The Fibonacci sequence (1, 1, 2, 3, 5, 8, 13, 21, 34...) converges to the golden ratio φ ≈ 1.618 as each term is divided by the prior term. The retracement levels derive from ratios between non-adjacent terms: 61.8% (1/1.618), 38.2% (1 - 0.618), and 23.6% (0.382²). The 50% level is not a Fibonacci ratio but is included because markets frequently reverse at exact midpoints, a pattern observed empirically across asset classes and time horizons. The 78.6% level is the square root of 61.8%, included for similar empirical reasons.

To apply Fibonacci retracement on a chart, identify a significant swing high and swing low for an uptrend (or swing high for a downtrend). Draw from the swing low to the swing high. The tool automatically plots the retracement levels as horizontal lines at the percentage distances from the swing high. In a subsequent pullback, these levels mark where buying support might emerge. The 38.2% and 61.8% levels have the strongest empirical backing; the 61.8% is particularly significant because it represents the 'golden ratio' retracement and is associated with trend continuation.

In an established uptrend, Fibonacci retracement provides entry zones for adding to positions during normal pullbacks. The shallow 23.6% retracement is often the first support in a very strong trend — aggressive buyers step in early. The 38.2% level is the moderate retracement that provides cleaner risk/reward: the stop goes below the 50% level or the prior swing low, and the target is the previous high or an extension. The 61.8% level is the deepest retracement consistent with trend continuation — a pullback to 61.8% in an uptrend technically holds the prior swing low structure and can still be a valid continuation setup.

Confluence dramatically improves Fibonacci reliability. A 38.2% retracement that also coincides with a previous area of price resistance (now acting as support), a rising 50-day moving average, and a volume dry-up creates a high-probability entry zone. Any single indicator in isolation produces many false signals; aligning multiple independent technical frameworks at the same price level reduces false signal rates substantially. This confluence analysis is why experienced traders use Fibonacci alongside, never instead of, other technical tools.

Fibonacci extensions project potential price targets beyond the original swing high, answering 'where might this rally go?' after a retracement completes. Extension levels commonly used: 100% (equal move), 127.2%, 161.8% (golden ratio extension), and 261.8%. To draw extensions, anchor from the swing low through the swing high to the retracement low. The 161.8% extension is the most widely watched and frequently acts as resistance in extended rallies. In strong momentum environments, stocks can reach the 261.8% extension before consolidating.

Fibonacci clusters form when multiple independent Fibonacci measurements (from different swing points, or from different time frames) produce levels at or near the same price. These clusters create stronger support/resistance zones than any single measurement. Professional traders often plot three or four independent Fibonacci grids on a chart and highlight price levels where multiple grids converge — those are the zones where institutional order flow is most likely to concentrate.