## What Is the Moving Average Convergence Divergence (MACD)?

The moving average convergence divergence (MACD) is a popular technical momentum indicator, calculated for use with a variety of exponential moving averages (EMAs) and used to assess the power of price movement in a market.

### Key Takeaways

- Moving Average Convergence Divergence (MACD) is calculated by subtracting the 26-period exponential moving average (EMA) from the 12-period EMA.
- MACD triggers technical signals when it crosses above (to buy) or below (to sell) its signal line.
- The speed of crossovers is also taken as a signal of a market is overbought or oversold.
- MACD helps investors understand whether the bullish or bearish movement in the price is strengthening or weakening.

## Calculating MACD

There are several calculations involved in the creation of the total (MACD) indicator, all involving the use of exponential moving averages.

An EMA is calculated as follows:

- Calculate the simple moving average (SMA) for the chosen number of time periods. (The EMA uses an SMA as the previous period’s EMA to start its calculations.) To calculate a 12-period EMA, this would simply be the sum of the last 12 time periods, divided by 12.

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Weight Multiplier = K = 2/(n+1) where n = period

Weight Multiplier = K = 2/(n+1) where n = period

- Calculate the weighting multiplier using this equation:

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Calculate the 12 EMA sequentially as:

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left(Close – EMA_{previous~period}right)* 0.1538 + EMA_{previous~period}

(Close−EMAprevious period)∗0.1538+EMAprevious period

Putting together the MACD requires simply doing all of the following EMA calculations for any given market instrument (a stock, future, currency pair, or market index):

- Calculate a 12-period EMA of the price for the chosen time period.
- Calculate a 26-period EMA of the price for the chosen time period.
- Subtract the 26-period EMA from the 12-period EMA to create the MACD line.
- Calculate a nine-period EMA of the MACD line (the result obtained from step 3) to create the signal line.
- Subtract the signal line from the MACD line to create the histogram.

This nine-period EMA line is overlaid on a histogram that is created by subtracting the nine-period EMA from the result in step 3, which is called the MACD line, but it is not always visibly plotted on the MACD representation on a chart.

The MACD has a zero line to indicate positive and negative values. The MACD has a positive value whenever the 12-period EMA is above the 26-period EMA and a negative value when the 12-period EMA is below the 26-period EMA.

## The Bottom Line

The MACD uses exponential moving averages in sequence to produce a popular indicator of momentum, which allows technical traders to spot trends and reversals.