Fibonacci Calculator

Generate Fibonacci retracement and extension levels for stock trading.

Status: Algorithmic Audit (CPA Review Pending)
Jurisdiction: United States (IRS & SSA Standards)
Tax Year / Constants: 2026 Statutory Limits
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The Mathematical Formula

Retracement Level = Swing High - (Swing High - Swing Low) × Ratio (23.6%, 38.2%, 50.0%, 61.8%, 78.6%) ; Extension = High + Range × Ratio

Variable & Parameter Definitions

  • Swing High The peak price peak established during a distinct market impulse wave.
  • Swing Low The trough base price where the prior advance began.
  • Price Range Total vertical distance between the Swing High and Swing Low.
  • Golden Ratio (61.8%) Key mathematical ratio derived from the Fibonacci sequence (1.618 / 0.618).
  • Extension Levels Target projection levels (127.2%, 161.8%, 261.8%) used for profit-taking in breakout trends.

Real-World Worked Scenario: Analyzing an Uptrend Pullback from $150 to $200

A leading technology stock surges from a swing low of $150 to a swing high of $200 (a $50 advance) and begins a technical corrective pullback.

  1. Total Price Range: $200 - $150 = $50.00.
  2. 23.6% Retracement Floor: $200 - ($50 × 0.236) = $188.20.
  3. 38.2% Retracement Floor: $200 - ($50 × 0.382) = $180.90.
  4. 50.0% Retracement Floor: $200 - ($50 × 0.500) = $175.00.
  5. 61.8% Golden Retracement Floor: $200 - ($50 × 0.618) = $169.10.
  6. Trade Execution: Institutional limit buy orders cluster around the 61.8% golden pocket ($169–$175) to enter with favorable risk-to-reward ratios.
Key Financial Takeaway: Healthy bull market trends regularly retrace 38.2% to 61.8% of their prior advance before resuming their primary trend direction.

Strategic Insights & Pitfalls to Avoid

  • ✓ Confluence Trading: Fibonacci levels are most powerful when they align with other indicators (e.g. 200-day moving average or horizontal support).
  • ✓ The 50% Level: While 50% is not a pure mathematical Fibonacci ratio, Charles Dow discovered markets frequently retrace half of prior moves.
  • ✓ Extension Profit Targets: The 161.8% extension level is the most common target for setting trailing stop-losses on trend breakout trades.

Frequently Asked Questions

Where do Fibonacci ratios come from?

Derived from the Fibonacci sequence (1, 1, 2, 3, 5, 8, 13, 21...), where dividing any number by its successor approaches 0.618, and by its preceding number approaches 1.618.

What happens if a stock breaks below the 61.8% retracement level?

Breaking firmly below the 61.8% and 78.6% levels indicates the prior trend has likely failed and a full reversal is underway.

Can Fibonacci levels be used on intraday 5-minute charts?

Yes. Fibonacci ratios are fractal and apply across 1-minute, daily, weekly, and monthly charts.

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