Indicator Formula

Technical Details — Average Directional Index (ADX)

Overview

The ADX is derived from the Directional Movement System. It measures trend strength by smoothing the ratio of directional movement to true range.

Key Concepts:

+DM/-DM: Directional movement (expanding highs vs expanding lows)
+DI/-DI: Directional indicators (normalized by ATR)
DX: Directional Index (ratio of directional difference)
ADX: Smoothed DX (the final trend strength value)

Mathematical Derivation

Step 1 — Calculate Directional Movement

Purpose: Determine if highs or lows are expanding.

$$+DM = High[t] - High[t-1] \text{ (if positive and > -DM, else 0)}$$ $$-DM = Low[t-1] - Low[t] \text{ (if positive and > +DM, else 0)}$$

What This Measures: Which direction price is expanding

Step 2 — Calculate DI Lines

Purpose: Normalize directional movement by ATR.

$$+DI = \frac{RMA(+DM, n)}{ATR(n)} \times 100$$ $$-DI = \frac{RMA(-DM, n)}{ATR(n)} \times 100$$

Where:

$$n$$ = DI period

What This Measures: Directional strength as percentage of range

Step 3 — Calculate ADX

Purpose: Smooth the directional index.

$$DX = \frac{|+DI - -DI|}{+DI + -DI} \times 100$$ $$ADX = RMA(DX, m)$$

Where:

$$m$$ = ADX smoothing period

What This Measures: Smoothed trend strength

Compact Formula Summary

$$+DI = RMA(+DM, n) / ATR(n) \times 100$$ $$-DI = RMA(-DM, n) / ATR(n) \times 100$$ $$DX = |+DI - -DI| / (+DI + -DI) \times 100$$ $$ADX = RMA(DX, m)$$

Complete Calculation Example

With DI Period = 14, ADX Period = 14: If +DI = 30 and -DI = 15: DX = |30-15|/(30+15) × 100 = 33.3 ADX smooths this over 14 bars, typically settling around 20-40 in trending markets.

Key Takeaways from the Example

Double Smoothing: ADX smooths already-smoothed DI values — very stable but laggy
Direction Blind: ADX of 40 could be a strong uptrend or strong downtrend
Typical Ranges: <20 = no trend, 20-25 = emerging trend, 25-50 = strong trend, >50 = extremely strong