Fibonacci Retracement Calculator

What this calculator does

A price runs up, then pulls back. Traders want to know how deep that pullback has gone, and where it might pause. Fibonacci retracement is the standard way of marking those depths on a chart, and this calculator produces the levels without the chart.

You give it the two ends of a price move, a start point and an end point, and it returns the five retracement levels between them: 23.6, 38.2, 50, 61.8 and 78.6 percent, along with the two ends themselves. It works in either direction. Feed it a rise and it measures the pullback downward from the high; feed it a fall and it measures the bounce upward from the low. Either way, the output is always listed from the highest price down to the lowest.

Where those odd percentages come from

The percentages look arbitrary until you meet the sequence behind them. The Fibonacci sequence starts 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, and keeps going with each number being the sum of the two before it. What matters here is not the numbers themselves but the ratios between them, which settle into fixed values as you go further along.

• 61.8 percent. Divide any number by the one directly after it. 55 ÷ 89 = 0.618. This is the reciprocal of the golden ratio, 1.618, and it is the level most traders watch.
• 38.2 percent. Divide by the number two places ahead. 233 ÷ 610 = 0.382. It is also exactly 1 minus 0.618.
• 23.6 percent. Divide by the number three places ahead. 233 ÷ 987 = 0.236.

Those three are genuine, and they are stable: the ratios converge no matter where in the sequence you start. The golden ratio itself turns up in enough unrelated places, from leaf arrangements to the proportions of buildings, that people have long found it satisfying to look for it in price charts too. Whether markets have any reason to respect it is a separate question, taken up further down.

The two levels that are not Fibonacci at all

Now the part that rarely gets said plainly, even though the calculator prints both numbers alongside the real ones. Two of the five levels have nothing to do with the Fibonacci sequence.

50 percent is simply the halfway point of the move. It is not in the sequence, it is not derived from any ratio in it, and it is on the tool by inheritance rather than mathematics. The idea traces back to Dow theory and Charles Dow's observation that markets often give back around half of a move. It survives on the chart because traders have watched it for over a century, not because Fibonacci put it there.

78.6 percent is the square root of 0.618, which comes to 0.786. Taking a square root of a Fibonacci ratio does not produce another Fibonacci ratio, so this one is a derived convenience that traders found useful and kept.

This is not a reason to ignore either level. The 50 percent line in particular is watched closely by a great many people, and that is a real thing about markets whatever its pedigree. It is a reason to be accurate about what you are looking at, and to notice that "these levels come from a famous mathematical sequence" is only true of three of the five.

Picking your two points, and why they decide everything

The calculator asks for a start point and an end point and it will faithfully work with whatever you give it. This is the step where the real judgement lives, and it is worth more attention than the arithmetic.

Convention is to anchor to a clear swing: for a rise, from the swing low to the swing high, and for a fall, from the swing high to the swing low. The word doing the work is "clear". A significant turning point that stands out on the chart gives levels other traders will draw in roughly the same place. A minor wiggle chosen because it happens to put a line where you wanted one gives levels nobody else is looking at.

The honest consequence is that these levels are not objective. Two people can open the same chart, pick different swing points, and produce completely different sets of lines, sometimes supporting opposite conclusions. The mathematics is fixed and the inputs are a judgement call, which means the output inherits the judgement. Anyone presenting Fibonacci levels as though the chart handed them over should be asked which swing they anchored to.

A clean swing, worked through

Take a price that rose from 100 to 200, so the move is 100 points. Entering a start of 100 and an end of 200, the calculator measures the pullback down from the high:

• End point (the high): 200
• 23.6 percent retraced: 200 − 23.6 = 176.4
• 38.2 percent retraced: 200 − 38.2 = 161.8
• 50 percent retraced: 150
• 61.8 percent retraced: 138.2
• 78.6 percent retraced: 121.4
• Start point (the low): 100

With a 100-point range the arithmetic is transparent: each level sits that percentage of the range below the high. A shallow pullback stalls near 176, a deep one that reaches 121 has given back most of the advance, and if the price drops through 100 the original move has been fully undone and these lines have stopped describing anything. Reverse the inputs, entering a start of 200 and an end of 100 for a fall, and the same logic runs upward from the low, putting 23.6 percent at 123.6 and 61.8 percent at 161.8.

What the lines can and cannot tell you

Worth being straight about, since money rides on it. These levels are a way of describing a price move, not a forecast of what it will do next. The calculator is doing arithmetic on two numbers you supplied. Nothing in it knows anything about the asset, and no mechanism obliges a price to stop at 61.8 percent of anything.

The most defensible explanation for why the levels sometimes seem to work is that a very large number of traders watch the same handful of lines, drawn by the same default tool settings, and act near them. That makes the reaction partly self-fulfilling, which is a genuine market effect rather than a mystical one, and also an unreliable one, since it depends on enough people having anchored to the same swing you did. Traders who use these levels seriously tend not to treat a line as a signal on its own. They look for it to coincide with something else already on the chart, a previous high or low, a moving average, a round number, and treat the overlap as the point of interest.

So the sensible use is as a consistent, shared vocabulary for measuring pullbacks, and as a way of marking places where other people are likely to be paying attention. Used that way it earns its place. Used as a prediction, it is a set of horizontal lines drawn from two numbers you chose yourself.

Questions people ask

Which value goes in start and which in end?

Start is where the move began, end is where it finished. For a rise, that is low then high; for a fall, high then low. The calculator handles either direction and always lists results from the highest price down.

Is 50 percent a Fibonacci level?

No. It is the midpoint of the move, kept on the tool by long convention from Dow theory. The 78.6 percent level is also not from the sequence; it is the square root of 0.618.

Which level matters most?

Traders watch 61.8 percent most closely, since it is the golden ratio level, with 50 percent close behind. That attention is itself much of the reason those lines see reactions.

Are these levels reliable?

They are a description, not a prediction, and their apparent power depends heavily on how many traders drew the same swing you did. Most people who use them look for the level to line up with other evidence rather than trading it alone.

References

The retracement percentages derive from ratios within the Fibonacci sequence: 61.8 percent from dividing a term by the next, 38.2 percent from dividing by the term two places later, and 23.6 percent from three places later, with 61.8 percent corresponding to the reciprocal of the golden ratio. The 50 percent level is not a Fibonacci ratio but the midpoint of the move, retained by convention from Dow theory, and 78.6 percent is the square root of 0.618. The sequence and the golden ratio itself are described in the mathematical reference below.

1. Encyclopaedia Britannica, Fibonacci numbers. https://www.britannica.com/science/Fibonacci-number
2. Encyclopaedia Britannica, Golden ratio. https://www.britannica.com/science/golden-ratio