# Fib Wave Relationships A Elliott & Harmonics concept (Elliott grammar) in the LuxAlgo Library, with 1 indicator implementation. ## What are Fib Wave Relationships? Fib wave relationships are the Fibonacci proportions Elliott practitioners use to relate waves to one another: guidelines for how long a wave tends to be relative to the waves before it. Commonly cited ranges for an [impulse](https://www.luxalgo.com/library/concept/impulse/): wave 2 retraces 0.5 to 0.618 of wave 1, wave 3 extends to 1.618 to 2.618 times wave 1, wave 4 retraces 0.236 to 0.382 (usually measured against wave 3), and wave 5 runs 0.618 to 1.0 times wave 1. In corrections, wave C is commonly projected at equality with wave A or at 1.618 times it. Exact ranges vary by source; these are tendencies drawn from the Elliott literature, not laws. The Fibonacci basis was Elliott's own late addition: he connected his wave counts to the sequence in his final work, and the Frost-Prechter tradition systematized the ratio guidance that modern practice quotes. The result is a two-layer system, structure from the wave rules, measurement from the ratio set, with the proportions serving as the count's arithmetic conscience. The relationships convert a wave count from a narrative into measurable, testable prices. Retracement ratios are read with a [fib retracement](https://www.luxalgo.com/library/concept/fib-retracement/) across the prior wave; multiples of a completed wave are projected forward with a three-point [fib projection](https://www.luxalgo.com/library/concept/fib-projection/). They also separate cleanly from the [Elliott hard rules](https://www.luxalgo.com/library/concept/elliott-hard-rules/): a rule violation kills a count outright, while a missed relationship merely makes it less typical. Where several relationships point at the same price, for instance a wave 5 projection landing on a larger-degree retracement, the overlap forms the kind of confluence practitioners treat as a meaningful target zone. Two guidelines discipline the measurements. Alternation warns that waves 2 and 4 tend to differ in character and depth, so identical retracements in both is atypical; and degree consistency demands that proportions make sense at each scale of the nested count, a wave 3 of one degree simultaneously serving as waves 1-through-5 of the smaller one. Practitioners also keep the equality guideline close: when wave 3 extends, waves 1 and 5 tend toward equality, the relationship that most often nominates fifth-wave [terminal zones](https://www.luxalgo.com/library/concept/potential-reversal-zone/). ## How to measure wave relationships Every measurement is anchored on labeled wave extremes; the relationships grade the count as it develops. 1. Label the count first under the hard rules; relationships refine legal counts rather than rescue illegal ones. 2. Measure retracements across the prior wave: wave 2 as a fraction of wave 1, wave 4 as a fraction of wave 3, watching the typical bands (deep for 2, shallow for 4). 3. Project the actionary waves with three-point tools: wave 3 as multiples of wave 1 from the wave-2 low, wave 5 from the wave-4 low, wave C from the B point. 4. Apply alternation: waves 2 and 4 matching in depth and shape argues the count is forced. 5. Check equality when 3 extends: wave 5 near 1.0 of wave 1 is the standard terminal expectation in extended-third impulses. 6. Stack the projections across degrees: overlapping measurements from different scales form the target zones worth planning around. ## How it's calculated Fibonacci ratio guidelines that relate Elliott wave lengths to one another for retracement checks and target projection. ``` 1. Label the impulse legs 1 through 5 and the corrective legs A, B, C on confirmed swing points. 2. Measure each wave's length in price: Len(W) = abs(P_end - P_start). 3. Wave 2 guideline: Len(2) = 0.500 to 0.618 × Len(1). 4. Wave 3 guideline: Len(3) = 1.618 × Len(1), sometimes 2.618; wave 3 is never the shortest impulse leg. 5. Wave 4 guideline: Len(4) = 0.382 × Len(3). 6. Wave 5 guideline: Len(5) = 1.000 × Len(1), or 0.382 to 0.618 × the net travel from the start of wave 1 to the end of wave 3. 7. Correction guideline: Len(C) = 1.000 × Len(A), sometimes 1.618 × Len(A); wave B commonly retraces 0.382 to 0.786 of wave A. 8. Project targets from the new wave's start, e.g. wave 3 target = end of wave 2 + 1.618 × Len(1) in the trend direction. W: wave label placeholder, 1 to 5 for impulse waves and A, B, C for corrections P_start: price where wave W begins P_end: price where wave W ends Len(W): price length of wave W 0.382, 0.500, 0.618, 0.786: retracement ratios derived from the Fibonacci sequence 1.000, 1.618, 2.618: equality and extension ratios (1.618 = phi, 2.618 = phi^2) phi: the golden ratio, approximately 1.618 ``` These are the guideline ratios from Frost and Prechter's Elliott Wave Principle, not strict rules; counts satisfying more of them are considered better formed. The strict rules are separate: wave 2 never retraces past the start of wave 1, wave 3 is never the shortest, and wave 4 does not enter wave 1 price territory in a standard impulse. For large percentage moves, some analysts measure the ratios on a log scale. ## How traders use it - For price targets: project wave 3 from the end of wave 2 as a multiple of wave 1, wave 5 from the end of wave 4, and the C leg of a [corrective wave](https://www.luxalgo.com/library/concept/corrective-wave/) at equality with wave A; the projections give a count concrete objectives. - For count selection: when two labelings are both legal under the hard rules, the one whose waves land near common proportions is usually preferred, and unusual proportions everywhere is a hint the count is forced. - As early warning: relationships degrade before rules break. A wave 2 pushing past 0.786 toward a full retracement has not invalidated anything yet, but it is already outside the typical range, so exposure gets reduced before the hard stop. - For confluence zones: overlapping projections from different degrees, or a projection meeting a channel line or prior level, mark the areas where practitioners look for fifth waves and C waves to terminate. - In complex corrections: equality between the W and Y legs of double corrections, and the standard C-versus-A ratios, extend the same measuring discipline to sideways structures, where proportions often carry more information than shape. ## Fib Wave Relationships vs related concepts - **Elliott Hard Rules** (https://www.luxalgo.com/library/concept/elliott-hard-rules/): The rules are binary: wave 2 exceeding 100%, a shortest wave 3, or a 1-4 overlap invalidates the count. Fib relationships are soft expectations about typical proportions; missing one costs a count plausibility, not validity. - **Harmonic & Fib Ratio Set** (https://www.luxalgo.com/library/concept/harmonic-and-fib-ratio-set/): The ratio set is the raw vocabulary of levels shared across fib tools and harmonic patterns. Fib wave relationships are one specific application: mapping those ratios onto wave proportions within an Elliott count. - **Fib Extension** (https://www.luxalgo.com/library/concept/fib-extension/): The extension tool projects ratios beyond a single swing with no wave framework attached. Wave relationships use the same arithmetic but tie each measurement to a labeled wave and its role in the count. ## FAQ ### What is the most common Fibonacci relationship for wave 3? The most cited figure is 1.618 times the length of wave 1, projected from the end of wave 2, with 2.618 the usual next reference when wave 3 extends. That is a guideline about typical proportion; the only binding constraint is the rule that wave 3 can never be the shortest of waves 1, 3, and 5. ### Are Fibonacci wave relationships rules or guidelines? Guidelines. Elliott's rules (the wave 2, wave 3, and overlap constraints) are the only count-invalidating conditions. Ratio relationships describe how waves often proportion to each other, and published ranges differ between sources and markets. A count that hits none of the common relationships can still be valid; it is just less typical and usually less trusted. ### How do you measure wave relationships on a chart? Use a retracement drawn across the prior wave for waves 2 and 4, reading the pullback as a fraction of that wave. For waves 3, 5, and C, use a three-point projection: measure the reference wave, then project its multiples (1.0, 1.618, 2.618) from the end of the retracement that precedes the wave being projected. Consistent anchoring on the swing extremes matters more than the tool. ### What relationships does wave 5 typically show? The workhorse expectations: equality with wave 1 when wave 3 extended (the most quoted case), 0.618 of wave 1 in weaker fifths, or 0.618 of the whole wave 1-through-3 travel projected from the wave 4 low. Fifth waves are also where truncation risk lives, so the projections mark zones to watch for terminal behavior rather than prices the wave owes anyone. ### How are wave C targets set in corrections? Equality with wave A is the base case, projected from the B extreme, with 1.618 of A as the extended alternative in steep zigzags and 0.618 in shallow flats. The same projection lands differently by structure, which is why C targets are read alongside the correction's shape: a flat's C typically terminates near A's end, a zigzag's C well beyond it. ### What does it mean when no standard relationship fits? One miss means little, since the ranges are tendencies. Proportions failing everywhere across the count is the meaningful case: it usually signals a forced labeling, a count at the wrong degree, or a corrective structure being read as motive. The standard response is recounting rather than special pleading, because a count that needs every guideline waived has stopped being evidence. ## Implementations in the Library - Elliott Wave (LuxAlgo): https://www.luxalgo.com/library/indicator/elliott-wave/ ## Related concepts - Motive Wave: https://www.luxalgo.com/library/concept/motive-wave/ - Impulse: https://www.luxalgo.com/library/concept/impulse/ - Corrective Wave: https://www.luxalgo.com/library/concept/corrective-wave/ - Diagonals: https://www.luxalgo.com/library/concept/diagonals/ - Wave Extension: https://www.luxalgo.com/library/concept/wave-extension/ - Truncation: https://www.luxalgo.com/library/concept/truncation/ - Flat: https://www.luxalgo.com/library/concept/flat/ - Triangle: https://www.luxalgo.com/library/concept/triangle/ - Wave Degree Hierarchy: https://www.luxalgo.com/library/concept/wave-degree-hierarchy/ - Elliott Hard Rules: https://www.luxalgo.com/library/concept/elliott-hard-rules/ --- Source: https://www.luxalgo.com/library/concept/fib-wave-relationships/ (LuxAlgo Library, the encyclopedia of trading & technical analysis). Free to use with attribution: https://www.luxalgo.com/library/license/