How do we calculate cloud base?

I'm not sure exactly what you want with this question. The pilot never needs to 'calculate' the cloud base, the Met man does that. If you mean how is the cloud base expressed, it depends on the forecast you're reading. A Graphical Area Forecast gives cloud base above sea-level and an aerodrome forecast (TAF) or (TTF), gives cloud base above ground level.

See also AIP GEN 3.5 para 3.7.1

You can calculate the convective cloud base if you know the surface temp and dewpoint temperature.

Cloud Base in feet = (Air temperature at surface – dew point temperature at surface) x 400'

The calculated base will be the height above the surface observation.

If you grab an F160 you should be able to derive this formula for yourself.

Cloud base AGL

(Temp - dew point ) / 2.5 x 1000

word is its sneaking into the exams

Rising unsaturated air cools at about 3° per thousand feet and dew point temperature lapses at about 0.5° per thousand feet. So the difference between the rising air's temperature and dew point temperature reduces by about 2.5° per thousand feet of ascent.

So the approximate height of the cloud base above ground level can be calculated as:-

Cloud base in thousands of feet = (Surface air temperature - Surface dew point temperature) ÷ 2.5

For example, if the surface air temperature was 18°C and the surface dew point temperature was 6°C, the cloud base would be approximately 4800 feet.