The exponential moving average (EMA) is a weighted moving average (WMA) that gives more weighting, or importance, to recent price data than the simple moving average (SMA) does. The EMA responds more quickly to recent price changes than the SMA. The formula for calculating the EMA just involves using a multiplier and starting with the SMA.
[Note: Simple and exponential moving averages are just one form of technical analysis. Successful traders use many forms of technical analysis to make informed decisions. Investopedia's Technical Analysis course will show you how to use both chart patterns and technical indicators to identify opportunities and manage risk with over five hours of ondemand video, exercises and interactive content.]
The calculation for the SMA is very straightforward. The SMA for any given number of time periods is simply the sum of the closing prices for that number of time periods, divided by that same number. So, for example, a 10day SMA is just the sum of the closing prices for the past 10 days, divided by 10.
The three steps to calculating the EMA are:
 Calculate the SMA.
 Calculate the multiplier for weighting the EMA.
 Calculate the current EMA.
The mathematical formula, in this case for calculating a 10period EMA, looks like this:
SMA: 10period sum/10
Calculating the weighting multiplier: (2 / (selected time period + 1)) = (2 / (10 + 1)) = 0.1818 (18.18%)
Calculating the EMA: (Closing priceEMA (previous day)) x multiplier + EMA (previous day)
The weighting given to the most recent price is greater for a shorterperiod EMA than for a longerperiod EMA. For example, an 18.18% multiplier is applied to the most recent price data for a 10 EMA, whereas for a 20 EMA, only a 9.52% multiplier weighting is used. There are also slight variations of the EMA arrived at by using the open, high, low or median price instead of using the closing price.

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