What is Exponential moving average (EMA) formula and how to calculate EMA?


Exponential moving average (EMA) is a weighted moving average (WMA) that gives more weight, or importance, to recent price data than the simple moving average (SMA) does. EMA reacts faster to price changes than the SMA. The formula for calculating EMA simply involves the use of a multiplier, and starting with the AGR.

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The calculation for the AGR is very simple. SPF for any given number of time periods is simply the sum of the closing prices for the number of time periods divided by the same number. For example, the 10-day SMA is simply the sum of the closing prices for the last 10 days divided by 10.

Three steps to calculate the EMA are:

  • To calculate the AGR.
  • Calculate the multiplier for the weighting of the EMA.
  • Calculate the current EMA.
  • Mathematical formula, in this case, to calculate a 10-period EMA looks like this:

    SMA: 10 period sum/10

    The calculating the weighting multiplier: (2/(time period selection + 1) ) = (2/(10 + 1) ) = 0.1818 (18.18%)

    The calculation of EMA: (closing price-EMA(previous day)) x multiplier + EMA(previous day)

    Weighting to reflect the most recent price more in a shorter period of EMA, the longer the period of EMA. For example, 18.18% multiplier applied to the most recent data during the 10 EMA, while the 20 EMA is used only 9.52% multiplier weighting. There is also a slight variation of the EMA profit using open, high, low or average price instead of closing price.

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