How this instrument works
The Relative Strength Index converts a ratio into a fixed scale. Relative strength (RS) itself is just average gain divided by average loss over a lookback window — typically Wilder's original 14 periods — and that ratio alone runs from zero to infinity, which makes it awkward to read at a glance or compare across instruments. The transform RSI = 100 − 100 ⁄ (1 + RS) squeezes any RS value into a fixed 0-to-100 band, with 50 marking the point where average gains and losses are exactly equal — RS = 1 — and larger or smaller gains pulling the reading toward one end without ever touching it.
J. Welles Wilder introduced the index in 1978 to measure the speed of price change, not price itself — two instruments can post an identical percentage move over a period and still show different RSI readings if one climbed steadily while the other lurched. Wilder's own average gain and average loss are not simple period averages either: after the first 14-period calculation, each new average blends in the latest gain or loss while carrying forward most of the prior average, a smoothing method sometimes called Wilder smoothing that this instrument's two input fields already assume you have produced upstream.
Momentum and swing traders read the resulting number against two conventional thresholds — above 70 as overbought, below 30 as oversold — to flag a move that has run further or faster than its own recent history. Wilder described those lines as a guide for a ranging market, not a trigger: during a strong trend RSI can sit above 70 for weeks while price keeps climbing, and treating the threshold as an automatic sell signal is the single most common misreading of the indicator.
- Enter the Average gain over the period — the smoothed average of up-moves over your chosen lookback window, typically 14 periods.
- Enter the Average loss over the period — the smoothed average of down-moves over that same window, entered as a positive number.
- Read Relative strength (RS) — the ratio of the two, recalculated the instant either input changes.
- Read Relative Strength Index (RSI) — the same ratio rescaled onto the fixed 0-to-100 index.
- Compare the RSI reading against the conventional 70 and 30 thresholds to see whether momentum looks stretched in either direction.
Worked example — an RSI of 65.22
Take an average gain of 1.5 against an average loss of 0.8 over the lookback period — the same units Wilder used, typically 14 days of price change. Dividing gives RS = 1.5 ⁄ 0.8 = 1.875: gains have been running nearly twice as large as losses over the window, before the ratio is rescaled onto the fixed 0-to-100 index.
Feeding that RS into RSI = 100 − 100 ⁄ (1 + 1.875) returns 65.2173913043, roughly 65.22 on the standard reading. That sits below the conventional 70 overbought line but well above the neutral midpoint of 50, describing a market where up-moves have dominated recent history without yet reaching the threshold traders watch most closely — a distinction the raw percentage change alone would not show.
Questions
Why does RSI use a ratio instead of just showing the percentage price change?
A percentage change over a period can only be compared to the identical asset over the identical window, but RS — and the RSI built from it — divides gain by loss, a shape that reads the same way whether the underlying instrument is a $5 stock or a $500 one. The 100 − 100 ⁄ (1 + RS) transform then fixes that ratio onto the same 0-to-100 scale for every instrument, which a raw percentage move never does.
Why isn't the average gain here just a simple average of the up days?
Because Wilder's original method smooths it. After the first 14-period average, each new period blends in the newest gain or loss while carrying forward most of the prior average — roughly 13 parts old average to 1 part new data — so one unusually large move nudges the average rather than resetting it. The Average gain over the period and Average loss over the period fields here expect that already-smoothed figure, not a raw arithmetic mean.
Is a reading above 70 always a sell signal and below 30 always a buy?
No — Wilder described those lines as guidance for a market moving sideways, not a fixed rule. In a strong uptrend RSI can hold above 70 for an extended stretch while price keeps rising, and selling the first overbought reading has cost traders a large part of the move. The threshold flags that momentum looks stretched, not that a reversal is imminent.
What counts as a bullish or bearish divergence on RSI?
A divergence is when price and RSI disagree about direction: price makes a new high while RSI makes a lower high (bearish), or price makes a new low while RSI makes a higher low (bullish). Neither this calculator nor the indicator itself times when that divergence resolves — it only flags that the two series have stopped confirming each other, which some traders treat as a signal worth watching more closely, not acting on alone.
Can RS ever be undefined or the calculator reject an input?
Yes — RS = average gain ⁄ average loss is undefined when the average loss is zero, since dividing by zero has no result, so this instrument requires Average loss over the period to be greater than zero. An average loss of exactly zero means every period in the window closed higher, a rare condition some charting platforms handle by capping RSI at 100 instead of leaving it undefined.
Does a longer or shorter lookback period change what RSI means?
Yes — Wilder's original 14 periods is the convention, but a shorter window such as 7 or 9 reacts faster to recent gains and losses and crosses 70 or 30 more often, while a longer one such as 21 or 25 smooths out more noise and stays inside the middle range longer. Neither is more correct; the choice trades responsiveness for stability, and the figures entered here should already reflect whichever window was chosen.
References
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