Relative Strength Index (RSI) Calculator
Understand how is rsi calculated with real-time math and visual plotting.
RSI Visual Momentum
Dynamic visualization of how is rsi calculated over the given sequence.
Step-by-Step Calculation Table
| Step | Price | Change | Gain | Loss | RSI |
|---|
What is How is RSI Calculated?
When traders ask how is rsi calculated, they are diving into the mechanics of the Relative Strength Index, a momentum oscillator developed by J. Welles Wilder Jr. It measures the speed and change of price movements on a scale from 0 to 100. Understanding how is rsi calculated is fundamental for technical analysts who want to identify overbought or oversold conditions in various markets.
Anyone involved in technical analysis should use this calculation to avoid entering trades at the peak of a trend. A common misconception is that RSI shows if a stock is "cheap" or "expensive." In reality, the RSI indicates momentum strength relative to its own history.
How is RSI Calculated Formula and Mathematical Explanation
The calculation is a two-part process involving an initial simple average and a subsequent smoothing technique. The core formula is:
Where RS = Average Gain / Average Loss
| Variable | Meaning | Unit | Typical Range |
|---|---|---|---|
| n | Lookback Period | Periods | 14 (Standard) |
| RS | Relative Strength | Ratio | 0 to ∞ |
| Avg Gain | Average of upward price changes | Currency/Points | Variable |
| Avg Loss | Average of downward price changes | Currency/Points | Variable |
The Smoothing Process
Wilder used a specific smoothing method to ensure the how is rsi calculated results remain stable over time. After the first 14-period average is found, the next averages are calculated as:
Average Gain = [(Previous Average Gain * 13) + Current Gain] / 14
Practical Examples (Real-World Use Cases)
Example 1: Stock Recovery
Imagine a stock trading at $100. Over 14 days, it has 9 days of $1 gains and 5 days of $0.50 losses. Total Gain = $9. Total Loss = $2.50. Initial Average Gain = 9/14 = 0.64. Initial Average Loss = 2.5/14 = 0.18. RS = 0.64 / 0.18 = 3.55. RSI = 100 – (100 / 4.55) = 78.02. This indicates an overbought condition.
Example 2: Crypto Volatility
In a volatile crypto market, if the average loss significantly outweighs the average gain over a 14-period lookback, the RS will be close to 0, leading the RSI to drop below 30, signaling an oversold state. This is exactly how is rsi calculated to assist in trading strategies.
How to Use This RSI Calculator
- Enter Period: Type your preferred lookback period (usually 14).
- Input Prices: Paste a series of closing prices separated by commas.
- Observe the Result: The main green box shows the current RSI.
- Analyze the Chart: View the trend line to see momentum shifts.
- Review the Table: Check the "Step-by-Step" section to see the exact gain/loss breakdown for every period.
Key Factors That Affect How is RSI Calculated Results
- Lookback Period: Shorter periods (e.g., 9) make the RSI more sensitive, while longer periods (e.g., 25) make it smoother but lagging.
- Price Volatility: Sudden large price gaps significantly impact the how is rsi calculated output due to the smoothing factor.
- Data Quality: Missing or incorrect closing prices will yield inaccurate RS values.
- Smoothing Technique: While Wilder's method is standard, some platforms use simple moving averages, which changes the result.
- Timeframe: RSI on a 5-minute chart behaves differently than on a weekly chart.
- Market Context: In strong trending markets, RSI can remain overbought or oversold for extended periods.
Frequently Asked Questions (FAQ)
- Can RSI be above 100?
- No, the mathematical structure of the how is rsi calculated formula limits the output between 0 and 100.
- Why is 14 the default period?
- Wilder originally proposed 14 days as it represented half of a lunar cycle, which he believed influenced market sentiment.
- What does RS mean in the formula?
- RS stands for Relative Strength, which is simply the ratio of average gains to average losses.
- Is RSI better than MACD?
- They measure different things. RSI measures price velocity, while momentum indicators like MACD measure the relationship between moving averages.
- How many data points do I need?
- Technically, you need n+1 points for one RSI value, but more are recommended to allow the smoothing to "settle."
- What is a divergence?
- A divergence occurs when the price makes a new high but the RSI does not, suggesting a trend reversal.
- Can I use this for Forex?
- Yes, how is rsi calculated applies to any asset class with closing prices, including Forex and Commodities.
- What are overbought and oversold levels?
- Typically, 70 is considered overbought and 30 is considered oversold.
Related Tools and Internal Resources
- Financial Modeling Guide – Learn how to build complex trading models.
- Stock Market Indicators – A comprehensive list of technical tools.
- Relative Strength Index Deep Dive – Advanced RSI strategies.
- Volatility Calculators – Tools to measure market risk.