rallies from $45.00 (swing low) to $68.00 (swing high), then begins to pull back.
Move distance: $68.00 - $45.00 = $23.00
| Fib Level | Calculation | Price |
|---|---|---|
| 23.6% | $68.00 - ($23.00 x 0.236) | $62.57 |
| 38.2% | $68.00 - ($23.00 x 0.382) | $59.21 |
| 50.0% | $68.00 - ($23.00 x 0.500) | $56.50 |
| 61.8% | $68.00 - ($23.00 x 0.618) | $53.79 |
| 78.6% | $68.00 - ($23.00 x 0.786) | $49.92 |
If the stock pulls back and finds support near $59.21 (the 38.2% level), a trader might consider this a buying opportunity with a stop below the 50% level at $56.50.
Worked Example (Downtrend):
A stock declines from $92.00 (swing high) to $71.00 (swing low), then bounces.
Move distance: $92.00 - $71.00 = $21.00
| Fib Level | Calculation | Price |
|---|---|---|
| 23.6% | $71.00 + ($21.00 x 0.236) | $75.96 |
| 38.2% | $71.00 + ($21.00 x 0.382) | $79.02 |
| 50.0% | $71.00 + ($21.00 x 0.500) | $81.50 |
| 61.8% | $71.00 + ($21.00 x 0.618) | $83.98 |
| 78.6% | $71.00 + ($21.00 x 0.786) | $87.51 |
A trader expecting the downtrend to resume might look to sell short near the 38.2% retracement at $79.02 with a stop above the 50% level at $81.50.
Calculating Extension Levels
Extensions project where price might travel after completing a retracement.
Formula: Extension Level = Retracement Low + [(Original High - Original Low) x Extension Ratio]
Worked Example:
Using the uptrend example: Original low $45.00, original high $68.00, retracement held at the 38.2% level ($59.21).
The trader expects price to resume upward from $59.21.
Move distance: $68.00 - $45.00 = $23.00
| Extension | Calculation | Target Price |
|---|---|---|
| 100% | $59.21 + ($23.00 x 1.000) | $82.21 |
| 127.2% | $59.21 + ($23.00 x 1.272) | $88.47 |
| 161.8% | $59.21 + ($23.00 x 1.618) | $96.43 |
If entering long at $59.21 with a stop at $56.50, the risk is $2.71 per share. The 161.8% extension target at $96.43 offers potential reward of $37.22, a reward-to-risk ratio of 13.7:1. The 127.2% target at $88.47 offers 10.8:1.
These ratios look attractive but require the trend to resume and extend significantly. Partial profit-taking at the 100% extension ($82.21, above the prior high) is a more conservative approach.
Confluence: When Fibonacci Levels Align
Fibonacci levels gain significance when they align with other technical factors:
Types of confluence:
- Fibonacci level coincides with a horizontal support or resistance zone
- Fibonacci level aligns with a moving average (50-day, 200-day)
- Multiple Fibonacci measurements from different swing points cluster at similar prices
- Fibonacci level matches a previous gap fill level
- Round number ($50, $100) near a Fibonacci level
Example:
A stock has a 38.2% retracement at $78.50. The 200-day moving average sits at $78.20. A prior resistance-turned-support zone exists at $78.00-$79.00. This cluster of factors at approximately $78-79 creates stronger potential support than any single factor alone.
Fibonacci Time Clusters (Brief Overview)
Some traders project Fibonacci ratios along the time axis, not just price. Common applications include measuring the time duration of a prior move and projecting 61.8%, 100%, or 161.8% of that duration forward to identify potential reversal dates.
Example: A rally lasted 34 trading days. Multiplying by Fibonacci ratios:
- 61.8%: 21 days from the high
- 100%: 34 days from the high
- 161.8%: 55 days from the high
These time projections are more speculative than price levels and should be treated as supplementary context rather than primary signals.
Risks and Limitations
No predictive power. Fibonacci levels do not cause price reversals. They identify zones where reversals may occur based on historical tendencies, but price can move through any Fibonacci level without pausing.
Subjective swing point selection. Different traders may choose different swing highs and lows, producing different Fibonacci levels. This subjectivity reduces the reliability of any single measurement.
Self-fulfilling tendencies. Because many traders watch the same Fibonacci levels, orders cluster at these prices. This can create short-term reactions without underlying fundamental significance.
Cherry-picking bias. After the fact, it is easy to find a Fibonacci level that "worked." Confirmation bias leads traders to remember hits and forget misses.
Not all retracements are equal. A 38.2% retracement in a strong trend differs from a 38.2% retracement in a weak, choppy market. Context matters more than the specific ratio.
Practical Application Guidelines
Use Fibonacci as zones, not precise prices. A "38.2% retracement" at $59.21 is better treated as a zone from $58.50 to $60.00. Price rarely reverses at exact calculated levels.
Require confirmation before acting. Wait for price to reach a Fibonacci zone and then show reversal signals (candlestick patterns, momentum divergence, volume surge) rather than placing limit orders blindly at Fibonacci levels.
Define invalidation clearly. If using the 38.2% level as support, determine in advance that a close below the 50% or 61.8% level invalidates the setup.
Combine with risk management. Fibonacci levels help identify where to enter and exit. They do not eliminate the need for position sizing and stop-losses based on your maximum acceptable loss.
Next Steps
- Identify a recent clear trend (up or down) in a stock or index and draw Fibonacci retracement levels from the swing low to swing high (or high to low for downtrends)
- Observe whether price reacted at any Fibonacci level during pullbacks and note which levels saw the strongest response
- When a retracement holds at a Fibonacci level, calculate extension targets at 100%, 127.2%, and 161.8% to establish potential profit-taking zones
- Look for confluence by checking whether Fibonacci levels align with moving averages, prior support/resistance, or round numbers
- Practice on historical charts before applying to live trades, documenting which Fibonacci setups succeeded and which failed
Related: Average True Range and Volatility Stops | Chart Patterns: Triangles, Flags, and Pennants | Support, Resistance, and Trendline Construction
Source: CMT Association, Technical Analysis: The Complete Resource for Financial Market Technicians. Murphy, John J. Technical Analysis of the Financial Markets (1999).