What RSI is

What the line is made of 

The input is a series of closing prices and nothing else. Each period's close is subtracted from the one before it, which produces a change that is either positive or negative. Every period therefore contributes to exactly one of two running lists: the list of gains, or the list of losses. A period that closed higher contributes its rise to the first list and a nought to the second. A period that closed lower contributes the size of its fall, stated as a positive quantity, to the second list and a nought to the first.

Those two lists are then averaged over a fixed number of recent periods, called the lookback, which is conventionally fourteen because that is the number the indicator was first published with. Dividing the average gain by the average loss produces a single ratio, and that ratio is what the whole construction is about. The final step converts the ratio onto the bounded scale, which is a presentational change rather than an analytical one.

It is worth being exact about what that construction throws away, because most misreadings of the indicator are misreadings of the discarded material. The order of the periods inside the window is discarded, so a window whose gains arrived first and a window whose gains arrived last average to the same pair of numbers. Everything that happened before the window is discarded entirely. The high and the low of each period are discarded too, since only closes are differenced, so a period that travelled a long way and returned contributes only the distance between its close and the previous one. What remains is two averages and the ratio between them.

The calculation, once through 

The arithmetic is short enough to follow by hand, and following it once removes most of the mystery from the line. The gains over the window are totalled and divided by the lookback. The losses are totalled and divided by the same lookback. The first average is divided by the second to give the ratio. The formula then subtracts from one hundred the result of dividing one hundred by one plus that ratio, and the number this leaves is the reading.

Only the first reading in a series is calculated that way. Every reading after it is conventionally produced by a smoothing step instead: the previous average is multiplied by one less than the lookback, the current period's contribution is added, and the total is divided by the lookback. The effect is that older periods fade out of the average gradually rather than dropping out of the window all at once, so a large single period keeps influencing the line long after it has passed. Some software instead recomputes a plain average over the last fourteen periods, and the two methods return different lines from identical prices.

What the scale from nought to one hundred represents 

The ratio itself has no ceiling. Average gain can be any multiple of average loss, and where a window contains no losing period at all the divisor is nought and the ratio is undefined. The final step exists to fold that unbounded quantity into a fixed range so that the same visual scale serves every instrument at every price. The scale therefore records one thing: the size of recent gains relative to the size of recent losses, over the chosen window, on the chosen price series.

Three points on the scale are structural rather than conventional. The midpoint is where the two averages are equal. The ceiling is where the window contains no losing period. The floor is where it contains no winning period. Everything between them is a compressed rendering of the ratio, and the compression is severe at both ends: the reading moves a long way for small changes in the ratio near the middle, and barely at all for large changes near the extremes.

Where the two thresholds came from 

Two horizontal lines are drawn across the panel by nearly every charting package, at seventy and at thirty, and they were proposed in the original published account of the indicator rather than derived from any test a reader can inspect. A reading above the upper line is conventionally labelled overbought. A reading below the lower line is conventionally labelled oversold.

Both words carry a strong implication that the arithmetic underneath them does not contain. Overbought sounds like a judgement that a price is too high, and oversold like a judgement that a price is too low. Neither reading knows anything about price levels. A reading above the upper line states that recent gains were large relative to recent losses over the last fourteen periods. A reading below the lower line states the reverse. The labels are names for regions of a scale, and the scale is a restatement of what has already happened.

The thresholds are also not fixed by anything. Some traditions widen them to eighty and twenty on instruments whose readings reach the extremes often, on the reasoning that a line crossed constantly divides nothing. Others narrow them in quiet conditions for the mirror reason. Others discard the pair entirely and treat only the midpoint as meaningful, on the reasoning that it is the one point on the scale with an unambiguous arithmetic definition. Each of those practices produces a different set of dates on the same chart, and the choice between them is a convention rather than a finding.

Why a reading can sit at an extreme for a long time 

This is the single most consequential property of the construction, and it follows directly from the arithmetic above rather than from any observation about markets. During a sustained move in one direction the window keeps refilling with periods that mostly went that way, so the average on one side stays large while the average on the other stays small, and the ratio stays high. The reading has a ceiling. Once the line is near it, further movement in the same direction cannot push it any higher, because there is no higher.

The consequence is that the largest and longest directional moves are precisely the conditions under which the reading pins itself at one end of the scale and stays there. An instrument can hold a reading above the upper line for weeks while price continues to rise, and hold a reading below the lower line for weeks while price continues to fall. That is not the indicator behaving unusually. It is the indicator behaving exactly as its formula requires.

A second and less obvious consequence is that the line can fall while price is still rising. The reading responds to the ratio of the averages, not to the direction of price, so a rise that continues at a slower pace than before produces a smaller average gain and therefore a lower reading, even though every closing price in the window is higher than the last.

What an extreme reading does not mean 

The reading is a summary of the fourteen periods behind it. Four things it does not contain are worth stating flatly, because the conventional labels invite each of them.

1. It does not say that a move is exhausted. Oversold describes the ratio of averages in the window that has just closed, and a window can be followed by another window exactly like it, and then by another.
2. It does not say that price is too high or too low. No price level enters the calculation at any point, only differences between consecutive closes, so the reading is identical for an instrument at any absolute price.
3. It does not say when a crossing back through a threshold will occur, or that one will occur at all within any period a reader is watching.
4. It does not say what price does after a crossing, in either direction or by any distance. This page publishes no figure for how often anything follows a crossing, and the omission is deliberate: any such figure would depend entirely on the lookback, the smoothing method, the threshold and the holding period chosen before the counting began, and moving any one of them moves the figure.

Divergence, and what it actually describes 

The most discussed pattern in the panel is a mismatch between the peaks on the price chart and the peaks on the line. Price reaches a higher high than its previous one, while the corresponding peak on the line is lower than its previous peak. Momentum traditions call this a divergence and describe it as a picture of an advance that covered more ground with less one sided pressure behind it.

Arithmetically that description is accurate and unremarkable. A lower peak on the line means only that in the window around the second high, average gains were smaller relative to average losses than they were around the first. A move can travel further while being interrupted more often, and the two peaks record exactly that. The description carries no further content than the arithmetic that produced it.

Three limits are usually stated by the practitioners who use the pattern most. There is no agreed rule for which two peaks are compared, so the same chart yields several divergences or none depending on which pairs are selected. Both peaks have to exist before the pattern can be identified, so it is visible only after the second one has formed and been left behind. And a divergence can persist across many successive peaks while price continues in the same direction throughout, which is why the phrase can turn up repeatedly on the same chart with nothing resembling a turn between the occurrences.

Where practitioners disagree 

The first disagreement is about the lookback. Fourteen is inherited rather than derived, and shortening it makes the line reach the extremes far more often while lengthening it makes the line reach them rarely. Neither version is a better description of the instrument. They are descriptions of different windows, and the practice of adjusting the lookback until the historical crossings look convincing is fitting the setting to the chart it will be judged on.

The second is about the input series. The published construction differences closing prices, and the argument for that is that a close is where trading in a period came to rest. Variants difference an average of the high, low and close instead, on the argument that a close is one transaction and the period contained many. The two produce visibly different lines from identical data, and there is no test on the chart that settles which one is the instrument's momentum.

The third and largest disagreement is about whether the panel adds anything at all. The sceptical account is that the line is a deterministic transformation of the same closes plotted above it, so every reading was already present in the price series, and that a bounded scale mostly makes strong moves look like extremes because it has nowhere else to put them. The answer from practitioners is that a bounded, comparable scale makes the pace of a move legible across instruments and periods in a way that raw prices do not, which is a claim about legibility rather than about prediction. Both positions are held by people who read charts for a living, and the honest statement is that the reading is a description of past closes whose predictive content is disputed, not established.