1. CLARIFY:
   1. Is it OK to focus on standard commercial flights (ex. not military flighters, freight flights, etc.)? Yes.
   2. Is it OK to exclude flights flying over the US to land in another country? Yes.
   3. Assume that we are discussing pre-COVID times when flying was more normal? Yes.
2. EQUATION: # of passengers in planes = # of planes in sky * average # of passengers / plane
3. BREAKDOWN UNKNOWNS: 
   1. # OF PLANES IN SKY:
      1. Total Airport Runways: Let’s assume there are 3 types of airports.

         1. Airport	# of Airports	# Runways on Average / Airport	Total Runways
            Major	10	4	10 * 4 = 40
            Medium	20	2	20 * 2 = 40
            Small	100	1	100 * 1 = 100

      2. # of Planes Flying throughout Day on 1 Runway:
         1. Let’s assume that planes arrive / leave the runway in the same manner across each airport type. We can split the flying behavior peak hours v. off peak hours.
         2. Let’s calculate the number of planes flying from an airport assuming it has 1 runway.

         3. Type of Behavior	Time	Hours / Day	Description	# of Planes / Hour	Total Planes / Day on 1 Runway
            Peak	6AM – 9 PM	15 hours / day	Plane flies every 5 min	60 minutes per hour / 5 minutes = 12 planes per hour	12 planes / hour * 15 hours = 180 planes / day during peak hours
            Off Peak	9PM – 6AM	9 hours / day	Plane flies every 15 min	60 minutes per hour / 15 minutes = 4 planes per hour	4 planes per hour * 9 hours / day = 36 planes during off peak hours

      3. Total # of Planes Flying throughout Day on All Runways:

         1. Airport Type	# of Runways	Total Planes on Peak All Day	Total Planes Off Peak All Day	Total Planes / Day
            Major	40	40 runways * 180 planes / day = 7200 planes	40 runways * 36 planes / day = 1440 planes	7200 + 1440 = 8640 planes per day
            Medium	40	40 runways * 180 planes / day = 7200 planes	40 runways * 36 planes / day = 1440 planes	7200 + 1440 = 8640 planes per day
            Small	100	100 runways * 180 planes / day = 18,000 planes	100 runways * 36 planes / day = 3600 planes	18,000 + 3600 = 21,600 planes per

      4. Total Planes Flying all Day: 8640 planes + 8640 planes + 21,600 planes = 38,880 planes in day
      5.  Average Total Planes Flying Now: 
         1. Let’s say of the 38,880 planes flying all day, the average flight is 3 hours – i.e. every 3 hours the planes land. There are 24 hours day / 3 hours flight = 8 intervals of planes flying and landing.
         2. The average number of planes in the air at any moment is equivalent to average number of planes that took off during the last 3 hours.
         3. At any point, there are 38,880 / 8 = 4860 planes in the sky now.
   2. # PASSENGERS IN SKY OVER US FLYING OFF:
      1. Let’s assume the average commercial flight has 120 people.
      2. Given that there are 4860 planes flying now, 4860 planes * 120 people / flight = 583,200 people in the sky at this minute over the US.

What passenger planes are in scope among commercial, personal, charter? Commercial

Are we including international flights in scope? Yes

There are 300 million people in US

Each person travels average 4 times in a year (assumption)

• Some don’t travel by flight
• Some travel once or twice
• Some travel 3 or 4 times
• Some travel 5 to 12 times
• Others travel more than 12 times a year

That translates to 1.2B passengers riding in a year

Number of passengers flying is uniformly distributed on all days (assumption)

That brings the daily rider volume to 1.2B riders / 365 days = 3.3M riders

Each ride takes an hour (assumption)

3.3M passengers flying are uniformly distributed during the 24 hrs (assumption)

So with 1 hr ride duration, there will be 3.3M / 24 = 137K passengers in the air at any time

If the average ride takes 2 hrs and not 1 hr then there will be twice that many passengers in the air, 137K * 2 = 275K

So at any time, there are 275K passengers in the air

Add 10% more people to account for international flight passengers (assumption)

The total passengers (domestic + intl) in the air at any given time is 275K + 27.5K = 302500 people in the air

The key to answering this estimation interview question is to think about what information you have (or can estimate), which can help you get to the answer. You need to be clear about your logic and assumptions, and be clear-minded enough to be able to sense-check the ultimate answer you arrive at.

First, I clarify the question – what is meant by “airplanes”? All planes, private jets, commercial flights only, military, fly-overs? And what is meant by “right now” – literally right this second? What is meant by “over the US”? Landmass only? Does this include ocean territory? What about Alaska and Hawaii?

I will assume that “airplanes” can be divided into four categories: commercial passenger, freight, small private and military. There will be other types (like charters and crop-dusters) but to simplify things I will leave them aside.

I assume that these flights are only those flying domestically or to an international destination (but still over the US). I will exclude planes flying over the US from one country to another.

I assume that “right this second” means 6.45pm.

I assume that “over the US” means over the landmass of the contiguous 48 states.

Then I look at each type of plane to look for drivers of the ultimate number.

For commercial passenger planes, I assume a good driver would be the number of airports in the USA. I assume there are:

10 giant airports
20 major airports
50 medium airports
100 small airports

Giant airports would have about 20 flights per hour taking off, 18 hours per day. So, about 360 flights per day. At any one time, perhaps 15 per cent of these flights would be in the air. I would assume that the average plane would contain 250 people. So, that’s 360 x 15% x 250 x 10 airports = 135 000 people.

Major airports would have about 10 flights per hour, 18 hours per day. Fifteen per cent would be in the air at any one time, with an average of 200 people on board. That’s 108 000 people.

Medium-sized airports would have about 10 flights per hour, 15 hours per day. Fifteen per cent would be in the air at any one time, with an average of 100 people on board. That’s 112 500 people.

Small airports would have about five flights per hour, 12 hours per day. Fifteen per cent would be in the air, with an average of 50 people on board. That’s 45 000 people.

Freight is trickier to estimate. I would estimate that there are an average of 100 cargo flights per major city in the US per day, and I’d estimate there are 200 major cities. Fifteen per cent of these flights would be in the air at any one time. They would have an average crew of five. That’s 15 000 people.

For small private planes, I’d say there is one private plane for every 500 head of population (300 million people), and that one per cent of these planes might be in the air at any one time, with an average of four people on board. That’s 600 000 x 1% x 4 = 24 000 people.

For military I am less sure. Let’s assume there are 10 000 military planes in the US (big and small). Let’s say five per cent are airborne at any one time with an average of 10 people aboard. That’s 5000 people.

Now I can add up all the people. The total equals 444 500 people in the air right now over the US.

To sense-check this, let me just divide by 200 (the average number on board a commercial airliner). That’s 2222 planes in the air, or 46 over each of the 48 states.

Hmm, this seems a bit on the high side, so I may have over-estimated somewhere. I can go back through my assumptions and calculations to see if I can trim the number a bit. However, I don’t think I’m far off.