Relative Strength Index (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.

Chart

Reference data (CSV) · Chart (SVG)

Chart metadata i

Outputs

• outReal: line · zero · positive · levels: 30, 70

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.

Notes

• While the input has not changed since the first bar the call reads, there is neither a gain nor a loss and RSI is 0/0: the output is the neutral 50. Up to 0.8.1 it was 0, which read as oversold. Input that has only risen gives 100 and input that has only fallen gives 0.
• After a move, an unchanged input holds the last value until the two averages decay to rounding residue: about a thousand unchanged bars at period 2, about ten thousand at period 14. The output then drifts and settles on 50. Input that had only risen or only fallen stays at 100 or 0, except at period 2.

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

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

☐ Can Output NaN or ±Inf
☐ Identity at Period 1
☐ Uses Transcendental
☐ Input Must Be Positive

Example

C

#include <stdio.h>
#include <ta_libc.h>

int n = 252;
double series[252]; /* your data, oldest first */
double out[252];
int outBegIdx, outNBElement;

TA_Initialize();
TA_RSI( 0, n - 1, series, 14, &outBegIdx, &outNBElement, out );
printf( "%d values from bar %d; last out = %f\n", outNBElement, outBegIdx, out[outNBElement - 1] );

Rust

use ta_lib::Core;

let series = vec![0.0; 252]; // your data, oldest first
let mut out = vec![0.0; 252];

let core = Core::new();
let range = core.rsi(0, series.len() - 1, &series, 14, &mut out)?;
println!("{} values from bar {}; last out = {}", range.count, range.beg_idx, out[range.count - 1]);

Java

import io.github.talib.Core;
import io.github.talib.OutRange;

double[] series = new double[252]; // your data, oldest first
double[] out = new double[252];

Core core = Core.DEFAULT;
OutRange r = core.rsi(0, series.length - 1, series, 14, out);
System.out.println(r.count() + " values from bar " + r.begIdx() + "; last out = " + out[r.count() - 1]);

C#

using System;
using TALib;

var series = new double[252]; // your data, oldest first
var outReal = new double[252];

var core = Core.Default;
OutRange r = core.Rsi(0, series.Length - 1, series, 14, outReal);
Console.WriteLine($"{r.Count} values from bar {r.BegIdx}; last outReal = {outReal[r.Count - 1]}");

TypeScript

import { rsi } from 'ta-lib';

const series = new Float64Array(252); // your data, oldest first

const { begIdx, values } = rsi(series, { timePeriod: 14 });
console.log(values.length + ' values from bar ' + begIdx + '; last values = ' + values[values.length - 1]);

Implementation

Added in 0.4.0.

TA-Lib Definition: rsi.c · rsi.yaml

Native	File
C	ta_RSI.c
Rust	rsi.rs
Java	Core_RSI.java
C#	Core_RSI.cs
TypeScript	rsi.ts

Python: talib.RSI, see ta-lib-python.

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

Aliases

relative strength index

See Also

CMO · STOCHRSI

References

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