The cloud base altitude is the minimum height at which a cloud can form. It is the point at which the (dry-bulb) temperature and dew-point temperature meet. If you know the temperature and the dew point temperature, the cloud base can be determined using the following equation:
(Dry-Bulb Temperature (ºC) - Dew Point Temperature (ºC))/8 = Cloud Base Altitude (km)
This came to me during an earth science test. I wasn't the first to come up with it, but I came up with it by myself. I swear!
Knowing that the dry adiabatic lapse rate is 10ºC per kilometer, and the dew point lapse rate is 2ºC per kilometer, I set up this equation:
Let T = Temperature in ºC
Let D = Dew Point Temperature in ºC
Let X = Cloud Base Altitude in Kilometers
Step 1) T - 10X = D - 2X
Step 2) + 10X +10X
Step 3) T = D + 8X
Step 4) -D -D
Step 5) T - D = 8X
Step 6) /8 /8
(T-D)/8=X