Fibonacci retracements and extensions
The answer
A Fibonacci retracement marks a set of horizontal levels at fixed percentages of a prior price move, usually 23.6%, 38.2%, 50%, 61.8% and 78.6%. There is no accepted mechanism by which those particular numbers govern markets, and the levels do something mainly because a very large number of traders are looking at the same lines and because the band they sit in is where pullbacks normally end anyway.
Why this costs you money
The Fibonacci tool has a property that no honest instrument should have: it can never be wrong.
Draw it on any chart. You get 5 or 6 lines. Add the extensions and you get 4 or 5 more. The lines are close enough together that price is almost always near one of them. When price turns, there is a level nearby, and the level gets the credit. When price does not turn at a level, it simply "went to the next one".
A tool that produces a correct-looking result in every outcome gives you no information at all. It gives you something worse than no information, because it gives you confidence.
Here is what that costs, specifically. You take a position because price reached the 61.8% retracement. You size it large, because the level looked precise to 2 decimal places. Price goes through it. You are now holding a losing position and you have a ready explanation: it must be going to the 78.6% level. So you add. The tool that got you in has now supplied the reason to stay in, and it will keep supplying reasons all the way down, because it always has another line below.
There is a second cost, and it is intellectual. Time spent adjusting anchor points is time not spent on the 3 questions that actually matter: what the trend structure is, where real orders sit, and how much you can afford to lose. A Fibonacci grid takes 10 seconds to draw and can absorb an hour of decision making.
How it works
The sequence and where the numbers come from
The Fibonacci sequence starts 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, and each number is the sum of the 2 before it. Leonardo of Pisa, known as Fibonacci, introduced it to Europe in Liber Abaci in 1202 using a problem about breeding rabbits. It was described in Indian mathematics several centuries earlier, by Virahanka and later by Hemachandra, in work on the patterns of long and short syllables in Sanskrit poetry. the exact dates of Virahanka and Hemachandra.
Divide any number in the sequence by the next one and the answer settles near 0.618. Divide by the number 2 places later and it settles near 0.382. These are the 2 ratios the tool is named for.
The rest of the grid is arithmetic on those:
| Level | Where it comes from |
|---|---|
| 23.6% | 0.618 cubed |
| 38.2% | 0.618 squared |
| 50% | Not a Fibonacci ratio at all |
| 61.8% | The limit of the sequence's ratio |
| 78.6% | The square root of 0.618 |
Read that table again. The 50% level, which is the one most traders find most reliable, has nothing to do with Fibonacci. It is in the tool because Dow theory and Gann's work used halves and thirds long before anybody applied the Fibonacci sequence to a price chart. It was added to the grid and it stayed.
Retracements
A retracement measures a pullback inside a move.
- Find a swing low and the swing high after it, or the other way round in a downtrend.
- Anchor the tool from the start of the move to the end of it.
- The tool draws horizontal lines at each percentage of that range, measured back from the end.
If a market rose from 20,000 to 25,000, the range is 5,000. The 38.2% retracement is 25,000 − 1,910 = 23,090. The 50% is 22,500. The 61.8% is 21,910.
That is the whole calculation. There is nothing hidden in it. It is a percentage of a distance you chose.
Extensions
An extension projects levels beyond the end of the prior move, at 127.2%, 138.2%, 161.8%, 200% and 261.8% of it. The idea is that the next leg of a trend will travel some multiple of the last one.
Extensions have the same arithmetic and a bigger problem. A retracement at least sits inside a range where price has actually traded. An extension sits in empty space where no order has ever rested. Whatever weak case exists for retracements does not carry over.
Anchoring, which is where the honesty problem starts
Every Fibonacci grid requires you to pick 2 points. Change either point and every line moves.
On a 2 year chart of any index there are perhaps 12 defensible swing lows and 12 defensible swing highs. That is well over 100 possible anchor pairs, each producing 5 retracement lines. You are choosing from hundreds of candidate lines.
And you choose after seeing where price went. This is the same error as drawing a trendline through data you have already read, and it is harder to see here because the tool looks like a calculation.
What it tells you, and what it does not
What is actually true
Three things in this subject survive examination.
1. Pullbacks in trends usually end somewhere between about a third and about two-thirds of the prior move. This is a plain statistical fact about how price moves behave, and it does not require the sequence. A pullback that ends after 5% of the prior move is barely a pullback. One that goes past 80% has probably ended the trend. So most real pullbacks end in a band, and 38.2%, 50% and 61.8% are 3 marks inside that band. Any 3 marks inside that band would look right about as often.
2. A great many people watch these levels. Every charting platform ships the tool. Every trading course teaches it. Institutional desks publish Fibonacci levels in daily notes. When enough people place orders at the same price, orders genuinely exist at that price. This is a real cause. It is also a circular one: the level works because people believe it, not because of anything about markets.
3. The percentage depth of a pullback is a useful measurement. Saying "this pullback retraced 45% of the prior advance, and the last 3 retraced 22%, 25% and 30%" is a factual comparison and it tells you the character of the trend is changing. That is the tool used as a ruler, which is honest, rather than as a prediction, which is not.
What is not true
There is no known mechanism connecting 0.618 to order flow. None. No paper establishes one. No exchange rule produces it. No hedging requirement generates it. This is the central fact of this article and almost nobody selling Fibonacci courses will say it.
Compare this with the mechanisms in the previous article. Round numbers cluster because people type round numbers into order boxes, and that has been measured. Option strikes attract price near expiry because hedgers must trade the underlying, and that has been measured. For 0.618, there is nothing of this kind — only the observation that people watch it.
The sunflowers and the Parthenon
You will be told that the golden ratio appears in sunflowers, in seashells, in the Parthenon and in the human body, and therefore in markets. Take these separately, because they are not the same claim.
Sunflowers are real. Seed spirals in sunflowers and scales on pinecones do come in Fibonacci numbers. There is a genuine mechanism: each new seed forms at an angle of about 137.5 degrees from the last, which is the golden angle, and that angle packs seeds more evenly than any other. Plant growth has a reason to produce this number.
The Parthenon is not. The claim that the Parthenon was designed on the golden ratio does not survive measurement. The result depends entirely on which points of the building you choose to measure between, and the ratio can be made to appear or disappear at will. The Greek description of the ratio, in Euclid, comes after the building was constructed. Mario Livio went through the major art and architecture claims in 2002 and found most of them to be added afterwards by enthusiasts, not by the builders.
And neither of them is an argument about markets. Even taking the sunflower entirely at face value, the mechanism is a rule about how a plant places its next seed. There is no comparable rule inside an order book. A person entering a sell order is not growing a seed head. The step from "this number appears in plant growth" to "this number appears in the price of an index" is not an argument. It is a change of subject.
How dense is the grid, really
Do this arithmetic once and you will never be impressed by a Fibonacci hit again.
Take a market that rose 10% and is now pulling back. The retracement lines at 23.6%, 38.2%, 50%, 61.8% and 78.6% of a 10% move are spaced 1.46%, 1.18%, 1.18% and 1.68% apart in price. Add the 0% and 100% ends and the extension levels above.
If your idea of "the level worked" is that price turned within 0.5% of a line, then roughly half of all prices in the retracement zone qualify. You are not running a test. You are covering the board.
A demonstration of retrofitting
Here is a fit found in a few minutes, presented so you can see how it is made.
The NIFTY 50 rose from roughly 7,511 in March 2020 to roughly 26,277 in September 2024, a range of about 18,766 points. A 23.6% retracement of that advance sits at about 21,848. The index's low in early April 2025 was around 21,743. That is within about 0.5%.
That looks striking. It is not evidence. It was found by searching for a fit after both prices were known, from a menu of dozens of anchor pairs and 5 levels each. Any procedure that searches hundreds of candidates and reports the best one will find something. all 4 of these price figures before publication. Even if every number is exact, the reasoning is worthless, and being able to see why is the entire point of this section.
The decision rule
Use a Fibonacci level only where it agrees with something that has a mechanism.
If a retracement level falls within your tolerance of a round number, a heavily traded option strike, or a price zone where large volume actually changed hands, then you have a level worth watching — and the reason it is worth watching is the round number or the volume, not the ratio.
If the level stands alone in empty space, treat it as decoration. Watching it costs nothing. Sizing a position on it is paying for a story.
Unless you are using the tool as a ruler rather than a forecast, in which case measure the depth of pullbacks as a percentage and compare them over time. That use requires no belief about 0.618 and it is genuinely informative.
Never use an extension level as a target on its own. If you need a target, take it from a level where price has actually traded, or from a fixed multiple of your risk, which at least has arithmetic behind it.
Try this now
Five minutes, on a chart you already follow. This is the test that settles the question for most people.
- Open a daily chart, 2 years. Find the clearest large move: a rise or a fall of at least 15%, followed by a pullback.
- Draw the Fibonacci retracement from the start of that move to the end of it. Write down the price of the 61.8% line and the 38.2% line.
- Now calculate the plain 50% level yourself. Add the start and end prices and divide by 2. Write it down.
- Find the nearest round number to that 50% level. For an index ending in many digits, use the nearest 100 or 500. For a stock, use the nearest ₹50, ₹100, $5 or $10, whichever is roughly 1% to 3% of the price.
- Now measure the distance between your 4 numbers, as a percentage of the price. Just subtract and divide.
What you should see. On most charts, the 38.2%, 50% and 61.8% levels sit within about 2% to 4% of one another, and the nearest round number sits inside that same band. All 4 lines are describing the same small region of the chart.
Now ask the honest question. When price turned somewhere in that region, which line did it turn at? You cannot answer, because they are all within noise of each other and the market does not tell you which one it was using. Whichever line was closest received the credit afterwards.
The second step, which takes 60 seconds. Move the top anchor of your Fibonacci tool to the next swing high, 1 that is also defensible. Watch every level move. Note how far the 61.8% line travelled. That distance is the size of your own choice, and it is usually larger than the distance you were treating as precise.
Three real cases
1. The NIFTY 50, March to November 2020 (India) — a strong trend ignores the grid The index fell to roughly 7,511 intraday on 24 March 2020 and then recovered its entire pre-crash level within about 9 months. Through April and May 2020, Fibonacci retracement levels of the crash were published in nearly every market report in the country. The recovery passed through the 38.2%, 50% and 61.8% retracement levels without any of them producing a durable turn. This is the normal behaviour of a strong trend, and it is the case that Fibonacci material never features. the exact dates on which each retracement level was crossed.
2. The S&P 500, 16 August 2022 (United States) — one price, 3 explanations The index closed at a record 4,796.56 on 3 January 2022 and fell into the middle of the year. The summer rally peaked in mid-August around 4,325, and the market then resumed falling to a lower low in October. That peak was described at the time, and afterwards, as the 50% retracement of the decline, as the 61.8% retracement of the decline, and as the 200-day moving average. All 3 explanations were published. They cannot all be the reason, and the arithmetic shows the actual retracement fell between the 50% and 61.8% lines rather than at either. the exact intraday peak on 16 August 2022 and the exact retracement percentage. The general point stands regardless of the decimals: when several incompatible tools all claim the same turn, none of them predicted it.
3. The NIFTY 50, September 2024 to April 2025 (India) — the level was found afterwards The index reached about 26,277 in late September 2024 and fell to about 21,743 by early April 2025. The low sits close to the 23.6% retracement of the entire 2020 to 2024 advance, as shown in the demonstration above. It also sits close to a round number, and close to price zones from 2024 where large volume had traded. Anybody could pick whichever of those explanations they preferred, after the event. Nobody published the 23.6% level as the target in September 2024, because in September 2024 there were 40 other candidate levels with equal claim. every price and date in this case.
The question that resolves it
A novice looks at a Fibonacci level and asks: did price react there?
An expert asks: how many other levels were within 1% of that price, and would I have chosen this one in advance?
The second question is answerable, it takes 30 seconds with a calculator, and it almost always dissolves the result. That is what a real test feels like.
What would make this wrong
This article makes a falsifiable claim, so here is exactly what would overturn it.
If Fibonacci levels carried information beyond crowding and beyond the ordinary depth of pullbacks, then a fixed rule — anchor points chosen by a stated algorithm, tolerance fixed in advance, applied across hundreds of instruments and several decades — would show price turning at 61.8% significantly more often than at randomly chosen prices in the same band, and more often than at 47% or 65%. Published attempts of this kind have generally not found such an edge. If a careful, pre-registered study did find one, this article would be wrong and should be rewritten. whether any recent peer-reviewed study of this design exists; the literature is thin and mostly negative.
Three honest limits on the criticism itself.
First, "no mechanism has been found" is not the same as "no mechanism exists." It is, however, the correct default, and the burden of proof sits with the person selling the course.
Second, self-fulfilment is a real effect and this article does not deny it. If millions of traders place orders at the 61.8% line, orders are there. That justifies watching the level. It does not justify the mystical story, and it means the effect can fade whenever the crowd's attention moves.
Third, using the tool as a ruler is genuinely useful and this article recommends it. Criticising the forecast is not criticising the arithmetic.
In India
Fibonacci levels are quoted constantly in Indian market commentary, on television and in broker research notes, usually on the NIFTY 50 and BANK NIFTY. Three Indian specifics matter.
The levels are often reported without the anchor. A note will say "support at the 61.8% retracement" and not state which swing high and swing low were used. Without the anchor, the number cannot be checked or reproduced. Ask for the anchor. If it is not given, the level is an assertion.
Index option strikes crowd the same region. NIFTY 50 strikes are listed at 50-point intervals. On a 4,000-point range, the retracement levels are spaced roughly 500 to 700 points apart, which means each one has 10 or more strikes within a few hundred points. Any retracement level will sit near some strike. When a level and a high open interest strike coincide, the strike is the one with a hedging mechanism behind it. Give the credit to the strike. current NIFTY 50 strike intervals and weekly expiry schedules, which SEBI and the exchanges have revised repeatedly.
Indian share prices span a very wide range of magnitudes. A retracement level on a ₹40 stock may be 30 paise away from the next level, which is inside a single tick for many stocks. Precision that is finer than the tick size is not precision.
There is also a pleasant historical fact worth knowing, given how the tool is usually sold. The sequence was described in Indian mathematics, in the study of Sanskrit prosody, several hundred years before Liber Abaci. Virahanka and later Hemachandra worked out the counting rule for arrangements of long and short syllables and produced the same numbers. the dates. It is a genuine piece of Indian mathematical history and it has exactly as much to do with the NIFTY 50 as the rabbits did.
In the United States
The tool is equally common in US markets and the surrounding material is equally uncritical. Three US specifics.
Competing tools crowd the same prices. US commentary uses the 50-day and 200-day moving averages very heavily, and those averages frequently sit in the same region as a retracement level during a pullback. When price turns there, you will see both explanations published on the same afternoon. The August 2022 case above is the clearest recent example.
Extension levels are used as headline targets. A great deal of US technical commentary quotes a 161.8% extension as a price target for an index. Remember that this is a multiplication of a range you selected, projected into a region where no trading has occurred. It has no order book behind it.
Policy events, not levels, cause most large US turns. The sharp reversal in US indices in April 2025 followed a specific announcement on a specific afternoon. Levels near the low were credited afterwards. The turn was caused by new information arriving at a known time, which is a different kind of explanation altogether. the exact dates and index levels of the April 2025 low and reversal.
Where they differ, and what that tells you
The tool is identical in both markets, so the honest difference is in the surrounding structure, and it points in a useful direction.
In the United States, the levels most often competing with a Fibonacci line are moving averages, which are also drawings with no mechanism. Two decorations agreeing with each other is not confirmation.
In India, the levels most often competing with a Fibonacci line are option strikes with very large open interest, and those do have a mechanism: somebody must hedge. So an Indian trader has an unusually clean way to settle the question. When a retracement level and a high open interest strike sit close together, watch what happens as expiry approaches. The hedging flow is observable, and the open interest is published free on the NSE option chain, updated through the session.
What that tells you is a habit worth building. Whenever 2 levels coincide, ask which of the 2 has somebody obliged to trade at it. A strike with large open interest near expiry has hedgers who must act. A round number has limit orders that people genuinely typed. A retracement ratio has nobody under any obligation at all. Confluence is only worth something when at least 1 of the things converging is real, and the Indian market makes it unusually easy to see which one that is.
Carry this
- No mechanism is known. The levels work partly because many people watch them.
- The 50% level is not a Fibonacci ratio, and it is the one traders trust most.
- Use the tool as a ruler for measuring pullback depth, never as a forecast.