Last fact-checked: October 6, 2026. Educational content only, not investment advice.
The Magic Numbers from Pisa
The Fibonacci sequence (1, 1, 2, 3, 5, 8, 13, 21...) was introduced to European readers by Leonardo of Pisa (Fibonacci) in his 1202 book Liber Abaci through a rabbit-breeding problem. R.N. Elliott, and later Frost and Prechter, used it as the mathematical basis for proportions in the Wave Principle.
The Golden Ratio 0.618
Dividing a number in the sequence by the next one approaches 0.618 as the numbers grow (e.g., 21 ÷ 34 ≈ 0.6176); dividing by the previous one approaches 1.618 (34 ÷ 21 ≈ 1.619); dividing by the number two places later approaches 0.382 (21 ÷ 55 ≈ 0.3818). Technical analysts use these ratios as reference points for potential support and resistance.
Application in Markets
- Retracement: Corrections often retrace 61.8% or 38.2% of the previous wave.
- Multiples: Wave 3 is often compared with 1.618 or 2.618 times the length of Wave 1. When Wave 3 is the extended wave, Wave 5 frequently is roughly equal to Wave 1 or relates by a 0.618 factor.
These ratios provide predefined reference zones, not guaranteed price targets.
Further Reading
- Elliott Wave Basics (Technical Analysis)
- Support and Resistance (Technical Analysis)
- Trendline Practical Application (Technical Analysis)
- Risk-Based Position Sizing (Risk Management)
References
FAQ
Q: Which Fibonacci retracement level is the most important?
A: In practice, the 38.2%, 50%, and 61.8% levels are the most commonly used. The 61.8% (golden ratio) level is often treated as the most critical; if price clearly breaks beyond 61.8%, many analysts start to question whether the prior trend is still intact. This is a rule of thumb, not a fixed probability. While 50% is not a Fibonacci ratio, it is widely used as a reference level.
Q: Why do Fibonacci ratios work in markets?
A: This may partly stem from a "self-fulfilling prophecy" effect. Because large numbers of traders watch the same Fibonacci levels, their buying and selling behavior creates real support or resistance at these prices. Additionally, Fibonacci ratios reflect proportional relationships found throughout nature, and markets as reflections of collective human behavior may follow similar patterns.
Q: How do you use the Fibonacci retracement tool on a chart?
A: Most charting software has a built-in Fibonacci retracement tool. In an uptrend, draw from the swing low to the swing high; in a downtrend, from the swing high to the swing low. The tool automatically displays key retracement levels at 23.6%, 38.2%, 50%, 61.8%, etc. These levels represent potential support or resistance zones.
Q: How are Fibonacci extension ratios used to set price targets?
A: Fibonacci extensions are commonly used to project where a trend might reach. For example, Wave 3's target is often 1.618 or 2.618 times the length of Wave 1. Calculate by multiplying Wave 1's range by the extension ratio, then measuring from Wave 2's endpoint in the trend direction. This gives a reference for profit targets, but price may never reach it.