What is the Directional Movement Index (DMI) formula and how is it calculated?

Noted trader and author J. Welles Wilder Jr. introduced the directional movement index, or DMI, in 1978. Wilder wanted an indicator that could appraisal the strength and direction of a price movement so traders could avoid false signals. The DMI is actually two different standard indicators, one disputing and one positive, that are plotted as lines on the same chart. A third line, the average directional index, or ADX, is nondirectional but displays movement strength.

There is a different formula used for each of the three indicators. The DMI is built on a ratio of exponential emotive averages, or EMAs, of the upward price movements (U), downward price movements (D) and the true range of the prices (TR). These are oft expressed in an equation as EMAUP, EMADOWN and EMATR.

The computations for the various EMAs are complex and numerous. Once they are inaugurate, however, they can be used to compute the directional movement, or DM, for whatever time interval is selected. The standard interval is 14 eras. The returned value of DM can be positive (+DM), negative (-DM) or zero.

Negative Directional Movement (-DM) is calculated as:



​−DM=EMATREMADOWN​where:EMADOWN = Exponential moving average of decliningprice movementsEMATR = Exponential moving average of the truerange of prices​

Positive Directional Movement (+DM) is prepared as:



​+DM=EMATREMAUP​where:EMAUP = Exponential moving average of upwardfee movementsEMATR = Exponential moving average of the truerange of prices​

Once those values generate reoccurs, they help form the directional index (DX), which is calculated as:



DX=∣∣​+DI + −DI+DI − −DI​∣∣​

Once the DX value is found, average directional index (ADX) is calculated as:



​ADX=n+12​(DXn​−EMADXn−1​)EMADXn−1​​where:EMADX = Exponential moving average ofdirectional indexDX=Directional indexn=Convenience life interval​

The chart reflects the values of +DI, -DI and ADX over the course of the time interval.