# Average directional movement index

The average directional movement index (ADX) was developed in 1978 by J. Welles Wilder as an indicator of trend strength in a series of prices of a financial instrument. ADX has become a widely used indicator for technical analysts, and is provided as a standard in collections of indicators offered by various trading platforms.

## Calculations

The ADX is a combination of two other indicators developed by Wilder, the positive directional indicator (abbreviated +DI) and negative directional indicator (-DI). The ADX combines them and smooths the result with a smoothed moving average.

To calculate +DI and -DI, one needs price data consisting of high, low, and closing prices each period (typically each day). One first calculates the directional movement (+DM and -DM):

UpMove = today's high − yesterday's high
DownMove = yesterday's low − today's low
if UpMove > DownMove and UpMove > 0, then +DM = UpMove, else +DM = 0
if DownMove > UpMove and DownMove > 0, then -DM = DownMove, else -DM = 0

After selecting the number of periods (Wilder used 14 days originally), +DI and -DI are:

+DI = 100 times the smoothed moving average of (+DM) divided by average true range
-DI = 100 times the smoothed moving average of (-DM) divided by average true range

The smoothed moving average is calculated over the number of periods selected, and the average true range is a smoothed average of the true ranges. Then:

ADX = 100 times the smoothed moving average of the absolute value of (+DI − -DI) divided by (+DI + -DI)

Variations of this calculation typically involve using different types of moving averages, such as an exponential moving average, a weighted moving average or an adaptive moving average.