How much does a single cloud weigh?
— Even a small puffy cloud carries the water weight of 100 elephants
A white cloud floats in the blue sky, fluffy and seemingly weightless. But do the maths, and even one small puffy cloud is thought to hold around 500 tonnes of water. And here's the truly surprising part: the air in that same patch of sky is roughly 2,000 times heavier than the cloud's water.
A clear autumn afternoon. You're lying on the grass in a park, looking up at the sky. Sheep-like white clouds drift slowly by.
Your child asks, "How many kilos does that cloud weigh?" It looks like cotton candy, so you're tempted to say "a few kilos, tops."
But a cloud is really just a mass of water droplets. Something that big must hold a serious amount of water. Let's actually count it up.
Just two numbers decide a cloud's weight
A cubic metre of air inside a cloud is thought to contain only about 0.5 grams of water droplets in total — half the weight of a small coin.
Even a small puffy cloud is roughly 1 kilometre wide, deep, and tall — the size of a billion one-cubic-metre boxes lined up together.
A tiny amount of water, multiplied by an enormous number: that's the secret behind a cloud's weight. Multiplying something small by something huge is exactly where human intuition tends to go wrong.
What happens when a billion half-coins add up
Standing inside a cloud, the one cubic metre of space right in front of you contains only about 0.5 grams of water. That's why getting caught in mountain fog doesn't soak you through.
But the whole cloud is a different story. A cube 1 kilometre on each side holds a billion one-cubic-metre boxes. A billion lots of 0.5 grams comes to 500 million grams — about 500 tonnes. Taking one elephant as 5 tonnes, that's roughly 100 elephants' worth.
Figure 1 shows the whole cloud on the left, and on the right, a single cubic-metre box cut out from inside it. A researcher at a US atmospheric research institute used the same reasoning to estimate that a single puffy cloud weighs "about 500,000 kilograms."
500 tonnes, so why doesn't it fall?
Look again at the bars on the right of Figure 1. Within that same one-cubic-metre box, the air alone weighs about 1 kilogram. At cloud height the air is a bit thinner than at ground level, but it's still about 2,000 times the water.
In other words, a cloud isn't so much "a lump of water floating in the sky" as "air with a tiny amount of water mixed in." The air making up one cloud comes to roughly 1 million tonnes. The 500 tonnes of water is just thinly scattered through it.
What's more, each water droplet is tiny — about a fifth the width of a human hair. Small droplets meet strong air resistance, so they're thought to fall at only about 1 centimetre per second. Below the cloud, an upward wind faster than that is constantly blowing. So the droplets get held up before they finish falling, or evaporate in the dry air lower down.
This mechanism is explained in detail in "Clouds are made of water, so why don't they fall?"
A summer thundercloud can top 10 kilometres in height and holds far more water droplets than a puffy cloud. A single thundercloud is said to contain anywhere from several hundred thousand tonnes to over a million tonnes of water. The reason a sudden downpour can turn a street into a river in minutes is that all this water falls in a very short time.
The more water there is per cubic metre, the harder it is for light to pass through. Clouds look dark before rain because they hold more water and are thicker. See "Why do rain clouds look dark?" for more.
Summary
A cloud's weight can be found by multiplying the water per cubic metre (about 0.5 grams) by the cloud's volume (about 1 billion cubic metres for a puffy cloud). The answer is roughly 500 tonnes — about 100 elephants' worth. The cloud stays afloat because the surrounding air is about 2,000 times heavier, and the water is just thinly dissolved within it.
Clouds don't float because they're light.
They're just thinly dissolved in air that's far heavier.
How clouds grow tall is covered in "Why do towering thunderclouds (cumulonimbus) grow so high?"
- On a clear day, pick a single puffy cloud floating in the sky. Compare it against a nearby mountain or building to guess its width.
- Assume the cloud's height (thickness) is about the same as its width. If the width is 500 metres, the volume is 500 × 500 × 500, or about 125 million cubic metres.
- Multiply that volume by 0.5 grams, then divide by 1 million to get tonnes. It's fun to guess "how many elephants" as a family.
Without knowing the distance to the cloud, you can't estimate its width either. Pick a cloud with some size reference nearby, such as one sitting near a mountain peak seen from its base, to make a better guess.
Want to know more? — Terms, formulas, and links to textbooksLabels show whether each part is junior-high, high-school, or university-level
- JHSCovered in junior-high school science
- HSCovered in high-school "Earth Science Basics" / "Physics Basics"
- HS+Advanced high-school content, or textbook sidebar material
- UnivNot covered in high school — university-level specialist content (meteorology, cloud physics)
- ResearchNot yet settled as "textbook fact" even at university — an active research question
JHSTerminology: this phenomenon has names
- Cloud droplet: a water droplet making up a cloud. Most are thought to have a radius around 0.01 millimetres.
- Liquid water content: the weight of cloud-droplet water per cubic metre of air. In puffy clouds this is thought to be roughly 0.2–1 gram.
- Cumulus cloud: a clear-edged, cotton-like cloud that floats on fine days. When it develops further, it becomes a cumulonimbus.
JHSHSChecking with a formula: the weight of water in one puffy cloud
Flip "density = mass ÷ volume" around and you get "mass = density × volume." Liquid water content is "the density of water within the cloud," so multiplying it by the cloud's volume gives the weight of the water.
| In symbols | M = w × V (V = L × L × L) |
| In words | Weight of water in cloud = weight of water per cubic metre (liquid water content) × cloud volume |
| Where it comes from | The definition of density (density = mass ÷ volume), solved for mass. The same formula gives the air's weight if you swap w for the air density ρ |
| M | Mass of water in the cloud (in grams, converted to tonnes later) |
| w | Liquid water content: mass of water per cubic metre of air (g/m³) |
| V | Cloud volume (m³); treated here as a cube with side L |
| ρ | Air density (kg/m³) |
| Side length L of puffy cloud | ~1000 m |
| Liquid water content w (typical for puffy clouds) | ~0.5 g/m³ |
| Air density ρ at 1–2km altitude | ~1 kg/m³ |
| Weight of one elephant (typical) | ~5 tonnes |
| Base area | 1000 × 1000 = 1000000 m² |
| Cloud volume V | 1000000 × 1000 = 1000000000 m³ |
| Weight of water M (grams) | 0.5 × 1000000000 = 500000000 g |
| Converting to tonnes | 500000000 ÷ 1000000 = 500 tonnes |
| Same volume of air (kilograms) | 1 × 1000000000 = 1000000000 kg |
| Converting air to tonnes | 1000000000 ÷ 1000 = 1000000 tonnes |
| How many times heavier is air than water | 1000000 ÷ 500 = 2000 times |
A single puffy cloud's water comes to about 500 tonnes. But the same volume of air is about 1 million tonnes — the water is only 1/2000th of that. The numbers show it isn't "a heavy cloud floating," but "heavy air with a tiny bit of water mixed in."
| How many elephants | 500 ÷ 5 = 100 |
| How many 2-litre bottles (2kg each) | 500000 ÷ 2 = 250000 bottles |
HSHS+Where does a cloud's water come from, and why that amount?
HSWhen moist air near the ground rises, the pressure drops, the air expands, and its temperature falls (adiabatic expansion). Once the temperature drops below the dew point, water vapour the air can no longer hold turns into cloud droplets. This is how cloud formation is taught in Earth Science Basics.
HS+Liquid water content depends on how much the rising air has cooled. The higher air rises, the more water vapour converts to liquid, so liquid water content tends to be higher toward the top of a cloud. In real clouds, though, mixing with surrounding dry air means the actual value comes in lower than the theoretical maximum.
UnivHow fast cloud droplets fall, and cloud physics
The falling speed of a sphere as small as a cloud droplet can be estimated with Stokes' law (the terminal velocity at which viscous drag balances gravity). Terminal velocity is proportional to the square of the radius, so a cloud droplet with a radius of 0.01 millimetres falls at around 1 centimetre per second, while a raindrop with a radius of 1 millimetre falls at several metres per second. Droplets only reach a size that can fall as rain after "collision-coalescence," where droplets collide and merge, and the "Bergeron process," where ice particles grow by taking up water vapour. These processes are studied in a field called cloud physics.
📖 For the derivation of the formula and further reading: Stokes' law (Japanese Wikipedia) / Terminal velocity (Japanese Wikipedia)
ResearchWhat isn't fully understood yet
- How water is distributed inside a cloud Liquid water content varies greatly from place to place within a cloud. Accurately measuring a single cloud's total water requires combining aircraft and radar observations, and measurement methods are still being refined.
- Mixing with dry air When dry air mixes in at a cloud's edges, how the droplets evaporate and how the cloud's lifespan changes are both difficult to reproduce even in computer simulations.
- Clouds and climate How much water a cloud holds affects how much sunlight it reflects. How that amount of water will change under warming remains one of the biggest uncertainties in climate projections.
In other words, this article too reflects "our best current understanding." The figure of 500 tonnes is an estimate based on typical values for cloud size and liquid water content.
Links to textbooks (by level)
| Level | Subject/Unit | Where in this article |
|---|---|---|
| JHS | Science: density / weather changes (how clouds form) | The calculation of cloud weight via mass = density × volume |
| HS | Earth Science Basics: atmospheric structure and cloud formation | How cloud droplets form via adiabatic expansion and the dew point |
| HS+ | Earth Science: the water cycle in the atmosphere (advanced) | How liquid water content changes with altitude and mixing |
| Univ | Meteorology, cloud physics, fluid dynamics | Stokes' law, terminal velocity, collision-coalescence |
| Research | Cloud observation, numerical modelling, climate prediction | The distribution of liquid water content and its effect on climate |
| — | Everyday connections | How downpours fall, reading the weather by looking at the sky |
- Japan Meteorological Agency, "Frequently Asked Questions on Weather Observation, Clouds and Precipitation" (気象庁)
- Cumulus cloud (積雲, Japanese Wikipedia)
- Yoshimitsu Ogura, General Meteorology, 2nd revised edition (一般気象学、東京大学出版会), University of Tokyo Press
- R. R. Rogers, M. K. Yau "A Short Course in Cloud Physics" 3rd ed., Pergamon Press
- Peggy LeMone of the US National Center for Atmospheric Research (NCAR/UCAR), estimate of the weight of a single cumulus cloud (widely cited in general-audience explanations)
*This article is a general-audience science explainer. The figures given are approximate, meant to illustrate the underlying mechanism. Cloud size and liquid water content vary widely from cloud to cloud.