A cloud is made of droplets so small that thousands would fit across a millimeter. Most clouds never rain. To fall as rain, droplets must grow enormously, and you can measure how much with the volume of a sphere. The type of cloud and its temperature decide which of two growth processes does it.
Key idea
A typical cloud droplet has a radius of about 10 μm; a raindrop about 1 mm (1000 μm), 100 times wider. Volume grows as the cube of the radius, so one raindrop holds about $100^3 = 1{,}000{,}000$ cloud droplets. Drops grow by collision and coalescence (bigger drops fall faster, hit smaller ones and join them) or by the ice-crystal process (in clouds colder than 0 °C, ice crystals grow while the water droplets around them evaporate).
Why it works
A droplet 10 μm in radius falls only about a centimeter per second through still air, so even a gentle updraft holds it up, and it would evaporate long before it fell out of the cloud. A 2 mm raindrop falls about 6.5 m/s. So size is everything. In a cold cloud, vapor condenses onto ice more readily than onto water: at −10 °C, saturation over ice is about 10% lower than over water. Air that is just saturated for the water droplets is supersaturated for the ice crystals, so the crystals grow fast and the droplets shrink. The crystals become snowflakes heavy enough to fall, and many melt into rain on the way down. Much of the rain in the middle latitudes starts as snow high in the cloud.
Worked example: How many droplets?
How many cloud droplets of radius 10 μm make one raindrop of radius 1 mm?
- Same units: 1 mm = 1000 μm.
- Ratio of radii: $1000 \div 10 = 100$.
- Volume goes as the cube: $100^3 = 1{,}000{,}000$ droplets.
Answer: About a million
Worked example: A drizzle drop
A drizzle drop has a radius of 0.1 mm. How many 10 μm droplets does it hold?
- 0.1 mm = 100 μm, and $100 \div 10 = 10$.
- $10^3 = 1000$ droplets: a drizzle drop is still a thousand times smaller in volume than a raindrop.
Answer: About 1000
Worked example: Too slow to fall
A droplet falls about 1.2 cm/s. How long would it take to fall 1 km?
- 1 km = 100,000 cm.
- Time: $100{,}000 \div 1.2 \approx 83{,}000$ s, about 23 hours. It would evaporate in the drier air below the cloud long before.
Answer: About 23 hours
Common mistake
Thinking cloud droplets simply get heavy and fall. A droplet is so small that the slightest updraft holds it up, and in the dry air below the cloud it would evaporate in seconds to minutes. It must grow about 100 times wider, a million times in volume, before it can fall out as rain. Check: (R ÷ r)³ should come out near a million for real raindrops.