RSI: Formula, Smoothing and Threshold Limits

Read the ratio behind the line

For each close-to-close change, record a gain when the change is positive and the absolute loss when it is negative. The other column receives zero. Divide the average gain by the average loss to obtain RS, then calculate RSI = 100 − 100 / (1 + RS). Fidelity explains the RSI formula and conventional thresholds.

Wilder-style smoothing commonly starts with simple averages and then updates each using (previous average × (n − 1) + current observation) / n. This carries information beyond the latest n bars. Replacing it with a fresh simple average changes the series even if both displays say “14.” Starting history and initialization therefore matter when comparing two platforms.

An original calculation

Assume a five-change seed window contains +2, −1, +3, −2 and +1 price units. Gains total 6 and losses total 3. Average gain is 1.2, average loss is 0.6, RS is 2 and RSI is 66.6667. Six closes are needed to create those five changes; confusing observations with differences creates an off-by-one error.

The next change is −1. Using the five-period smoothing convention, average gain becomes (1.2 × 4 + 0) / 5 = 0.96. Average loss becomes (0.6 × 4 + 1) / 5 = 0.68. RS is approximately 1.4118 and RSI is approximately 58.5366. This is a hypothetical arithmetic example, not a suggested five-period trading setting.

When the loss average is zero and gains are positive, the limiting RSI is 100. With positive losses and zero gains, it is zero. When both are zero, the ratio is undefined; platforms may choose a display convention. A completely flat price series therefore needs an explicit implementation rule rather than an unexplained division by zero.

Thresholds are descriptions, not obligations

The familiar 70 and 30 lines label relatively strong upward or downward momentum under a chosen lookback. They do not force the next bar to reverse. A persistent advance can repeatedly produce positive changes, keeping the ratio high. Calling that condition overbought does not measure how much any particular account has bought or whether its position must be liquidated.

A divergence also needs an objective definition: which two price pivots, how many bars confirm them, and which RSI values correspond to them? Selecting convenient pivots after a reversal imports hindsight. The comparison should be reproducible before it becomes a candidate rule.

Check the implementation before the interpretation

Write down symbol, timeframe, close source, lookback, smoothing and whether the most recent bar is complete. An open candle can change its RSI reading before the close. Compare a small exported sample against the calculation rather than trying to reconcile two screenshots by eye.

Contrast this gain/loss construction with the stochastic oscillator’s range position and Williams %R. If you turn a threshold into an order rule, use a cost-aware testing protocol and define exposure separately. Copying an executed trade does not copy the assumptions behind its indicator signal.