A Fibonacci retracement calculator takes two prices — a swing high and a swing low that you choose — and divides the distance between them by a fixed set of fractions: 23.6%, 38.2%, 50%, 61.8% and 78.6%, with extensions beyond the far anchor at 127.2% and 161.8%. That is the entire operation. It is arithmetic on a distance, and this page performs it accurately in either direction and to whatever precision your instrument is quoted at.
Arb Digital publishes this in its free tools library beside the Fibonacci calculator, which generates the underlying number sequence itself rather than applying its ratios to prices, and the pivot point calculator, which derives levels from the previous session's high, low and close instead of from a chosen swing. Where the moving average calculator smooths a price series, this page divides a single distance. All of them describe past prices, and past price behaviour does not predict future prices.
What Is Actually Known About These Levels
This section comes first deliberately, because the rest of the page is arithmetic and this part is not.
The ratios used in Fibonacci retracement derive from a number sequence described by Leonardo of Pisa in 1202, in which each term is the sum of the two before it. The ratio of consecutive terms converges on 0.6180339887, the reciprocal of the golden ratio. That is a genuine and elegant mathematical fact. There is no established causal mechanism connecting it to the price of a security. No theory of market microstructure, corporate finance or economics predicts that a stock recovering from a fall should pause after retracing 61.8% of it rather than 57% or 65%.
These levels are, at the same time, extremely widely used. They appear on default chart software, in trading education and on the screens of a very large number of market participants. Whether they work is genuinely disputed, and the dispute is not settled. Academic tests of technical trading rules have produced results in both directions across different markets and different eras, and the studies that do find profitability generally also find it decaying over time as the rules become widely known.
There is a specific and well-documented reason why levels like these might appear to work without predicting anything: they may be self-fulfilling. If enough participants place orders at the same prices, transactions cluster there, and prices genuinely do behave differently around those levels — not because the ratio has meaning, but because the orders do. The Federal Reserve Bank of New York's staff report on currency orders and exchange-rate dynamics examined actual stop-loss and take-profit orders at a large foreign exchange dealing bank and found their requested execution rates strongly clustered at conventional levels, offering a microstructural explanation for technical analysis that requires no predictive power in the ratios at all.
The honest summary: the arithmetic below is exact, the ratios have no demonstrated causal link to price, the evidence on whether the levels predict anything is contested rather than conclusive, and any apparent effect may come from the crowd watching the same numbers. This page therefore describes what the arithmetic produces. It does not describe any level as support, as resistance that will hold, as an entry, or as a signal, because none of those claims can be made honestly.
How to Use It
- Choose the two anchors. A swing high and a swing low from the same move. This choice is subjective, which is the largest source of variation between two people running the same calculation on the same chart.
- Set the direction. An upward move places 0% at the high and 100% at the low, so levels are measured downward. A downward move reverses it. Getting this backwards produces a completely different set of prices.
- Set the decimal places to match the instrument. Two places suits most equities; four or five suits currency pairs, where rounding to two places would collapse several distinct levels into one number.
- Read the range figure first. If the swing you selected is small relative to normal daily movement, the levels sit within ordinary noise and the exercise is measuring randomness.
- Treat the output as a description, not a plan. The levels are where the fractions fall. Whether anything happens at them is a separate question this page does not answer.
The Formula and How It Is Calculated
Let H be the swing high, L the swing low, and R = H − L the range. For an upward move, where retracement is measured downward from the high:
Level(ratio) = H − (R × ratio)
For a downward move, where retracement is measured upward from the low:
Level(ratio) = L + (R × ratio)
The ratios themselves come from the sequence in a specific way. 0.618 is the limit of Fn ÷ Fn+1. 0.382 is 0.618 squared. 0.236 is 0.618 cubed. 0.786 is the square root of 0.618. The extension at 1.618 is the golden ratio itself, and 1.272 is its square root. 50% is not a Fibonacci ratio at all — it is a halving, inherited from Dow theory, which observed that moves often retrace about half their extent. It sits in the set purely by convention, and knowing that is a useful check on anyone presenting the whole group as mathematically unified.
Worked example, matching the values the page loads with. A swing high of 148.50 and a swing low of 96.25 give a range of 52.25. On an upward move the 23.6% level is 148.50 − (52.25 × 0.236) = 148.50 − 12.331 = 136.17. The 38.2% level is 148.50 − 19.9595 = 128.54. The 50% level is 148.50 − 26.125 = 122.38. The 61.8% level is 148.50 − 32.2905 = 116.21. The 78.6% level is 148.50 − 41.0685 = 107.43, and 100% returns to the low at 96.25. The extensions carry past it: 127.2% is 148.50 − 66.462 = 82.04 and 161.8% is 148.50 − 84.5405 = 63.96.
The Anchor Problem
Every level on this page depends entirely on two numbers you chose by eye, and that dependency is rarely acknowledged in discussions of the technique.
There is no rule that defines a swing high. Is it the highest intraday print, or the highest close? Over what window — twenty sessions, sixty, the whole year? Does a brief spike on thin volume count as a swing, or is it an outlier to be excluded? Two chartists looking at the same instrument on the same day will routinely select different anchors, and because every level is a fraction of the distance between them, different anchors produce entirely different sets of prices.
The effect is not marginal. Move the swing high by 5% and every retracement level moves. Use closing prices instead of intraday extremes and the whole grid shifts. Change the timeframe from daily to weekly and the anchors themselves change identity.
This creates an unfalsifiability problem that is worth naming. With enough plausible anchor pairs on the same chart, some Fibonacci level lands near almost any price. When a level "works", it is nearly always possible to find the anchors that make it so afterwards. Retrospective fitting of this kind is not evidence, and a technique that cannot fail a test also cannot pass one.
If you use these levels at all, the discipline that makes them at least checkable is to fix the anchor rule in advance — a stated timeframe, a stated definition of a swing, stated use of intraday or closing prices — and never adjust it to fit an outcome.
Retracements Versus Extensions
The two halves of the output are doing different things and are worth separating.
Retracement levels between 0% and 100% divide a move that has already completed. Every one of those prices was traded at some point during the move, so the calculation is entirely backward-looking: it partitions observed territory.
Extension levels beyond 100% — 127.2% and 161.8% here — project past the far anchor into prices that have not traded in this move at all. That is a categorically stronger claim. A retracement level says "this is 61.8% of the way back"; an extension says "this is 1.618 times the distance, in a direction the price has not gone". The first is a description of the past. The second is an extrapolation with nothing behind it but the ratio.
Both are computed here because both are conventional. But an extension level is not a price target, and the arithmetic that produces it carries no information about whether the price will reach it. The relevant honest framing is that extension levels are where the fractions land, and nothing more.
What This Page Deliberately Does Not Tell You
Most Fibonacci calculators are wrapped in language this one avoids, and the omissions are the point rather than an oversight.
It does not label any level "support" or "resistance". Those words describe a claim about future behaviour — that buying or selling will appear at a price — which the arithmetic cannot establish.
It does not identify entries, exits, stop placements or targets. Position sizing and risk are separate questions handled by separate arithmetic; the risk reward ratio calculator and the margin trading calculator deal with those explicitly, and neither depends on any view about whether a level means anything.
It does not describe confluence between levels as confirmation. Two techniques agreeing is not independent evidence when both are derived from the same price history.
And it makes no claim about probability. Short-term trading carries substantial risk of loss, and the US Securities and Exchange Commission's bulletin on margin rules for day trading sets out the specific account requirements and risks that apply to frequent trading in a margin account. Technical indicators of every kind describe past prices, and past behaviour does not predict future prices.
Arb Digital builds marketing analytics where the causal link between input and outcome is testable rather than assumed — attribution, experiments and reporting that survive scrutiny.
See Web Growth Services Talk to Arb DigitalCommon Mistakes to Avoid
- Reversing the direction — measuring down from the high when the move was downward produces a valid-looking grid of entirely wrong prices. Check which anchor holds 0%.
- Moving the anchors after the fact — refitting the swing so a level lines up with what already happened turns the exercise into curve-fitting and destroys any information it might have carried.
- Rounding away the difference — on a currency pair quoted to five decimals, rounding levels to two places merges several distinct prices into one and makes the output useless.
- Treating 50% as a Fibonacci ratio — it is a halving from Dow theory, not a term derived from the sequence. Presenting the set as mathematically unified is inaccurate.
- Reading confluence as confirmation — when two indicators built from the same price history agree, that is one piece of information counted twice, not two independent ones.
Related Free Tools From Arb Digital
Generate the sequence itself with the Fibonacci calculator, derive session levels a different way with the pivot point calculator, and smooth a price series with the moving average calculator or measure momentum with the RSI calculator. For the arithmetic of an actual position, the stock profit calculator works out the outcome of a completed trade and the risk reward ratio calculator compares intended loss against intended gain. Everything else sits in the free online tools hub.
Frequently Asked Questions
It measures the distance between a swing high and a swing low that you choose, then subtracts or adds fixed fractions of that distance to produce a set of prices. The fractions are conventionally 23.6%, 38.2%, 50%, 61.8% and 78.6%, with extensions at 127.2% and 161.8%. The whole operation is arithmetic on one distance.
There is no established causal link between the Fibonacci ratios and the price of any security, and no accepted evidence that these levels predict future prices. They are widely used and genuinely disputed. Studies of technical trading rules have reached conflicting conclusions, and those finding an effect often find it decaying as the rules become widely known.
Because they may be self-fulfilling. A very large number of participants watch the same levels on the same default chart settings, so orders cluster at those prices and transactions genuinely concentrate there. Research on actual currency orders at a dealing bank found exactly this clustering, which explains apparent effects without requiring the ratios to have any predictive content.
No. It is a simple halving inherited from Dow theory, which observed that moves often retrace roughly half their extent. It is included in the standard set purely by convention. The genuinely sequence-derived ratios are 23.6%, 38.2%, 61.8% and 78.6%, which are powers and roots of 0.618.
There is no objective rule, and this is the technique's largest weakness. Whether to use intraday extremes or closing prices, and over what timeframe, is a judgement. Because every level is a fraction of the distance between the two anchors, different choices produce entirely different level sets from the same chart.
A retracement level falls between the two anchors, dividing territory the price has already traded through. An extension projects beyond the far anchor into prices that have not been reached in this move. The first partitions observed history; the second extrapolates, and the arithmetic behind it carries no information about whether the price will get there.
This page makes no recommendation of any kind and describes no level as an entry, an exit or a stop placement. It computes where the fractions fall. What anyone does with that is a decision involving risk of loss, and it belongs with a licensed adviser rather than with a calculator.
The arithmetic works identically on any price series and any timeframe, because it is just division of a distance. Whether the resulting levels mean anything is the disputed question, and it is not resolved by the market or the timeframe. Technical indicators describe past prices, and past behaviour does not predict future prices.
This tool performs arithmetic on two prices you supply. It is not investment advice, not a trading recommendation, and no level it produces is a signal, a target, an entry or a price that will hold. Trading carries a real risk of losing money. Decisions about your money should involve a licensed financial adviser who is regulated to advise on them.
