Overview

Developed by J. Welles Wilder Jr., ADX stands for average directional index. It is widely believed to confirm the presence of a price trend.

Formula

Calculating ADX is very involved. For greater clarification of any of the steps outlined, consult Wilder's book, New Concepts in Technical Trading Systems:

1. Calculate the current period's Directional Movement (DM)
   
   A = Today's High – Yesterday's High
   B = Yesterday's Low – Today's Low
   
   Depending upon the values of A and B, three possible scenarios are:

   Values	Scenarios
   Both A and B < 0	+DM=0, -DM=0
   A > B	+DM=A, -DM=0
   A < B	+DM=0, -DM=B

   
   Note: +DM and -DM are two components in the ultimate calculation of ADX. The positive and negative title, suggest highs and lows as opposed to positive and negative numbers.
    
2. Calculate the true range (TR), see ATR
   
   Wilder suggested using a period of 14 for calculations:
   • +DM14 = Wilder's exponential moving average* of +DM for 14 periods.
   • -DM14 = Wilder's exponential moving average* of -DM for 14 periods.
   • TR14 = Wilder's exponential moving average* of True Range for 14 periods.
3. Calculate the Directional Indicators
   
   Positive Directional Indicator (+DI14) = +DM14 divided by TR14
   Negative Directional Indicator (-DI14) = -DM14 divided by TR14
    
4. DI Difference = The absolute value of the difference between +DI14 and -DI14.
    
5. Directional Index (DX) = DI Difference divided by the sum of +DI14 and -DI14
    
6. ADX = EMA* of DX
   
   *Wilder calculated moving average differently, owing to the need for calculating averages quickly by hand. For example:
   

   Current +DM14 = 13/14 (Previous +DM14) + 1/14 (Current +DM).

   The first +DM14 value in the series, was simply the sum of the previous fourteen -DM14 values divided by 14 (SMA).