What is a Fibonacci retracement?
A Fibonacci retracement measures how much of a move price has given back, as a percentage of that move. You take the high and the low of a swing and cut the distance between them at the Fibonacci ratios, 23.6%, 38.2%, 61.8% and 78.6%, plus the 50% midpoint, to get the prices where a pullback is most often watched. The three levels past 100%, 127.2%, 161.8% and 261.8%, are extensions: the same move measured beyond its starting point.
The formula fits in one line. After a move up that is now pulling back, each level is the high minus the range times the ratio: level = high − (high − low) × ratio. After a move down that is now bouncing, it is the low plus the range times the ratio: level = low + (high − low) × ratio. The calculator does exactly that for every ratio in the table, in whichever direction you choose.
How to use the calculator: a worked example
Say a stock rallied from 100.00 to 120.00 and is now pulling back. Enter 120 as the high and 100 as the low, and choose “Up, and now it pulls back”. The range is 20.00 and the table returns 23.6% at 115.28, 38.2% at 112.36, 50% at 110.00, 61.8% at 107.64 and 78.6% at 104.28. Below the low, the 127.2% extension sits at 94.56, the 161.8% at 87.64 and the 261.8% at 67.64.
Now switch to “Which level am I at” and type the current price. At 107.64 the answer is 61.8%, the golden-ratio retracement; at 109.00 it is 55.0%, between the 50% and the 61.8% levels. If the move went the other way, choose “Down, and now it bounces” and the same ratios are measured up from the low instead.
Where the ratios come from
Take a sequence where each number is the sum of the two before it, and divide any number by the one after it. The result settles on 0.618, and it keeps settling there however far you go. Divide by the number two places along and you get 0.382; by the one before, 1.618. Those are the ratios on every retracement tool, and they were a property of the sequence long before anyone put them on a chart. The 78.6% that also appears is the square root of 61.8%, which is why it shows up on some tools and not on others.
Whether markets respect them because the mathematics is deep or because a large number of traders are watching the same three lines is a question this page cannot settle. What it can do is put the lines in the same place every time, so that what you are looking at is the level and not your arithmetic.
The 50% that is not Fibonacci
The 50% level sits in the middle of every retracement tool and does not belong to the sequence at all. It is there because half of a move is an obvious place to look, and because enough people watch it that it behaves like the others. We keep it, and we say what it is.
It is also the exact line that our Edo Premium Discount indicator calls equilibrium: the midpoint between the high and the low of a range. Same arithmetic, two names. Above it price is trading in the expensive half of the move, below it in the cheap half.
What a level holding does and does not mean
A retracement that stops at 61.8 and turns is worth noticing. A retracement that stops at 61.8, turns, and then comes back through it a week later is the same level behaving differently, and neither instance predicted the other. The line marks a price where reactions have been common. It does not carry an obligation.
Levels are most useful where something else agrees with them: a prior swing, a zone the market has already tested, the structure around the entry. On their own they are a grid drawn on top of a chart, and the chart does not know it is there.
Moving the anchors until it fits
The common mistake is not the arithmetic, it is the choice of high and low. Slide either anchor a few bars and every level moves with it, and there is almost always a pair of anchors that puts a line exactly where price already turned. A retracement drawn after the fact to explain a move that already happened explains nothing.
Pick the two points before you need the answer: the start and the end of the move you are actually trading, the ones you would point at if someone asked. Then read what comes out, including when what comes out is inconvenient.
The levels beyond the move
The last three rows of the table, 127.2%, 161.8% and 261.8%, are not retracements. They sit past the origin of the move, on the other side, and they exist because a price that breaks out of a range often stops somewhere related to the size of what came before. They are used as targets rather than as places to enter.
Read them for what they are: a projection of the same distance, not a forecast. If the move you measured was twenty points, the 161.8 extension is thirty-two points past its origin because that is what the arithmetic says, not because the market has agreed to go there.
The 3-point extension: projecting from the pullback
The third tab projects targets from the end of a pullback instead of from the swing itself. Mark A where the impulse started, B where it ended and C where the pullback that followed stopped. Each projection is C plus the length of the A→B move times the ratio: level = C + (B − A) × ratio, with ratios of 61.8%, 100%, 127.2%, 161.8% and 261.8%. If B is below A the move was down, B − A is negative and the same formula projects downwards.
A worked example: a rally from A = 100.00 to B = 120.00 pulls back to C = 110.00, half of the move. The impulse is 20.00 points, so the 61.8% projection is 110 + 20 × 0.618 = 122.36, the 100% is 130.00, the 127.2% is 135.44, the 161.8% is 142.36 and the 261.8% is 162.36. For a decline from 120.00 to 100.00 that bounces to 110.00, the same ratios land at 97.64, 90.00, 84.56, 77.64 and 57.64.
Reading each number
The table gives you the price of each level for the move you entered. The second tab does the reverse and answers the question you actually have with the chart open: this price, right now, is at what percentage of the retracement, and between which two lines does it fall. A price at 54% is between the 50 and the 61.8 and belongs to neither.
A level is a place to decide something, not a decision. Once you have one, the next question is whether the trade it implies is worth taking — which is arithmetic of a different kind, and what our risk / reward calculator is for. How we think about placing levels in the first place is in our methodology.
