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# How to Calculate Exponential Moving Average (EMA)

Moving Average (MA) is one of the most popular Trend following Indicator used in Technical Analysis of Charts.

In 1909 G. U. Yule (Journal of the Royal Statistical Society, 72, 721-730) described the “instantaneous averages” R. H. Hooker calculated in 1901 as “moving-averages.”

Yule did not adopt the term in his textbook, but it entered circulation through W. I. King’s Elements of Statistical Method (1912).

But, MA lags!

Why? Because the MA indicator gives equal weight to all data used in its calculation.

The Exponential Moving Average (EMA) indicator is designed to improve on the MA indicator by giving more weight to the most recent price data, which is considered to be more relevant/useful than older data.

Since new data carries greater weight, the EMA responds more quickly to price changes than the MA.

P. N. (Pete) Haurlan was the first to use exponential smoothing for tracking stock prices in the early 1960s. Haurlan was an actual rocket scientist. He did not call them “exponential moving averages (EMAs)”. Instead he called them “Trend Values”!

Today, we are going to find out how this EMA indicator is calculated.

The formula for calculating Exponential Moving Average (EMA) is as follows –

EMA = [today’s price * K] + [EMA(of yesterday) * (1-K)

where,

K = 2 /(N+1)

N = number of days in the EMA (EMA length chosen by the trader) 1. Choose the EMA length (N) .. let’s say for example we want to calculate a 10 day EMA.

2. Calculate (K) for the length of the EMA (N) … [K= 2/(N+1)]

3. On the first day of our calculation we won’t be having the value of previous days EMA. So only for the first day we use the value of a Simple Moving Average(SMA) for our chosen EMA length (10 days in this case) - (by adding closing prices for previous 10 days and dividing the sum by 10).

4. On the 11th day, multiply the days closing price by K … then … multiply the previous day’s SMA(calculated in step 3.) by (1-K), and add the two. The result is the 10 day EMA.

5. Keep repeating step 4 on each subsequent day to obtain the latest value for your 10 day EMA.

## Conclusion

We all use Computer software / mobile apps for our chart analysis.

So, for us EMA IS CALCULATED AUTOMATICALLY.

But, for me, if I am going to use any tool in my Chart Analysis, then I always feel more in control if I know how it is calculated.

So, just in case, if you want to try calculating it manually, Click here to Calculate EMA

Also, you can check out manual calculation guides for MACD and Stochastic indicators.

How is MACD indicator calculated?

How is STOCHASTIC indicator calculated?

So, How do you use Indicators in your Technical Analysis?

Which is your favorite Indicator?

Let me know in your comments below.