The left hand side is the height above ground of the base of the clouds. Now the height of the cloud base comes out in meters, and we have demonstrated the simple formula that was the basis of your question. Thus, the height of the cloud base in feet is equal to the surface dew point depression expressed in degrees Fahrenheit multiplied by 228, not 222. The condition under which the formula holds is rather specialized. As long as the parcel and its surroundings have the same temperature, vertical motion is freely permitted and the air will be well mixed.
Vertical motion is inhibited.
Well-mixed conditions occur most frequently on hot summer afternoons, especially following a sunny morning. In dry climates where the heating is intense, this layer can become 10,000 feet deep. The air close to the ground is normally not well mixed at night or in the early morning. At those times, the formula does not apply. I calculated the dew point lapse rate dew under a variety of conditions from an equation given by Bohren and Albrecht.