RSI

Summary

Wilder's Relative Strength Index, a momentum oscillator bounded 0-100 from the ratio of average gains to average losses over the period. Used to gauge overbought/oversold conditions. >70 overbought, <30 oversold.

Formula

\begin{aligned} U_t &= \max(X_t - X_{t-1},\ 0) & D_t &= \max(X_{t-1} - X_t,\ 0) \\[4pt] \overline{U}_t &= \begin{cases} \operatorname{SMA}(U, n)_t & \text{if } t = n \\[4pt] \dfrac{(n-1)\,\overline{U}_{t-1} + U_t}{n} & \text{if } t > n \end{cases} & \overline{D}_t &= \begin{cases} \operatorname{SMA}(D, n)_t & \text{if } t = n \\[4pt] \dfrac{(n-1)\,\overline{D}_{t-1} + D_t}{n} & \text{if } t > n \end{cases} \\[4pt] \mathrm{RS}_t &= \frac{\overline{U}_t}{\overline{D}_t} & \mathrm{RSI}_t &= 100 - \frac{100}{1 + \mathrm{RS}_t} \end{aligned}

where $X$ is the input series and $n$ the period.

Inputs

inReal — Price series (typically close)

Outputs

outReal — RSI value

Parameters

Parameter	Type	Default	Accepted values	Description
`optInTimePeriod`	integer	14	2–100000	Lookback for the gain/loss averaging

Properties

Numerical Stability: Initial Unstable Period

Display Flags
☐ Overlap Input
✅ Independent Y-Axis i
☐ Candlestick

Implementation

TA-Lib Definition: rsi.c · rsi.yaml

Native	File
C	`ta_RSI.c`
Rust	`rsi.rs`
Java	`Core_RSI.java`

TA-Lib is also available for Python, R and more using a wrapper.

Aliases

relative strength index

References

J. Welles Wilder, New Concepts in Technical Trading Systems, Trend Research (ISBN 0894590278)