Thinking in Millions — How to Conceptualize Numbers into the Millions, Billions, and Trillions
A word you hear a lot in the same sentence as funding, revenues, or dollars is “million”. It’s not large from a strictly mathematical or cosmological perspective, but arguably large from a conceptual one. I have a hard time visualizing even a few thousand of anything, so a mental trick for reframing large quantities is helpful for me in understanding such things. I’d argue that’s important for just about anything being dealt with at scale — if nothing else but for the sake of grasping the gravity of the numbers being discussed.
What does 1,000,000 look like?
To visualize a million of something, in general, it’s helpful to imagine a cube measuring 100 of that thing on each side. As you know volume is L × W × H, and 100 × 100 × 100 = 1,000,000. So for example, it turns out that 100 neatly stacked golf balls is 14 feet tall, so a million golf balls will perfectly fill a 14 × 14 × 14 ft cube (with no gap fill). That is to say, a million golf balls will fit in the average-sized master bedroom¹. That’s a million. This cube creates an image that can be translated again hundreds (or thousands) of times to sum to more millions.
In dollar terms, to visualize $1,000,000 we note that at a thickness of .0043 inches per bill, a stack of 10,000 × $100 bills equalling $1,000,000 would be 43 inches long. Split into two 21.5 inch stacks, a million dollars would fit inside a medium-sized briefcase.
What about 1 Billion?
To continue the golf ball example, we can imagine a 10 × 10 × 1 square of master bedrooms full of 100 million golf balls, or a 10 × 10 × 10 cube of master bedrooms as a billion golf balls. That’s 1,000 master bedrooms, each with 1 million golf balls. That’s a billion. Said another way, a billion golfballs would fit inside the Grand Central Terminal Main Concourse².
$1 Billion on the other hand would be one thousand 43 inch-long stacks of $100 bills. Noting that the width of a dollar bill is 2.61 inches and the length is 6.14 inches, a standard pallet measuring 40" by 48" would fit about 100 stacks of $1M (stacked vertically to a height of 43"), so a billion dollars would fit on ten standard pallets.
And finally, 1 Trillion?
Trillions extend into territory difficult to comprehend even using numerical gymnastics and convenient approximations. Nonetheless, it’s an interesting exercise and lends insight into the numbers used in Gross Domestic and World Product discussions. For example, the 2019 US GDP was $21.4T, and the 2019 GWP was $86.6T.
A trillion golf balls is…a lot. At a volume of 2.74 billion cubic feet, a trillion golf balls would fill the world’s 2nd largest domed structure, Dallas Cowboys Stadium, nearly 28 times over³.
And finally, we approximate a trillion dollars would fit on ten thousand standard 40" by 48" pallets. Put another way, $1T would cover a football field with full pallets of $100 bills…twice⁴.
Summary
1 Million golf balls would fit inside the average master bedroom.
1 Billion golf balls would fit inside Grand Central Terminal Main Concourse.
1 Trillion golf balls would fill Dallas Cowboys Stadium 27.7 times.
In $100 bills:
$1 Million would fill a briefcase.
$1 Billion would fit on ten standard pallets.
$1 Trillion would cover a football field to a depth of 7 feet.
Notes
¹ Using ball diameter d=1.68" and assuming no gap fill-in (still in the packaging, maybe) Avg Master Bedroom Volume= 309 sq ft floor × 8 ft height = 2472 ft³ ≈ 2744 ft³ = 14 × 14 × 14 ft³ million golf ball volume.
² GCT Main Concourse Volume = 200 ft L × 120 ft W × 120 ft H
³ Dallas Cowboys Stadium Volume = 104 million ft³, and 104 million ft³× 28 ≈ 14 × 14 × 14 ft³ × 1 million
⁴ Using field length 360 ft and width 160 ft, $1T/((360ft×12in/6.14in)×(160ft×12in/2.61in)×$100)×.0043in/12in = 6.92ft
If you liked this, follow me on Twitter @elitwilliams.
