Estimated cloud base
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Rising air cools by about 3 °C per 1000 ft (dry adiabatic). Its dew point drops only by about 0.5 °C per 1000 ft. So the spread closes by about 2.5 °C per 1000 ft.
Where temperature and dew point meet, the air is saturated and the cloud starts: spread ÷ 2.5 × 1000 ft = spread × 400 ft (or about 125 m per °C).
Input
Practise: estimate the base
Mental arithmetic like in the pre-flight briefing. Within about 10 % (at least ±200 ft) counts as correct.
When the rule works and when it does not
The formula gives the base of cumulus clouds that form from air rising from the ground on a sunny day. It says nothing about stratus, frontal cloud, cloud that drifts in from elsewhere or cloud over the mountains. The reported cloud in METAR and TAF always wins.
Small spread: think fog
A spread of 3 °C or less, especially in the evening, at night and with little wind, means the air is close to saturation. Mist and fog can form quickly when the temperature drops a little more.
Watch the trend: a spread shrinking from one METAR to the next is an early warning.
AGL and AMSL
The formula gives the base above the ground where temperature and dew point were measured. For planning, add the aerodrome elevation to get the base above sea level, and compare with terrain and your cruise altitude.
Distance from cloud (VFR)
In airspace C, D and E (SERA) you need 1000 ft vertical and 1500 m horizontal distance from cloud. Plan your cruise altitude so that it stays at least 1000 ft below the base.
In airspace G at or below 3000 ft AMSL or 1000 ft above terrain (whichever is higher), clear of cloud and with the surface in sight may apply. Check the national rules.
During the day
As the ground warms up, the temperature rises faster than the dew point, the spread grows and the cumulus base rises during the day. Early morning cumulus is usually lower than in the afternoon.