The odds of hitting a plane on the way down

Drop from 50,000 feet at a random spot on Earth and you fall through every altitude where planes fly. Your chance of hitting one on the way down is about 1 in 90 million.

The question

Picture it. You're dropped from 50,000 feet, higher than airliners cruise, over a spot picked at random anywhere on Earth. On the way down you pass through every altitude a plane could be flying at. Sit in a busy airport and the sky feels crowded. So how likely is it that something is in your way?

The question is fun because it pits two huge numbers against each other. There are a lot of planes. There is also a lot of Earth. The answer depends on which one wins, and by how much.

How many planes, and how big

Start with the count. At any given moment there are about 15,000 planes in the air. That figure is modeled from Flightradar24's daily flight counts and how long a typical flight lasts, and checked against live data from the OpenSky Network.

Next, size. What matters is how much of the ground a plane covers when you look straight down at it: wings, body and tail. Call that its top-down area. Using the mix of aircraft types in OpenSky's data, the average plane in the sky covers about 290 square meters, or about 3,100 square feet. The range is wide:

A Cessna 172, the classic small trainer, covers about 270 square feet.
The average plane in the air covers about 3,100 square feet.
A Boeing 777-300ER, one of the biggest twin-engine jets, covers about 10,000 square feet.

Small planes pull the average down. Wide-body jets pull it up.

If every plane stood still

Now slide all 15,000 planes together, wingtip to wingtip, into one patch of sky.

15,000 × 3,100 sq ft ≈ 47 million sq ft ≈ 1.7 sq mi

That's about 800 American football fields, end zones included. It sounds like a lot. But the surface of Earth is about 197 million square miles, and oceans count, because a random drop can land anywhere.

If the planes were frozen in place, you would hit one only if your landing spot happened to sit under one. So your chance is just the share of Earth's surface that planes cover:

1.7 ÷ 197,000,000 ≈ 1 in 120 million

The unrounded figures give about 1 in 117 million. Either way, it's very unlikely.

Planes don't stand still

Real planes move. An airliner cruises at about 500 miles per hour, and you need time to fall through the band of sky where planes fly. While you fall, a plane can slide sideways into your path.

It helps to look at it from the plane's seat. From there, you aren't falling straight down. You're drifting back toward the nose on a slanted line. That means it isn't only the top of the plane that can hit you. The front of it can too. As it flies, its nose, wings and tail sweep through extra sky.

How much extra depends on the plane's head-on area times its speed, divided by how fast you're falling. For the planes in the sky, that adds about 30% to your chance:

117 million ÷ 1.3 ≈ 1 in 90 million

Compared with the lottery

For scale, the published odds of winning the Powerball jackpot with one ticket are 1 in 292,201,338. Divide that by 90 million and you get about 3.2. So you're roughly three times more likely to hit a plane on your way down than to win the Powerball jackpot.

Both numbers are tiny. The comparison just shows how tiny. A jackpot that millions of people play for is rarer than a collision that almost nobody has ever had to worry about.

What a typical drop looks like

The 1 in 90 million is the chance of an actual hit. Most of the time you wouldn't even come close. Planes cover a sliver of the sky, most of Earth is open ocean, and flights bunch up along busy routes. In a typical drop, the nearest plane is hundreds of miles away.

That last part is easy to check for yourself. The plane drop game on this site drops you at a random spot through a real snapshot of every plane OpenSky was tracking at one moment, then tells you which plane came closest and how far away it was. Try a few drops. You'll see why the odds are so long.