GlossaryAverage Directional Index (ADX)

Average Directional Index (ADX)

The Average Directional Index measures how strong a trend is, regardless of its direction. The pane also shows the two directional lines +DI and −DI, which tell you whether upward or downward moves dominate. The system comes from J. Welles Wilder.

Calculation

$H_t$ , $L_t$ and $C_t$ are the high, low and close of a candle. $d$ is the DI length, $s$ the ADX smoothing. All smoothing is Wilder smoothing: the start value is the simple mean of the first $n$ values, and after that

\mathrm{RMA}^{(n)}_t(x) = \frac{(n-1)\,\mathrm{RMA}^{(n)}_{t-1}(x) + x_t}{n}

1. Directional movement. How far did the candle extend the previous high upward and the previous low downward?

u_t = H_t - H_{t-1}, \qquad v_t = L_{t-1} - L_t

{+\mathrm{DM}}_t = \begin{cases} u_t & \text{if } u_t > v_t \text{ and } u_t > 0 \\ 0 & \text{otherwise} \end{cases} \qquad {-\mathrm{DM}}_t = \begin{cases} v_t & \text{if } v_t > u_t \text{ and } v_t > 0 \\ 0 & \text{otherwise} \end{cases}

Only the larger of the two moves counts. An inside bar, which extends neither the high nor the low, counts on neither side. For the first candle, both are zero.

2. True Range as with the ATR:

\mathrm{TR}_t = \max\left(H_t - L_t,\ \lvert H_t - C_{t-1} \rvert,\ \lvert L_t - C_{t-1} \rvert\right)

3. Directional lines: the smoothed directional movement relative to the smoothed range:

{+\mathrm{DI}}_t = 100 \cdot \frac{\mathrm{RMA}^{(d)}_t(+\mathrm{DM})}{\mathrm{RMA}^{(d)}_t(\mathrm{TR})}, \qquad {-\mathrm{DI}}_t = 100 \cdot \frac{\mathrm{RMA}^{(d)}_t(-\mathrm{DM})}{\mathrm{RMA}^{(d)}_t(\mathrm{TR})}

4. DX: the distance between the two lines, relative to their sum:

\mathrm{DX}_t = 100 \cdot \frac{\lvert {+\mathrm{DI}}_t - {-\mathrm{DI}}_t \rvert}{{+\mathrm{DI}}_t + {-\mathrm{DI}}_t}

5. ADX: the smoothed DX:

\mathrm{ADX}_t = \mathrm{RMA}^{(s)}_t(\mathrm{DX})

Because smoothing is applied twice, the first ADX value only appears on candle $d + s - 1$ , which is candle 27 with the default settings.

How to read it

The ADX is the main line, orange from 25 and gray below that. +DI is green, −DI red. The scale runs from 0 to 100, with reference lines at 25 and 50.

Trend strength: Above 25 a trend is under way; below that the market tends to be directionless. Above 50 the trend is very strong. The threshold of 25 is Wilder's own.
Direction: The ADX itself has no direction. That is in the DI lines: +DI above −DI means upward moves dominate, −DI above +DI means downward moves do.
DI crossovers: When +DI crosses above the −DI line, the balance tips upward. This carries more weight if the ADX is rising at the same time or is above 25.
Rising or falling: A rising ADX means the trend is gaining strength, in whichever direction. A falling ADX after a high reading shows that the trend is tiring, even if the price keeps moving.

Settings

Setting	Default	Effect
DI length	14	Length $d$ of the smoothing of directional movement and True Range (1–50).
ADX smoothing	14	Length $s$ of the smoothing from DX to ADX (1–50).

Limitations

Because of the double smoothing, the ADX reacts late. By the time it crosses 25, a good part of the trend has often already played out.
In sideways phases, +DI and −DI often cross without a trend developing. Watch for a low ADX in those cases.
A very high ADX is not a reversal signal; it only describes a strong trend.