Fibonacci Retracement Calculator
From a swing high and low, compute the 23.6%, 38.2%, 50% and 61.8% retracement levels as potential support/resistance references.
Input Data
Results
At a glance:The Fibonacci Retracement Calculator computes the 23.6%, 38.2%, 50% and 61.8% retracement levels from a swing's high and low, for potential support/resistance. For an uptrend pullback: range = high − low; level = high − range × ratio. The ratios come from the Fibonacci sequence (61.8% is the inverse golden ratio; 50% is a convention). From shallow to deep: 23.6% gives back little, 61.8% gives back most of the rise. It is a subjective technical tool; price is not guaranteed to react there.
Formula
Range = high − low.
Level (uptrend pullback) = high − range × ratio.
Common ratios: 23.6%, 38.2%, 50%, 61.8%.
$$\text{Range} = P_{high} - P_{low}$$$$L_{ratio} = P_{high} - \text{Range} \times ratio$$How to Use
- Pick a clear price swing and find its high and low.
- Enter the high and low prices.
- View the 23.6%, 38.2%, 50% and 61.8% retracement levels.
Four Fibonacci retracement levels for a move from low 80 to high 120 (range 40)
| Ratio | Level | Drop from high | Meaning |
|---|---|---|---|
| 23.6% | HK$110.56 | ≈−8% | Shallowest, strong trend |
| 38.2% | HK$104.72 | ≈−13% | Common shallow pullback |
| 50% | HK$100.00 | −17% | Midpoint, Dow tradition |
| 61.8% | HK$95.28 | ≈−21% | Deepest common, golden ratio |
A move from 80 to 120 (range 40): on pullback, 23.6% is at 110.56 (little given back), 61.8% at 95.28 (most given back). Traders see these as buy-the-dip candidates; a break below 61.8% is often read as trend weakening. High/low choice changes levels — subjective.
Case Studies
Case 1: Retracement levels of an uptrend
Mr Chan watches a stock rise from low HK$80 to high HK$120 — a clear uptrend. He wants Fibonacci retracement to find where a pullback might find support.
Range = 120 − 80 = 40. 23.6% = 120 − 40×0.236 = HK$110.56; 38.2% = 104.72; 50% = 100.00; 61.8% = 95.28.
Interpretation: these four levels from shallow (110.56) to deep (95.28) are candidate zones where price might stop and bounce on a pullback. Mr Chan can use them as tranched buy-the-dip references or to set stops — e.g. a break below 61.8% (95.28) may mean the uptrend is weakening, worth re-evaluating.
Case 2: Different swing choice, completely different levels
Mr Chan's friend picks a larger swing: low 100, high 200 (range 100). Levels become: 23.6% = 176.4; 38.2% = 161.8; 50% = 150; 61.8% = 138.2.
Comparison: same stock, different high/low, totally different levels — exactly showing Fibonacci retracement's subjective nature; it is not an objective unique answer but depends on how you define 'the meaningful swing'.
Practical notes: (1) retracement only offers candidate levels, cannot predict — price does not reverse 'because' of a ratio; it sometimes works largely because many traders watch the same ratios (self-fulfilling); (2) seek confluence — a level coinciding with a trend line, prior high/low or moving average is more meaningful, pair with the moving-average calculator; (3) it is a trend tool, needs a trend first, less useful in ranges; (4) always set stops and size positions. Subjective and not guaranteed; educational reference only, not advice.
FAQ
How are the Fibonacci levels computed?
First pick a meaningful swing and its high/low. Second, range = high − low. Third, multiply the range by each ratio (23.6%, 38.2%, 50%, 61.8%) and subtract from the high (uptrend pullback) to get each level. Example: low 80 to high 120, range 40. 23.6% = 120 − 40×0.236 = 110.56; 38.2% = 104.72; 50% = 100; 61.8% = 95.28. Larger ratio = deeper pullback, lower price. These are candidate levels where price might stop falling on a pullback. This shows an uptrend's downward retracement; for a downtrend's upward bounce the direction reverses (add range×ratio to the low) but the concept is the same.
Why 23.6%, 38.2%, 61.8%, and what is 50%?
These odd percentages come from the Fibonacci sequence (1,1,2,3,5,8,13,21,34…). As the sequence progresses, the ratio of adjacent terms approaches about 0.618 (the inverse golden ratio) — that is the 61.8% level. Other ratios relate: 38.2% ≈ a term divided by the term two ahead (≈0.618²); 23.6% ≈ a term divided by the term three ahead. These ratios recur in nature, art and architecture, and technical-analysis believers hold that market crowd behaviour reflects them, so price reacts near these levels. The 50% is not strictly from the sequence; it is included because market observation (and Dow theory) finds price often retraces about half a move — an intuitive, common midpoint — so it is almost always used alongside the Fibonacci ratios. That is why 50% appears in nearly every Fibonacci tool; this calculator lists it as a default reference.
Is Fibonacci retracement reliable? Cautions?
It is popular but understand its nature and limits. (1) Highly subjective — the whole result depends on which high/low you pick; different people or different swings give completely different levels. It is a judgement-dependent framework, not an objective answer. (2) It cannot predict, only offers candidate levels — price does not reverse 'because' of a ratio; these levels sometimes work because many traders watch the same ratios and trade there (self-fulfilling), but not guaranteed, and price often breaks through. (3) Combine with other evidence — look for confluence: a level that also meets a trend line, a prior high/low or a moving average is more meaningful. (4) Trend must be clear — it is a trend-following tool; in a sideways range it is less useful. (5) Always manage risk — set stops and size positions. Fibonacci retracement helps organise thinking but is subjective and not guaranteed. Trading involves loss risk; educational reference only, not advice.
If a level breaks, should I sell? How to use with stops?
Many think 'price breaking a Fibonacci level means sell now' — a misunderstanding; it is never a mechanical signal, but a framework to organise judgement and set risk. In an uptrend, retracement levels are candidate support on pullbacks. A shallow pullback (holds at 23.6%/38.2%) suggests strong buying and trend; deeper pullback questions health. A break below 61.8% (the deepest common level) is often read as a warning — price has given back most of the rise, the uptrend may be weakening. But 'break 61.8% ≠ must sell unconditionally' because: (1) the levels are subjective and your high/low may be wrong; (2) price may dip and recover (false break); (3) a single signal is weak. How to use with stops: (1) place the stop just below a key level — e.g. if 61.8% (95.28) is the last defence, set stop slightly below (e.g. 94); a valid break admits the error and exits, capping loss; (2) scale in/out — buy in tranches at shallower levels (38.2%, 50%), reduce on deeper breaks; (3) seek confluence — a level coinciding with a trend line, prior low or moving average is a more reliable stop/support. Core principle: levels tell you where to defend and where to admit error; what protects you is pre-set, disciplined stops and position sizing, not the level's magic. Fibonacci is not guaranteed; educational reference only.
Fibonacci retracement vs extension?
Retracement and extension are two faces of the same Fibonacci toolkit but for different purposes: retracement answers 'where might price stop on a pullback (support)'; extension answers 'if price breaks the high and continues, where might it meet resistance / target'. Retracement (this calculator) handles the pullback inside a swing: levels (23.6%, 38.2%, 50%, 61.8%) all sit between low and high, estimating where the pullback might hold — a tool to find buy-the-dip and stop levels. Extension handles post-breakout targets: when price breaks the prior high and keeps rising, extension levels (127.2%, 161.8%, 200%, 261.8%) sit above the high, estimating where the continued move might meet resistance / take profit. So extension projects beyond 100% of the range — a take-profit tool. Traders often 'use retracement to find entry (buy at support on pullback), extension to find exit (take profit at resistance)'. Example: a stock from 80 to 120 (range 40) — retracement lets you consider buying near 100 (50%) on pullback; if it later breaks 120 and rises, extension (e.g. 161.8%) projects a target above 120 for profit-taking. Extension is also subjective and not guaranteed; selection of points affects results. This calculator offers retracement; real trading needs trend judgement, other signals and strict risk management. Educational reference only, not advice.
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References
Content review: Calculatorism Finance Team. Results are for reference only; please refer to the relevant authorities for the official figures.