Calculation: Exponential moving average

The EMA is a specific type of WMA that uses something called a “smoothing constant” to weight prices according to the following formula:

EMA = SC * P + (1 - SC) * EMA(yesterday)
where

SC = a smoothing constant between 0 and 1;

P = today’s closing price; and

EMA(yesterday) = the previous day’s EMA value.

You can approximate a particular SMA length for an EMA by using the following formula to calculate the equivalent smoothing constant:

SC = 2/(n + 1)
where

n = the number of days in a simple moving average of approximately equivalent length.

For example, a smoothing constant of .095 creates the EMA equivalent of a 20 day SMA, since 2/(20 + 1) = .095; a smoothing constant of .33 creates the EMA equivalent of a five-day SMA [2/(5 + 1) = .33]. The smaller the n is, the larger the constant; the larger the constant, the more impact the most recent price action will have on the EMA.