Fibonacci Calculator
Two prices from one swing give you the whole grid — retracements inside the move, extensions past the end of it.
Range: —
Retracements
Inside the swing
- 0%
- —
- 23.6%
- —
- 38.2%
- —
- 50%
- —
- 61.8%
- —
- 78.6%
- —
- 100%
- —
Extensions
Past the end of the swing
- 127.2%
- —
- 141.4%
- —
- 161.8%
- —
- 200%
- —
- 261.8%
- —
This is a calculator, not advice. It works only on the numbers you type in — it has no market data and no opinion on what you are trading. Nothing here is a recommendation to open, close or size a position, and technical analysis describes probabilities rather than outcomes. Which swing you measure is a judgement call, and a different pair of prices produces a different grid.
Finding the swing is the hard part
The arithmetic here is trivial; choosing which two points to measure is not, and it is the step that changes every level on the grid. Chart AI reads a photo of any chart and describes the trend and the swing structure on it, keeping each analysis in a history you can compare later.
What the grid actually is
Take one clear move — a low to a high — and call the distance between them the range. Every retracement level is that range multiplied by a ratio and subtracted from the end of the move. A 38.2% retracement of a rise from 100 to 120 is 120 − (20 × 0.382) = 112.36. That is the entire calculation, repeated for each ratio.
The ratios come from the Fibonacci sequence, where each number is the sum of the previous two. Divide any number in it by the one after it and the result converges on 0.618; divide by the number two places along and you get 0.382. The 78.6% level is the square root of 0.618, and 50% is not a Fibonacci ratio at all — it is a Dow theory convention that stayed on the chart because the midpoint of a range is worth marking regardless.
| Level | Where it comes from |
|---|---|
| 23.6% | A number divided by the one three places later |
| 38.2% | A number divided by the one two places later |
| 50% | Not Fibonacci — Dow theory convention |
| 61.8% | The golden ratio; each number divided by the next |
| 78.6% | The square root of 0.618 |
| 161.8% | The golden ratio inverted, projected past the swing |
The honest case for using them
The ratios have no demonstrated power of their own. What they have is company: the tool ships with every charting package, the obvious swing on a chart is obvious to everybody, and so a large number of people end up looking at the same handful of prices at the same time. Orders cluster there for that reason and no other, which is enough to make the levels worth knowing without needing them to be magic.
That also explains the failure mode. Levels drawn from a swing only you can see are watched by only you, and behave accordingly. The more arguable the swing, the less the grid is worth.
Retracement and extension are different measurements
A retracement lives between the two prices you entered — it answers how far a pullback has gone relative to the move that preceded it. An extension lives beyond the end of the move, and is measured from the far swing point: on a rise from 100 to 120, the 161.8% extension is 100 + (20 × 1.618) = 132.36, not 120 plus something. Charting packages that ask for a third point are measuring a different thing again, so two "161.8% extensions" of the same swing can legitimately disagree.
Questions
Which two prices do I use?
The two ends of one clear move: the low it started from and the high it reached, or the reverse for a fall. Both should be swing points that stand out on the timeframe you are looking at — a high with lower highs either side of it. Picking a different pair gives a different grid, which is the honest weakness of the whole technique: two people drawing the same chart often draw different levels.
Why is 50% in the list when it is not a Fibonacci number?
It is not one, and it is included anyway because it has been drawn on charts for a century — it comes from Dow theory, where a retracement of about half of a prior move was treated as ordinary. It survives on chart packages next to the real ratios out of convention, and because the midpoint of any range attracts attention regardless of where the idea came from.
How are the extension levels measured?
From the far end of the swing. On a move up from a low to a high, the 161.8% extension is the low plus 1.618 times the range, which lands above the high — that is the two-point convention charting packages use. It is worth knowing because some tools measure extensions from a third point instead, and the two methods give different prices from the same swing.
Do Fibonacci levels actually work?
There is no good evidence that the ratios themselves carry any special force, and the studies that have looked for one have generally not found it. What is true is that a lot of people draw the same grid on the same obvious swing, which makes some of these levels places where orders cluster. That makes them worth knowing about as crowded prices, which is a different claim from the mystical one usually attached to them.
Does the timeframe matter?
Only in that it decides which swing you are measuring. The arithmetic is identical on a one-minute chart and a monthly one. Levels drawn from a swing that took months to form are watched by more people than levels from a swing that formed over lunch, which is the whole of the difference.
