**Exponential Moving Average Formula (Table of Contents)**

## What is the Exponential Moving Average Formula?

The Exponential Moving Average (EMA) is a type of a moving average that gives more weight to the recent data in comparison to the simple moving average and is also known as the exponentially weighted moving average. Giving more weight to the most recent data makes the EMA sensitive to the recent price changes. Calculating the EMA requires a multiplier and the calculation needs to start with a simple moving average.

EMA is a type of technical indicator that is used to get buy and sell indicators based on historical averages. Traders usually use 20 days, 30 days, 90 days and 200-day moving averages.

Formula –

**EMA Today = Price Today * (Smoothing / (1 + Days)) + EMA Yesterday * ( 1 – (Smoothing / (1 + Days))**

**Example of Exponential Moving Average Formula (With Excel Template)**

Let’s take an example to understand the calculation of the Exponential Moving Average Formula in a better manner.

Below we will look at different ways in which exponential moving average can be used. We can calculate the moving average for one day, in another example we look at how different weights impact the data and in the third example, we look at the volatility of data using moving average for three and seven years and exponential moving average assigning different weights.

#### Exponential Moving Average Formula – Example #1

**Let us understand this concept by looking at a simple example. Consider the price of a commodity for the next ten days. Let us calculate a 15 day EMA considering Day 1 as the oldest and D15 as the latest value.**

**Solution:**

First, we calculated the Moving average of three days. Then using the moving average we calculated the exponential moving average.

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Moving average is calculated as

Similarly, we will Calculate the below.

Exponential Moving Average is calculated as

Calculating as the same,

Similarly, Calculated as below.

Similarly, the calculation of the remaining days can be done.

#### Exponential Moving Average Formula – Example #2

**Let us use the below sales data, forecast revenue for periods April through July using trend projections and simple exponential smoothing. Let us calculate what length of moving average and smoothing constant works best.**

**Solution:**

In the above example, we have calculated the absolute change trend and moving average of two, three and four periods by taking the average using those periods. To calculate the exponential average using the smoothing method we have considered the alpha to be 0.6, 0.7 and 0.8. Using these as weights we have calculated the average.

**Step 1:**Calculate the moving average for two periods in March – SUM({12,15})/2**Step 2:**Calculate exponential moving average for March- 0.6*15+(1-0.6)*12

#### Exponential Moving Average Formula – Example #3

**Below are the years and the factory sales of a firm A. Let us calculate the ESV using 0.25 and 0.50 weights and plot a graph to understand these trends.**

**Solution:**

MA for three years is calculated by using the average function in excel similarly MA for seven-year is calculated. The exponential moving average for (W = .25) is calculated by giving 0.25 weight to the sales and 0.75 to the value obtained by exponential average. While ESV at 0.5 gives equal weight to both the sales and the value obtained by exponential average.

Calculating Moving Average 3years for the year 1971.

Similarly, calculate for all the years.

Calculating Moving Average 7years for the year 1973.

Similarly, calculate for all the years.

Calculating ESV (W=25) for the year 1970.

Calculating ESV (W=25) for the year 1971.

Calculating, Similar to all the remaining years.

Calculating ESV (W=50) for the year 1970.

Calculating ESV (W=50) for the year 1971.

Calculating, Similar to all the remaining years.

Take a close look at the above graph, we observe that the sales are very volatile when taken without any average while using the weights we can see that the lines have averaged out and are more smooth even when compared to the moving average.

### Explanation

The formula for Exponential Moving Average can be calculated by using the following steps:

**Step 1:** Calculate the Simple moving average for a particular period. The calculation of the simple moving average is quite straight forward. First, we simply find the closing prices of the stocks for a particular period. Then we divide the total sum of all these prices with the same number of period.

**Step 2:** Next calculate the multiplier for finding weights. This is calculated as ( 2 / ( time period + 1)). So if we want to calculate the moving average for 90 day period we will calculate the multiplier as ( 2/(90 + 1)) = 0.021.

**Step 3:** Now finally to calculate the EMA we will use the formula above – (Closing Price – EMA of the previous day) * multiplier + EMA of the previous day.

### Relevance and Use of Exponential Moving Average Formula

Exponential Moving Average is suited for markets that are trending. These EMA’s are used with other indicators to understand the trend. It is particularly important for traders and trending fast-moving markets.EMA is an important indicator for analyzing trends on commodities. EMA’s are also known to be prone to recency bias. However, there is still a conflict between the traders; if more emphasis should be given on old data or emphasis should be given on new data.

### Recommended Articles

This is a guide to Exponential Moving Average Formula. Here we discuss how to calculate the Exponential Moving Average along with practical examples. We also provide an Exponential Moving Average a downloadable excel template. You may also look at the following articles to learn more –