Tools · Levels
Fibonacci Retracement Calculator, Levels and Extension Targets
Enter a swing high and a swing low and get every retracement level for a pullback in either direction, plus the extension targets used once the trend resumes.
Fibonacci retracement calculator
Where the ratios come from
A Fibonacci retracement calculator does nothing a pocket calculator could not: it divides one swing by a handful of fixed proportions. What matters is where those proportions came from, because only one of the five levels every Fibonacci retracement calculator prints is not derived from the sequence at all.
The Fibonacci sequence adds each pair of terms to make the next (1, 1, 2, 3, 5, 8, 13, 21), and as it runs on, the ratio of a term to the one after it converges on 0.618. The other levels are that number worked over: 0.382 is 0.618 squared, 0.236 is 0.618 cubed, and 0.786 is its square root. The extensions invert the relationship, 1.618 is the ratio the other way round, and 1.272 is its square root.
Fifty per cent belongs to none of this. It is the midpoint of the swing, carried over from Dow theory, and it sits in the list because it is watched. Stating that plainly matters, because it is also the most honest description of what the whole tool does.
Reading the levels
A retracement level is a place to look, not a reason to act. The shallow levels, 23.6 and 38.2 per cent, are typical of a strong trend that barely pauses; a pullback that reaches 61.8 or 78.6 has given back most of the impulse and the trend is in real question. Where price stops inside that range is a rough measure of how much conviction remains, which is why the level is only half the observation.
The other half is what the volume does when price gets there. A pullback into 61.8 per cent on steadily thinning volume is a market running out of sellers; the same level reached on expanding volume is a market finding new ones. The level tells you where the question will be asked, and the volume answers it, which is the pattern every tool on this site is arranged around.
A worked example: levels and extensions
Take the default values in the calculator: a swing low of 4,180 and a swing high of 4,620, a range of 440 points, in an uptrend that is now pulling back. Each retracement level is the high minus a fraction of the range, and each extension is the low plus a multiple of it.
| Level | Arithmetic | Price | Typically read as |
|---|---|---|---|
| 23.6% | 4620 − 103.8 | 4516.2 | A shallow pause in a strong trend. |
| 38.2% | 4620 − 168.1 | 4451.9 | An ordinary pullback; the trend is not in question. |
| 50% | 4620 − 220.0 | 4400.0 | The midpoint, watched, though not a Fibonacci ratio. |
| 61.8% | 4620 − 271.9 | 4348.1 | Most of the impulse returned; the level that gets quoted. |
| 78.6% | 4620 − 345.8 | 4274.2 | The last level of interest before the move has simply failed. |
| 161.8% | 4180 + 711.9 | 4891.9 | An extension target, used only once the trend resumes. |
Two observations follow from the numbers rather than from any theory. The levels are close together (4,451.9 and 4,400.0 are barely half a per cent apart on this range), so on a smaller swing several of them collapse into a band narrower than a normal day’s movement, and price touching "a Fibonacci level" becomes nearly unavoidable. And the deepest retracement sits only a hundred points above the origin of the whole swing, which is the arithmetic reason 78.6 per cent is usually treated as the end of the exercise.
Fixing the swing before you draw
A Fibonacci retracement calculator will accept any two prices you give it, which is exactly where the discretion in this method lives. Deciding the swing before computing anything is the whole discipline.
Every serious objection to this tool is really an objection to the discretion in choosing the two inputs, and the discipline that answers it costs nothing: decide the rule first. Pick the impulse that would be obvious to someone who had drawn no lines at all (a clear move from a pivot low to a pivot high, on the timeframe your decision actually spans), and write the two prices down before computing anything.
What that rules out is the common practice of nudging the anchor until a level lands where price already is. It always can be made to, because there are five retracement levels and an infinity of candidate swings, and the result is a chart that explains the past perfectly and forecasts nothing. Levels chosen in advance can be wrong, which is the property that makes them worth something.
Where it misleads
| Situation | What goes wrong |
|---|---|
| Ambiguous swing | Two reasonable analysts pick different pivots and get different levels from the same chart. Every criticism of this tool starts here. |
| Redrawing after the fact | Adjusting the swing until a level sits under the current price fits the tool to the answer and proves nothing. |
| Too many levels | Five retracements plus extensions put eight lines on a chart; price will touch several, and hindsight will always find the one that "worked". |
| Gaps in the swing | An overnight gap inside the measured move means the range never traded continuously, so the levels divide a distance rather than a market. |
| Thin instrument | The mechanism is other participants watching the same lines. Where few are, the levels are just arithmetic. |
Frequently asked questions
Why is 50 per cent in the list when it is not a Fibonacci ratio?
Because it is watched, not because it is derived. 23.6, 38.2, 61.8 and 78.6 come out of the Fibonacci sequence. 61.8 is the ratio each term approaches against the next, 38.2 is that ratio squared, 78.6 is its square root. Fifty per cent is simply the midpoint of the swing, inherited from Dow theory, and it survives on every platform because a large number of participants act on it. That is the honest reason, and it is the same reason the other levels do anything at all.
Which swing high and low should I measure?
This is the whole argument, and no formula settles it. A retracement drawn from the last three days and one drawn from the last three months produce entirely different levels on the same chart, and both are "correct" arithmetic. The workable discipline is to fix the rule before you look: use the swing that a trend-following eye would identify without the levels drawn — a clear impulse from a pivot low to a pivot high — and keep the timeframe consistent with the decision you are making. Redrawing until a level lands under the current price is fitting the tool to the answer.
What is the difference between a retracement and an extension?
A retracement divides the swing you already have: every level sits between the low and the high. An extension projects beyond it, 127.2 and 161.8 per cent of the swing measured from the far end, and is used to place targets once the retracement has held and the trend resumed. Retracements answer "how deep might this pullback go"; extensions answer "if it resumes, how far".
Do these levels work, or is it self-fulfilling?
The second, largely, and that is not a dismissal. Nothing in market structure privileges 61.8 per cent of an arbitrary swing. What is real is that the ratios are on every trading platform by default, computed identically from the same two points, so orders cluster near them, a genuine mechanism with a mundane explanation. It follows that the effect is strongest where the swing is obvious to everyone and weakest where analysts would disagree about which swing to draw.
Should I measure from the wick or from the close?
From the extreme of the range, the wick, if you want the levels most other participants are looking at, because that is what every platform draws by default. Measuring from the closing prices produces a smaller range and slightly shallower levels, and is defensible on the argument that a single spike is not where the market really traded. Both are consistent choices; the mistake is switching between them, or comparing your levels with someone else’s without establishing which convention each used.
Do the levels work on any timeframe?
The arithmetic does, and the coordination mechanism does not, equally. Levels drawn from a swing that is visible on a daily chart are watched by a great many people; levels from a three-bar swing on a one-minute chart are watched by almost nobody, so the only thing supporting them is the arithmetic: which supports nothing. As a rule of thumb, the more obvious the swing would be to someone who had drawn no lines at all, the more the levels are worth.
What does it mean when price cuts straight through 61.8 per cent?
That the impulse being retraced has given back nearly all of itself, which is a description of a failed move rather than a signal about the next one. Practitioners often treat 78.6 as the last level of interest and a close beyond the origin of the swing as the end of the exercise, at that point there is no retracement left to measure, only a new move in the other direction, and a new swing to identify if you want levels at all.
How do the extension targets relate to the retracement?
They are the same range projected past the far end of the swing, so they are only meaningful once a retracement has held and the trend has resumed. Implementations differ about the anchor, which is a real source of disagreement between two charts of the same swing: some measure the multiple from the origin of the impulse, others from the low of the retracement that followed it. This calculator uses the origin (in an uptrend, the swing low plus 161.8 per cent of the range), which is the form that needs only the two numbers you have already entered.
Is there a way to test whether the levels do anything?
Yes, and it has to be set up before the fact to mean anything. Fix a rule for identifying the swing, apply it mechanically across a long history without discretion, and record how often price reacted within a defined distance of each level compared with an equal number of arbitrary levels drawn in the same range. Almost nobody does this, which is why the literature is full of confident claims and short of measurements. Any study that identified swings by eye after seeing the outcome has measured the analyst.