# Rate of Change (ROC) Indicator: Definition and Formula

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> **Definition**
>
> The Rate of Change (ROC) is a momentum indicator that measures the speed at which prices are changing by determining the percentage change over a specified time period.

## What Is the Rate of Change (ROC) Indicator?

The Rate of Change (ROC) is a [momentum oscillator](https://www.investopedia.com/articles/active-trading/041814/four-most-commonlyused-indicators-trend-trading.asp) that calculates the speed of price changes. It is used primarily to identify overbought and oversold conditions, but some analysts use it to confirm trends and identify possible reversals. With zero as its reference point, the ROC is positive when prices are rising and negative when they're falling.

What determines overbought and oversold readings will depend on the volatility of the security being analyzed as well as the number of time periods chosen as the look-back period. [Divergences](https://www.investopedia.com/terms/d/divergence.asp) in between the ROC and price can also provide insights into trend strength.

### Key Takeaways

*   The Rate of Change (ROC) is a momentum oscillator that expresses the percentage change in a security's price over a chosen time period.
*   A positive ROC reading reflects a rising trend and upward momentum, while a negative ROC reflects a downtrend and downward momentum.
*   You can't rely on standardized readings for overbought and oversold. They will differ for different securities.
*   The optimum time period depends on trading style and holding period. Shorter time periods make the ROC more sensitive, while longer periods smooth out the noise.
*   Divergences and zero-line crossovers can signal reversals but also cause whiplash. Confirmation is needed.

![Image](https://www.investopedia.com/thmb/zWJirs_3IeqQfrkbvis608wq8gM=/1500x0/filters:no_upscale():max_bytes(150000):strip_icc()/dotdash_INV-final-Price-Rate-Of-Change-Indicator-ROC-June-2021-01-5224c778d19d411498cdfbddf3cd44b1.jpg)

*— Image by Sabrina Jiang © Investopedia 2021*

## Formula for the ROC

The formula to calculate the ROC is straightforward. It involves calculating the percentage change over a given period. This change is then plotted each day. (Most trading platforms include ROC among their standard indicators.)  

$\begin{aligned}&\text{ROC}=\bigg[\frac{\text{Today's Closing Price}-\text{Closing Price }n\text{ periods ago}}{\text{Closing Price }n\text{ periods ago}}\bigg] \times100\end{aligned}$

## Common ROC Lookback Periods

The main decision for traders using ROC is picking the appropriate lookback period (_n_). A trader should consider their holding period and trading style when making the decision.

*   _Shorter periods_ (e.g., 7-14 days) create a more sensitive indicator suitable for short-term trading, but can also produce false signals.
*   _Medium periods_ (e.g., 14-36 days) provide balanced sensitivity for swing trading.
*   _Longer periods_ (e.g., 36-200 days) create a smoother and more reliable indicator appropriate for identifying long-term trends, but opportunities take longer to manifest.

## Example ROC Calculation

Assume we're calculating a 10-day ROC for a stock:

*   _Current closing price_ (Day 10): $52.50
*   _Closing price 10 days ago_ (Day 0): $48.75

> ROC = \[(52.50-48.75) ÷ 48.75\] x 100 = \[3.75 ÷ 48.75\] x 100 = 7.69%

The stock's price has increased by roughly 7.7% over the 10-day period, suggesting positive momentum. If we were to calculate this value for each day in a series and plot the results, we would generate the complete ROC indicator line.

> **Tip**
>
> Selecting overbought and oversold thresholds on the ROC can be a challenge. Consider an individual security's volatility when doing so.

## Interpreting the ROC Indicator

The ROC indicator can be used to identify trends and price direction generally, but as an oscillator, it's best used to generate overbought and oversold signals, particularly in sideways markets. Like most indicators, it's best used alongside other technical analysis tools, especially those on the price chart, with one serving as confirmation of the other.

### Overbought and Oversold Conditions 

While many [oscillators](https://www.investopedia.com/terms/o/oscillator.asp) use standard levels to determine overbought and oversold—[RSI's](https://www.investopedia.com/terms/r/rsi.asp) 70 and 30, for example—with the ROC, it's more complicated. For one thing, the best reading for overbought and oversold will depend on the volatility of the underlying market. One security might be oversold at -5%, while another might reach oversold only at -15%.

Second, unlike many other oscillators, the ROC itself is not range-bound. That is, it has no upper limit, while its lower limit is reached only if the security's price goes to zero, so traders often use past price levels and ROC readings to decide whether a given market has reached an extreme level.

Thresholds should be chosen with both the security's volatility and ROC lookback period in mind:  

*   Examine the historical ROC data for a particular security throughout an extended period.
*   Examine historical price reversal patterns to establish upper and lower bounds.
*   Apply these levels to guide and inform your future trading choices.

Traders should understand that extreme ROC values do not necessarily mean immediate price reversals. Strongly trending markets frequently remain in [overbought](https://www.investopedia.com/terms/o/overbought.asp) or [oversold](https://www.investopedia.com/terms/o/oversold.asp) territory for long durations. It is best to wait for validation from price movement or other indicators before entering a trade.

### Center-Line Crossovers

A center-line crossover occurs when the indicator shifts from positive to negative territory, or vice versa. Generally, prices are considered rising when the ROC is in positive territory and falling when it isn't. A center-line, or zero-line, crossover can signal that a reversal is gaining momentum.

*   A bullish crossover appears when the ROC moves from below the zero line to above it, transitioning from bearish to bullish momentum.
*   A bearish crossover appears when the ROC moves from above the zero line to below it, transitioning from bullish to bearish momentum..

Zero-line crossovers deliver important trading signals yet require careful interpretation because choppy or range-bound markets can generate [false signals](https://www.investopedia.com/terms/f/false-signal.asp). Crossovers gain greater importance if they follow an extended movement in the opposite direction or if confirmed by other indicators.

### Divergence Signals

[Divergence](https://www.investopedia.com/ask/answers/05/052905.asp) occurs when the price and the ROC indicator move in opposite directions. Though it often signals a weakening trend and an impending [reversal](https://www.investopedia.com/terms/r/reversal.asp), divergence is better used as a warning sign for a potential reversal, rather than a definitive trigger.

*   **Bullish divergence** forms when price makes lower lows while the ROC makes higher lows, suggesting that bearish momentum [is waning](https://www.investopedia.com/articles/trading/04/012804.asp) despite continued price declines.
*   **Bearish divergence** appears when price makes higher highs while the ROC makes lower highs. This suggests that upward momentum is diminishing despite price advances.

To effectively use ROC divergences in trading:

1.  Identify clear price trends (either upward or downward).
2.  Look for contradictory movements in the ROC indicator.
3.  Confirm the divergence with additional technical tools or price action signals.
4.  Consider reducing position size or implementing tighter stop-losses when divergences appear.  
    

> **Tip**
>
> A falling ROC reading that remains in positive territory still reflects upward momentum, and vice versa.

## Limitations of the ROC Indicator

Despite its utility, the ROC indicator has several limitations that traders should consider:

1.  **Equal weighting**: The ROC formula gives equal weight to both the current price and the price "n" periods ago, disregarding the price action that occurred between these points. Applying an [exponential moving average](https://www.investopedia.com/ask/answers/122314/what-exponential-moving-average-ema-formula-and-how-ema-calculated.asp) can help attribute more weight to the current period.
2.  **Lagging nature**: As it is based on historical data, the ROC inherently contains a time lag, naturally delaying signal generation.
3.  **Scaling challenges**: The ROC can reach extreme values during quick, strong trends, making visual interpretation somewhat difficult without rescaling the chart.
4.  **Volatility sensitivity**: Securities with different volatility profiles require different interpretation frameworks, making standardized approaches problematic. High-volatility assets (e.g., cryptocurrencies) may require wider bands (e.g., ±20%), while stable stocks might use tighter thresholds (e.g., ±5%).

## Complimentary Indicators

As with any technical indicator, the ROC should never be used in isolation. Its greatest value comes when incorporated into a comprehensive trading system that includes other forms of analysis.

Traders often combine it with complementary technical tools:

1.  **Moving averages**: These can help confirm trend direction and filter out potential false ROC signals.
2.  **Support and resistance**: Combining ROC signals with key [support and resistance](https://www.investopedia.com/trading/support-and-resistance-basics/) levels enhances the probability of successful trades.
3.  **Volume indicators**: Volume confirmation of ROC signals provides additional evidence of momentum strength.
4.  **Volatility indicators**: These help contextualize ROC readings within the current market [volatility](https://www.investopedia.com/terms/v/volatility.asp) environment.
5.  **Pattern recognition**: [Chart patterns](https://www.investopedia.com/articles/technical/112601.asp) can provide confirmation of potential reversals signaled by the ROC.

A particularly effective approach involves using multiple timeframes, where the longer-term ROC establishes the primary trend direction while the shorter-term ROC lines identify potential entry and exit points within that larger trend.

## The Bottom Line

Traders use the Rate of Change indicator as a straightforward measure of price momentum and to spot potential trend changes. Its flexible nature enables it to function effectively across multiple time frames and markets. The ROC indicator shares common limitations inherent in technical analysis tools and performs optimally when integrated within a broader trading approach instead of being used alone.

> **Article Sources**
>
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>     
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