Fibonacci: retracements, projections and checks.

What the ratios mean.

In 1, 1, 2, 3, 5, 8, 13, each next number sums the previous two. Ratios of large adjacent terms approach 1.618 and its inverse 0.618; approximately 0.382 equals 1 − 0.618. These are mathematical relationships, not proof that markets must follow them.

The table lists common reference values. Ratios are rounded; 50% and equality at 100% are useful comparisons even though 0.5 is not the limiting ratio of adjacent Fibonacci terms. Do not treat these values as compulsory depths for waves 2 and 4.

Retracement: two initial points.

Let A=100 and B=120 mark the start and end of a rise. Its linear price length is 20. The ratio r measures the fraction returned from B toward A. Here the letters denote measurement anchors, not necessarily corrective waves A and B.

A 61.8% retracement gives 107.64. An actual low at 108 returns (120 − 108) / 20 = 60%; that is a nearby proportion, not exactly 61.8%. For a fall from 120 to 100, the same formula projects the retracement upward: r=0.618 gives 112.36.

R = B − r × (B − A)
A = 100; B = 120

Projection: a length and a new anchor.

Now A=100 and B=120 define length 20, while C=108 is the anchor for projecting in the original direction. Equal length gives 128; a multiple of 1.618 gives 140.36. Three points are needed because you measure one segment and transfer its length from another endpoint.

To compare C with A in a zigzag, measure wave A and project in C’s direction from B’s end. Equality and 1.618 are reference scenarios to test, not requirements. A 161.8% level measured from the original start differs from projecting 1.618 times its length from a new anchor when those anchors differ.

T = C + r × (B − A)
A = 100; B = 120; C = 108

The scale changes the measurement.

A linear scale compares absolute price differences. A logarithmic scale compares ratios: equal vertical distances represent equal percentage multipliers. For positive prices, calculate a logarithmic retracement with the formula below. ln is the natural logarithm; exp is its inverse.

For 100→200, half the absolute move gives 150, whereas half the logarithmic move is about 141.42. Record the scale and tool settings, especially for large ranges. Logarithmic formulas do not apply to zero or negative prices. This lesson explains both calculations without claiming that the product automatically uses them to set targets.

R_log = exp(ln(B) − r × (ln(B) − ln(A)))
T_log = exp(ln(C) + r × (ln(B) − ln(A)))
A = 100; B = 200; r = 0.5
R_linear = 150; R_log ≈ 141.42

Use proportions without fitting the answer.

1. Choose related waves

   Compare waves of the same degree and clear roles; label the start, end and projection anchor.

2. Validate the model first

   A ratio of 1.618 does not override overlap in an ordinary impulse or incorrect subdivisions.

3. Fix the measurement

   Record scale, completed-bar extremes, ratio, rounding and any tolerance zone in advance.

4. Review new evidence

   Several nearby levels warrant closer inspection, not an established probability. Compare alternatives and the rejection condition.

Give rules priority.

Using TradingView’s three-point Fibonacci projection

Original educational material by Student Wyckoff. This section was checked against the linked TradingView tool guide on 20 October 2026.

Choose Trend-Based Fib Extension and place its anchors at a move’s start, its end and the following retracement’s end. In the drawing’s settings, use Coordinates to enter the anchors’ bars and prices precisely. Use Style to edit the displayed level values, for example 0.618, 1 and 1.618. See the official tool guide.

For a linear teaching example, take P1 = 100, P2 = 120 and P3 = 110. The measured length is 20. Transfer a chosen multiple from P3: T = P3 + r × (P2 − P1).

Check scale settings before comparing a drawing with this arithmetic. TradingView documents a separate log-based level option when the chart is logarithmic. This example uses invented prices on a linear scale; it does not establish an Elliott count, a trade entry or a success probability. Review the wave rules alongside the dated market example.

How to calculate wave 5: a worked, conditional example

A fifth-wave calculation estimates a possible length from a proposed fourth-wave endpoint. It does not identify the waves for you. The prices below are invented teaching values on a linear scale, without dates, an instrument or a trading result. First assume that the proposed waves 1–4 have survived a separate check of their internal structures and larger-wave position.

1. Fix the points before choosing a ratio

The point lengths are L1 = 120 − 100 = 20 and L3 = 148 − 108 = 40. For an upward scenario measured from P4, use T5(r) = 132 + r × 20. For a downward scenario, subtract the chosen length from the proposed fourth-wave endpoint. Keep the scale and the definition of length consistent.

2. Compare several projections

Elliott Wave International describes equality and a 0.618 relationship as guidelines in Equality. Fibonacci Relationships explains the ratio background. The third row is a mathematical comparison we chose for this exercise; these rows have no measured hit rates or probabilities.

3. Reject a projection that breaks the structure

In this example L3 = 40 is longer than L1 = 20 and all three proposed L5 values. Percentage moves also pass: 20/100 = 20%, 40/108 ≈ 37.04%, and the largest candidate fifth is 32.36/132 ≈ 24.52%. Wave 3 is therefore not the shortest under either comparison. If another count had L1 = 30, L3 = 20 and L5 = 25 on the same arithmetic basis, its third wave would be shortest; a pleasing ratio would not repair it.

The starting assumptions also require P2 > 100, P3 > 120 and P4 > 108. Here P4 = 132 stays above wave 1’s territory. A fall below 120 would overlap that territory and reject this strict ordinary-impulse interpretation. A touch at 120 needs explicit boundary treatment; do not silently round it away. EWI’s Motive Waves and Impulse provide the structural rules and distinguish the ordinary impulse from special cases.

4. Distinguish an unfinished fifth from a truncation

The second path illustrates what a truncated fifth would need at one visible degree. EWI’s Truncation requires the necessary internal five waves. The table does not validate every smaller subdivision or establish that any real market made those moves. A rise stopping below 148 with only one or three visible legs remains unresolved; missing a Fibonacci level does not prove a completed truncation.

While the fifth is developing, a move below its proposed start at 132 cancels that particular start-point scenario and requires a recount; the fourth may still be extending. For this exercise, after an apparent five-leg finish, a later completed move below its internal fourth (143 or 139 respectively) is an additional review trigger, not a universal completion theorem or a trading instruction. Keep a corrective alternative, record the data cutoff, and use the rule checks and alternative-count comparison before treating a candidate endpoint as completed.

Study offline with the original PDF guide

Rules, counting, corrections and Fibonacci, with invented worked examples and an answer key. Available in this page language.

Download the study guide (PDF, 8 pages)

Books and edition checks

Looking for a book on Elliott waves and Fibonacci? The bibliography identifies authors and editions; this lesson explains the calculations. Books and edition checks.