Direct answer: what formula is used
Fibonacci Fan is calculated by drawing several straight lines (“fan rays”) that all start at one anchor point and extend through other points determined by Fibonacci ratios.
In its most common setup, you first measure a swing from a start point to an end point, compute the swing size (vertical distance), then use predefined Fibonacci ratios to create intermediate target levels. From each target level, you draw a line from the anchor.
A compact way to express the geometry (using a typical “linear projection” approach) is:
- Choose an anchor at time x0 with value y0.
- Choose a swing end at time x1 with value y1.
- Compute the swing size: Δy = y1 − y0.
- For each ratio r in a chosen set (for example: r ∈ {0.236, 0.382, 0.5, 0.618, 0.786, 1.0}), compute target values:
- y(r) = y0 + r · Δy
- For each r, draw a ray (a straight line) starting at (x0, y0) and passing through (x1, y(r)) or, in some implementations, through (x(r), y(r)) where x(r) may be tied to the measured swing duration.
Because charting tools implement different conventions for how x-coordinates are handled, the key verification step is to match the tool’s definition of “anchor,” “swing,” and how it maps ratios onto both time and price.
Mechanism or definition: what inputs the calculation needs
Fibonacci Fan is best understood as a geometric construction based on two user-defined points.
1) The two anchors (the only essential data)
You need:
- A start anchor (x0, y0), often the beginning of a swing.
- An end anchor (x1, y1), often the end of that swing.
The “swing” is the interval from x0 to x1. The calculation uses the swing’s size in value terms through Δy = y1 − y0.
2) The ratio set
A Fibonacci Fan uses a set of ratios derived from the Fibonacci sequence. Common ratios include 0.236, 0.382, 0.5, 0.618, and 0.786; some tools also include 1.0. The exact list is not universal, so your parameters matter.
The ratio r tells you how far along the swing (in value terms) the intermediate target level lies.
3) Mapping ratios into drawn rays
After you compute the target levels y(r), the tool draws rays that reflect those targets.
There are two common implementation styles:
- Style A (price-level first): the fan rays are based on intermediate value levels relative to the anchor, with a consistent mapping from time across the measured interval.
- Style B (ratio-to-point mapping): the tool maps each ratio to a distinct point (x(r), y(r)) and connects rays from the anchor to those points.
The mathematical “slope” of each ray is therefore determined by how your software assigns x(r). That is why two screenshots with the same ratios and anchors can look different between platforms.
4) Direction handling
If Δy is negative (the end value is below the start), the same formulas still apply, but target levels move downward because y(r) = y0 + r · Δy.
So the calculation is direction-agnostic; the drawn fan simply goes toward the end of the swing in the correct direction.
Evidence or example: a step-by-step numeric construction
Assume you define:
- Anchor start: (x0, y0) = (0, 100)
- Swing end: (x1, y1) = (10, 120)
Then:
- Δy = 120 − 100 = 20
Choose ratios r ∈ {0.236, 0.382, 0.5, 0.618, 0.786, 1.0}. Compute target values:
- y(0.236) = 100 + 0.236 · 20 = 104.72
- y(0.382) = 100 + 0.382 · 20 = 107.64
- y(0.5) = 100 + 0.5 · 20 = 110
- y(0.618) = 100 + 0.618 · 20 = 112.36
- y(0.786) = 100 + 0.786 · 20 = 115.72
- y(1.0) = 100 + 1.0 · 20 = 120
Now draw rays from the anchor (0, 100) toward points that reflect these targets. If your implementation uses the entire swing duration as the time reference, each ray can be visualized as a line that reaches its corresponding y(r) at the end time x1. In that case, a ray for ratio r would connect:
- from (x0, y0) = (0, 100)
- to (x1, y(r)) = (10, y(r))
For instance, the 0.618 ray connects (0, 100) to (10, 112.36). The slope of that ray is:
- slope = (112.36 − 100) / (10 − 0) = 12.36 / 10 = 1.236 per time unit.
If a platform instead chooses x(r) differently, the slope changes even though the y(r) values remain the same.
Limitations and risks: what can fail or mislead
1) Anchor selection changes the geometry
A Fibonacci Fan is highly dependent on where you place the two anchors. Small changes to (x0, y0) or (x1, y1) can produce noticeably different rays because Δy and the ray slopes both change.
2) Ratio settings are not standardized
Different tools may use different default ratio sets, and you may be able to adjust them. That changes the number of rays and their positions.
3) Time mapping differs across implementations
Even if two tools use the same ratio values, they may differ in how they map ratios to time coordinates. This is a common reason for inconsistent appearances between platforms.
4) It is not an isolated “signal”
The Fibonacci Fan is a visual construction. Interpreting it as a standalone buy/sell trigger can be misleading because it does not, by itself, define what should happen next.
5) Historical appearance is not proof of future outcomes
Even if a fan visually aligns with past structure, that does not establish a stable cause-and-effect relationship for future price behavior. Execution conditions and market movement can differ.
Verification or next question: how to check your own calculation
To independently verify Fibonacci Fan calculation details, use this checklist:
- Identify the tool’s definitions of “start,” “end,” and “anchor.”
- Confirm the ratio set it uses (or whether you selected it).
- Compute Δy = y1 − y0 and y(r) = y0 + r · Δy for each ratio.
- Check how the tool places each ray in time (whether each ray reaches its y(r) at x1, or at a ratio-specific x(r)).
- Recreate the same rays in a simple coordinate setup (even in a spreadsheet) using the slope formula implied by your platform’s mapping.