The temperature–dewpoint spread and cloud base
As a parcel of air is lifted, it cools at about the dry adiabatic lapse rate (roughly 3 °C or 5.4 °F per 1,000 ft) while the dewpoint falls more slowly (about 0.5 °C or 1 °F per 1,000 ft). The spread therefore closes at about 2.5 °C, or 4.4 °F, per 1,000 ft. When the spread reaches zero, the air is saturated and a convective cloud base can form:
cloud base AGL (ft) ≈ (T − Td) in °C / 2.5 × 1,000
cloud base AGL (ft) ≈ (T − Td) in °F / 4.4 × 1,000
The 2.5 °C form is the same as the familiar “spread in °C × 400 feet.” The two unit conventions differ slightly (2.5 × 1.8 = 4.5, not 4.4); this page uses each in its own unit and also shows the 400 ft/°C rule of thumb. Field elevation is added to report an MSL height.
Relative humidity and freezing level
Relative humidity is computed from the Bolton (1980) / Magnus-Tetens vapor-pressure formula, es(t) = 6.112 exp(17.67 t / (t+243.5)) with t in °C, and RH = 100 × es(Td) / es(T). The freezing-level estimate is a straight-line lapse from the surface temperature: AGL = T°C / lapse × 1,000 ft. You can use the standard 2 °C/1,000 ft, the dry adiabatic 3 °C/1,000 ft, or a moist rate of about 1.5 °C/1,000 ft. If the estimated cloud base sits at or above the freezing level, the base is in sub-freezing air and icing in cloud is more likely — still only a flag, not a forecast.
Worked example
OAT 20 °C, dewpoint 12 °C, sea-level field, standard lapse:
- Spread = 8 °C. Cloud base ≈ 8 / 2.5 × 1,000 = 3,200 ft AGL (the 400 ft/°C rule gives the same 3,200 ft).
- Relative humidity is about 60%.
- Freezing level ≈ 20 / 2 × 1,000 = 10,000 ft AGL, well above this particular cloud base.
Frequently asked questions
How do you estimate cloud base from temperature and dewpoint?
Divide the spread by 2.5 °C (or 4.4 °F) per 1,000 ft. A 5 °C spread is about 2,000 ft AGL. It is an estimate for convective bases, not a ceiling forecast.
Should I use the Celsius or the Fahrenheit formula?
Use the one that matches your units. The two conventions differ slightly; this page computes both.
How is relative humidity related to the spread?
RH is the ratio of vapor pressure at the dewpoint to saturation vapor pressure at the temperature. A zero spread is 100% RH.
How do you estimate freezing level from the surface temperature?
Divide the surface °C by the lapse rate and multiply by 1,000 ft. Use a sounding or forecast for icing decisions.