Fibonacci ratios in Elliott Wave analysis

By AnalytikCapital · Updated October 3, 2026

In Elliott Wave analysis, Fibonacci ratios such as 0.382, 0.618 and 1.618 are used to estimate how far a correction may retrace and how far a motive wave may extend, by comparing the length of one wave with another of the same degree.

Where the ratios come from

The Fibonacci sequence starts 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, and each number is the sum of the two before it. As the numbers grow, the ratio between neighbors settles near 1.618, the golden ratio, and its inverse, 0.618. Dividing a number by the one two places later gives about 0.382; three places later, about 0.236.

R. N. Elliott was the first to apply these proportions systematically to market waves. Elliott Wave International summarizes his two observations: corrections tend to retrace the prior impulse of the same degree by a Fibonacci proportion, and motive waves of the same degree within a larger impulse tend to be related to each other by Fibonacci proportions. It also stresses a point that is often skipped: a ratio means something only when it compares two waves that belong to the same valid count. Measuring between unrelated swings will always find some ratio somewhere.

Retracements and extensions

A retracement measures how much of a completed move a correction gives back. An extension projects how far a new move may travel, measured against an earlier one.

Lists differ between sources. StockCharts’ retracement tool shows four levels (23.6%, 38.2%, 50% and 61.8%) and explains that 50% comes from Dow Theory rather than from Fibonacci. Investopedia adds 78.6% and lists 127.2%, 150%, 161.8% and 261.8% as common extension targets. Some Elliott practitioners also use 76.4% (1 - 0.236), 85.4% and 14.6%. There is no single official grid, so any tool that draws Fibonacci levels has made a choice.

Typical relationships, wave by wave

The figures below are tendencies collected from Elliott literature. They overlap, they differ between authors, and none of them is a rule.

• Wave 2 is often deep: commonly 50% to 61.8% of wave 1, and some practitioners list 76.4% or 85.4% as well. The only hard limit is the rule that wave 2 never retraces more than 100% of wave 1.
• Wave 3 is frequently 1.618 times wave 1, and in strong trends 2.618 or more. Its length is limited only by the rule that it cannot be the shortest motive wave.
• Wave 4 is usually shallow: commonly 23.6% to 38.2% of wave 3, with some sources allowing 14.6% and treating 50% as an upper bound. A shallow wave 4 also fits the guideline of alternation with a deep wave 2.
• Wave 5 is often compared with wave 1. Elliott Wave International’s equality guideline says that when wave 3 is extended, waves 1 and 5 tend toward equal size, and if not equal, a 0.618 relationship is the next most likely. Another common measure sets wave 5 at 0.618 of the distance from the start of wave 1 to the end of wave 3.
• Corrections (A-B-C) commonly retrace the prior impulse by 38.2%, 50% or 61.8%. Inside a zigzag, wave C is often equal to wave A or 1.618 times wave A.

Because these ranges overlap, two counts that disagree about structure can both find a Fibonacci level nearby. That is why ratios are best used to rank counts that already satisfy the rules, not to decide which count is valid.

Tendencies, not rules

The distinction matters in practice. Elliott’s rules, covered on the Elliott Wave page, invalidate a count when broken. Fibonacci relationships do not: a wave 2 that stops at 45% instead of 50% does not break anything.

The evidence also calls for caution. Wikipedia’s article on Fibonacci retracement reports that backtests found the 38%, 50% and 62% levels no more likely to appear than other retracement values, and a 2005 study by Batchelor and Ramyar, cited in Wikipedia’s Elliott wave article, found no significant difference between Fibonacci ratios and chance in Dow Jones data. StockCharts describes the levels as alert zones rather than hard reversal points, to be confirmed with other evidence.

Sources also disagree on emphasis. Elliott Wave International treats Fibonacci analysis as meaningful only inside a valid wave count. General trading references, such as Investopedia, present the same levels as standalone support and resistance tools for any trending market. Both uses are common; they are not the same claim.

How AnalytikCapital uses Fibonacci ratios

AnalytikCapital’s Elliott engine works with a leaner grid than many charting tools. Its retracement set is 0.236, 0.382, 0.5, 0.618, 0.786, 0.854 and 1.0, and its extension set is 1.0, 1.236, 1.382, 1.618, 2.0 and 2.618. It adds 0.854, 1.236 and 1.382 to the common list and leaves out 1.272.

In its default configuration, these ratios do not decide whether a count is admitted. Admission depends on the structural rules, such as the limit that wave 2 cannot retrace beyond the start of wave 1. Each candidate wave is compared with a scoring band for its position, for example 0.382 to 0.854 of wave 1 for wave 2, centered on 0.618, and closeness to that band raises or lowers the candidate’s rank. A count that misses every band can still be valid; it simply ranks lower than an equally valid count that fits. The methodology page describes how this scoring fits with the rest of the engine.

Educational content, not financial advice. Trading involves substantial risk of loss.