Direct answer
A worked example of Fibonacci Extension shows how extension levels are calculated from a prior price “move” using fixed Fibonacci ratios. In a worked example, you must state the swing points you used, the direction (up or down), and the exact arithmetic, so someone else can recompute the same extension numbers.
This article gives a single numeric example with fully stated assumptions. It also highlights limitations, including the fact that historical swings used to compute the levels do not guarantee anything about future movement.
Mechanism or definition
Fibonacci Extension is a technique that starts from a measured move between two points, then projects additional levels beyond one of those points using Fibonacci ratios.
Stable mechanics (what does not depend on the market):
- Select swing points A and B and define the move A → B.
- Compute the move length:
- For an upward move: (\text{dist} = B - A)
- For a downward move: (\text{dist} = A - B) (so (\text{dist}) is positive)
- Choose Fibonacci extension ratios. A common set includes values like 1.272, 1.618, and 2.618.
- Compute level candidates beyond B:
- If the move direction is upward, extension levels are above B: (\text{Level} = B + (\text{ratio} \times \text{dist}))
- If the move direction is downward, extension levels are below B: (\text{Level} = B - (\text{ratio} \times \text{dist}))
Important: In real usage, people visually pick swing points from a chart. That swing selection is a major variable, not a property of the formula.
Evidence or example (worked, numeric)
Assumptions (explicit):
- We use a simplified price scale where “price” is just a number.
- No live prices, spreads, fees, or execution details are involved.
- We analyze an upward sequence.
- Swing points are chosen as:
- A = 100
- B = 115
- Therefore the measured move length is:
- (\text{dist} = B - A = 115 - 100 = 15)
- We will compute three extension levels using common ratios: 1.272, 1.618, 2.618.
Now calculate each extension level beyond B (upward formula):
- 1.272 level:
- (\text{Level}_{1.272} = B + 1.272 \times \text{dist})
- (= 115 + 1.272 \times 15)
- (= 115 + 19.08)
- (= 134.08)
- 1.618 level:
- (\text{Level}_{1.618} = 115 + 1.618 \times 15)
- (= 115 + 24.27)
- (= 139.27)
- 2.618 level:
- (\text{Level}_{2.618} = 115 + 2.618 \times 15)
- (= 115 + 39.27)
- (= 154.27)
Independent verification: anyone can confirm the arithmetic by recomputing (\text{dist}) from A and B, then applying the ratio to (\text{dist}), then adding to B for an upward case.
Limitations and risks
- Swing selection can change the result. If A and B are chosen differently (for example, using different highs/lows), (\text{dist}) changes, and all computed levels shift.
- The formula is not a standalone signal. Fibonacci Extension levels are level candidates derived from assumed points. They do not inherently state whether price will react there.
- Chart scaling and measurement consistency matter. If the input values are not on the same scale (or the direction is applied incorrectly), the math will produce misleading “levels.”
- Historical relationships do not ensure future outcomes. Even if a level coincides with prior behavior, market conditions, costs, and execution can differ.
Failure mode example: if you accidentally treat the move as upward when it should be downward, you will add ratios to B instead of subtracting them, producing levels on the wrong side of the reference point.
Verification or next question
To verify your own Fibonacci Extension work, write down four items before doing calculations: A, B, the direction (up/down), and the ratios you will use. Then recompute (\text{dist}) and each extension level using the relevant formula.
Next question you can answer independently: how should Fibonacci Extension be interpreted when multiple swing choices exist on the same chart, and what criteria you will use to choose A and B consistently?