# Cloud Base Calculator

Created by Davide Borchia
Last updated: Sep 05, 2022

You can calculate the cloud base height using quick and simple formula. Our calculator will explain you how to find the altitude of the cloud base, both in Farhenheit and Celsius.
Other than calculate the cloud base from the temperature and the dew point, you will learn how to use the cloud base in the formula to calculate the cloud temperature, and some examples that will show you the formula of the cloud base in action.

## What is a cloud? And what is the cloud base?

Say it's a beautiful summer day, and in the distance, you see some slow, puffy clouds lazily moving against the blue sky. Those are stratocumulus, and you can expect some rain later.

But... what is a cloud? Clouds are suspensions (aerosols) of water vapor, ice crystals, and other materials which become visible and confined in a particular region of the sky. We can find clouds on Earth and many other planets and moons with an atmosphere (though their composition changes with it: Titan has methane clouds, for example).

Clouds form when an air parcel containing water vapor moves upward, reaching a point where the vapor condensate around small nucleation points. The tiny droplets are now a cloud.

Though ethereal and seemingly random, clouds follow rigid physical rules, particularly for their formation parameters. It's time to learn what is the cloud base. The cloud base is the lowest possible altitude at which a cloud can form in a given layer and region of the atmosphere. We will see the formula for the cloud base calculations in a moment.

The cloud base is what we see when the clouds are right above us: it may change in appearance from white to very dark gray depending on the cloud thickness (the thicker, the more sunlight is scattered in, the higher layers).

## How to calculate the cloud base from temperature and dew point

For every point on Earth's surface, we can calculate the corresponding cloud base where — theoretically — the formation of a cloud becomes possible.

The cloud base formula requires you to know:

To calculate the dew point:

• Measure the spread (the difference) between temperature and dew point at your altitude;
• If you are calculating the height of the cloud base in Farhenheit, divide by $4.4$ and multiply by $1,000$;
• If you are calculating the cloud base in Celsius, divide the difference by $10$ and multiply by $1,000$.
• The result is the height of the cloud base relative to your elevation. Add your height above sea level to obtain the height of the cloud base relative to the sea level.

Let's put in number the formula for the cloud base height. If we are calculating the height of the cloud base starting in Farhenheit, we use this equation:

$h_{\text{base}} \!=\! \frac{T-T_{\text{D}}}{4.4}\!\cdot\!1,\!000 + h_{\text{ele}}$

Where:

• $T$ — The temperature at the station;
• $T_{\text{D}}$ — The dew point temperature;
• $h_{\text{base}}$ — The height of the cloud base; and
• $h_{\text{ele}}$ — The elevation of the station.

If you use Celsius, we calculate the cloud base height's formula this way:

$h_{\text{base}} \!=\! \frac{T-T_{\text{D}}}{10}\!\cdot\!1,\!247 + h_{\text{ele}}$

Clouds happen when the temperature and the dew point's temperature are the same. When this condition is satisfied, the water in the air can condensate. Starting from ground level, the two temperatures change according to two specific "rules":

• The temperature decreases by $5.4\ \degree\text{F}$ every $100\ \text{ft}$ of altitude ($0.984\ \degree\text{C}$ every $100\ \text{m}$);
• The dew point temperature changes a bit slowlier, with $1\ \degree\text{F}$ or $0.182\ \degree\text{C}$ in the same height intervals.

The spread reduces accordingly, with a rate of $4.4\ \degree\text{F}$ per $100\ \text{ft}$ or $0.802\ \degree\text{C}$ per $100\ \text{m}$. When the spread is $0$, we can find the bottom of our cloud.

🙋 Temperature conversions are notoriously hard to remember: use our temperature converter if you don't remember how to switch between Fahrenheit and Celsius!

Now that you know how to find the altitude of the cloud base, you can use this value to find the cloud temperature.

## Using the cloud base height to calculate the cloud temperature

The formula to calculate the cloud's temperature from the cloud base is:

$T_{\text{cloud}} = T - 5.4 \cdot \frac{h_{\text{base}}- h_{\text{ele}}}{1,\!000}$

If we measure the temperatures in Fahrenheit, and:

$T_{\text{cloud}} = T - 0.984 \cdot \frac{h_{\text{base}}- h_{\text{ele}}}{1,\!00}$

If we measure the temperature in Celsius.

🙋 Are you still interested in the science of our atmosphere? Visit our lightning distance calculator or our temperature at altitude calculator for other interesting facts and maths about the matter!

Davide Borchia
Temperature
°F
Dew point
°F
Elevation
ft
Cloud base altitude
ft
Cloud temperature
°F
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