Assembling the Average Directional Index from directional movement

What the Average Directional Index measures

The Average Directional Index is a smoothed ratio of directional movement that measures how strongly price is trending rather than which way it is going. It is assembled from ordered highs, lows, and closes, so the same steps can be repeated in a spreadsheet.

Editorial note: TradersWeek presents this construction as a transparent trend-strength filter for longer-horizon readers. That teaching angle is editorial and is not part of the historical workflow.

Split directional movement, then measure true range

Directional movement is first split into plus and minus components by comparing today's high-to-high change with today's low-to-low change and assigning the larger move, or zero if that move is not positive.

Plus directional movement is the upward high-to-high advance when it exceeds the downward low-to-low decline; otherwise it is zero. Minus directional movement is the downward low-to-low decline when it exceeds the upward high-to-high advance; otherwise it is zero.

True range is the largest of today's high-low span, the gap from yesterday's close to today's high, or the gap from yesterday's close to today's low. That range is the scale against which the later directional indicators are expressed.

Sum 14 periods, then smooth recursively

True range, plus directional movement, and minus directional movement are each summed over 14 periods, then recursively smoothed by subtracting one-fourteenth of the prior 14-period total and adding the newest observation.

Turn the smoothed totals into directional indicators, DX, and ADX

Plus and minus directional indicators are formed by expressing each 14-period smoothed directional-movement total as a percentage of the matching 14-period smoothed true range. A directional indicator is that 14-period smoothed directional movement expressed as a percentage of the matching smoothed true range. The original construction discards fractional remainders.

DX is one hundred times the absolute gap between the plus and minus directional indicators, divided by their sum. In the historical workflow that figure is the rounded percentage ratio of the absolute difference between the two directional indicators to their sum.

ADX is that DX series first averaged over 14 values and then recursively smoothed by weighting the prior ADX thirteen-fourteenths and adding one-fourteenth of today's DX.

A simple timing cue and a later confirmation

A 10-period and 40-period exponential moving-average pair can be read as a simple timing cue for the start of an uptrend or downtrend. That pair is a 10-period and 40-period exponential average whose cross is used as a simple start-or-end of trend timing cue. The historical workflow describes the cross as usable on every market and sampling interval.

Price-reversal formations are treated as confirmation after another indicator has already suggested a possible trend change, because those formations are said to appear less often than trends themselves change.

The same construction on longer bars

The same technical construction is presented as remaining valid from daily through weekly, monthly, quarterly, and occasionally yearly bars, with only the time and price scales growing larger. That multi-timeframe consistency means the same steps can be read on daily, weekly, monthly, or longer bars, with only the scale of time and price changing.

Weekly bars are preferred as a working staple because they reduce daily noise while producing earlier readings than a calendar-month close, which can only be evaluated after the month ends.