visual representation of a billion

ACADEME BLOG

The blog of academe magazine, visualizing a billion and a trillion dollars.

BY MARTIN KICH

Any budget number can be made to sound exorbitant if doing so serves a political purpose. But the scope of our governmental budgets, as well as the scope of our economy, has long exceeded the ability of most of us to grasp the numbers—both viscerally and intellectually—in any meaningful way. Given the new administration’s penchant for making large numbers sound negligible and small numbers sound huge, it seems especially important for everyone to appreciate the differences between millions, billions, and trillions of dollars.

For instance the total spending on the NEA and the NEH in 2016 amount to just under $296 million, which sound like an enormous amount of money. But it is just .18% of the $4.1 trillion federal budget (that is, less than one fifth of one percent), and 1.97% to 1.18% of the projected $15 to $25 billion projected cost of constructing a wall along the border with Mexico.

The purpose of this short video is ostensibly to allow us to visualize the difference between a billion dollars and a trillion dollars, but I came away thinking that it actually highlights how nearly impossible it is for us to grasp the size of either number:

Here’s another video:

If the videos fall short, perhaps the following images will be more helpful—or, if not that, at least marginally less unhelpful:

https://www.labnol.org/internet/visualize-numbers-how-big-is-trillion-dollars/7814/

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https://www.ainsliebullion.com.au/gold-silver-bullion-news/visualizing-the-us-debt-ceiling-in-24100-bills-/tabid/88/a/1478/default.aspx

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https://towerpointwealth.com/Trending-Today-Towerpoint-Wealth-8-3-2018eNewsletter.html

Lastly, here is a Facebook post that goes beyond these videos and images to visualize the U.S. debt:

Posted by Dan Asmussen on Wednesday, September 21, 2011

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4 thoughts on “ visualizing a billion and a trillion dollars ”.

Reblogged this on Ohio Politics .

It is of course also wrong. 1 Trillion is *not* 960 (the number of minutes in 16 hours) larger than 1 Billion, it is three orders of magnitude exactly, ie 1000 (16.5 would have at least been close, and 16 hours and 40 minutes would have been right). A quick bit of back of the envelope suggests their distances are even further off (1km = 1,000m = 1,000,000mm; I do not think paper is that thin). Perhaps the issue this video highlights is why a lack of numeracy amongst humanity faculty and graduates is a problem.

Thank you for the more precise calculations. The differences in the amounts are now much easier to visualize.

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Visualizing a Trillion: Just How Big That Number Is?

Courtesy the credit crisis and big bailout packages, the figure “trillion” has suddenly become part of our everyday conversations. One trillion dollars, or 1 followed by 12 zeros, is lots of money but have you ever tried visualizing how big that number actually is?

For people who can visualize one million dollars, the comparison made on CNN should give you an idea about a trillion - “if you start spending a million dollars every single day since Jesus was born , you still wouldn’t have spend a trillion dollars”.

Another mathematician puts it like this: “1 million seconds is about 11.5 days, 1 billion seconds is about 32 years while a trillion seconds is equal to 32,000 years “.

Now if the above comparisons weren’t really helpful, check another illustration that compares the built of an average human being against a stack of $100 currency notes bundles.

A bundle of $100 notes is equivalent to $10,000 and that can easily fit in your pocket. 1 million dollars will probably fit inside a standard shopping bag while a billion dollars would occupy a small room of your house.

With this background in mind, 1 trillion (1,000,000,000,000) is 1000 times bigger than 1 billion and would therefore take up an entire football field - the man is still standing in the bottom-left corner.

Related: Visualize Units of Measurement

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How Big Are Millions, Billions, and Trillions?

How Can We Think About Really Large Numbers?

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The Piraha tribe is a group living in the jungles of South America. They are well known because they do not have a way to count past two. According to Daniel L. Everett, a linguist and professor who spent decades living among and studying the tribe, the Piraha have no number words to distinguish between these two numbers. Anything more than two is a “big” number, so learning how to conceptualize a billion may prove to be difficult for them.

Most people are similar to the Piraha tribe. We may be able to count past two, but there comes a point where we lose our grasp of numbers. When the numbers get big enough, intuition is gone and all we can say is that a number is "really big." In English, the words "million" and "billion" differ by only one letter, yet that letter means that one of the words signifies something that is a thousand times larger than the other.

Do we really know how big these numbers are? The trick to thinking about large numbers is to relate them to something meaningful. How big is a trillion? Unless we’ve thought of some concrete ways to picture this number in relation to a billion, all that we can say is, "A billion is big and a trillion is even bigger."

How to Conceptualize a Million

First, consider a million :

One million is a thousand thousands.
One million is a 1 with six zeros after it, denoted by 1,000,000.
One million seconds is about 11 and a half days.
One million pennies stacked on top of each other would make a tower nearly a mile high.
If you earn $45,000 a year, it would take 22 years to amass a fortune of 1 million dollars.
One million ants would weigh a little over 6 pounds.
One million dollars divided evenly among the U.S. population would mean everyone in the United States would receive about one-third of one cent.

How to Conceptualize a Billion

Next up is one billion:

One billion is a thousand millions.
One billion is a 1 with nine zeros after it, denoted by 1,000,000,000.
One billion seconds is about 32 years.
One billion pennies stacked on top of each other would make a tower almost 870 miles high.
If you earn $45,000 a year, it would take 22,000 years to amass a fortune of one billion dollars.
One billion ants would weigh over 3 tons—a little less than the weight of an elephant.
One billion dollars divided equally among the U.S. population would mean that everyone in the United States would receive about $3.33.

How to Conceptualize a Trillion

After that is a trillion:

One trillion is a thousand billions, or equivalently a million millions.
It is a 1 with 12 zeros after it, denoted by 1,000,000,000,000.
One trillion seconds is 32,000 years.
One trillion pennies stacked on top of each other would make a tower about 870,000 miles high—the same distance obtained by going to the moon, back to Earth, then to the moon again.
One trillion ants would weigh over 3,000 tons.
One trillion dollars divided evenly among the U.S. population would mean that everyone in the United States would receive a little over $3,000.

What’s Next?

Numbers higher than a trillion are not talked about as frequently, but there are names for these numbers . More important than the names is knowing how to think about large numbers. To be a well-informed member of society, we really should be able to know how to conceptualize a billion, trillion, and million.

It helps to make this identification personal. Have fun coming up with your own concrete ways to talk about the magnitude of these numbers.

Everett, Daniel. (2005). " Cultural Constraints on Grammar and Cognition in Piraha: Another Look at the Design Features of Human Language ." Current Anthropology, vol. 46, no. 4, 2005, pp. 621-646, doi:10.1086/431525

" How Many Thousands Make 1million? " University of Regina, mathcentral.uregina.ca.

Milliman, Hayley. “ How Many Millions in a Billion? Billions in a Trillion? ” blog.prepscholar.com.

" How Much Is a Billion? " www.plainenglish.co.uk.

“ How Much Is a Trillion? ” NPR, 8 Feb. 2008.

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Visualizing One Million vs. One Billion

From the YouTube description: “ There are lots of ways to compare a million to a billion, but most of them use volume. And I think that’s a mistake, because volume just isn’t something the human brain is great at. So instead, here’s the difference between a million and a billion, in a more one-dimensional way: distance. ”

The video is more than an hour long, which is the point. In the last minute of the video, he mentions what a trillion would be in the same scenario.

What Does A Trillion Dollars Look Like?

What does 14 trillion of something look like.

The age of the universe is estimated to be 13.7 billion years . The United States national debt is currently just over 19 trillion dollars. We hear these HUGE numbers thrown out in daily conversations (yes, I have daily conversations about the age of the universe and so should you…) but does anyone really have a grip on what a BILLION or a TRILLION of anything really looks like?

Just for a refresher on how you get to a Trillion and beyond, recall from grade school the implications of adding three zeros after a “one”.1 = One 1,000 = Thousand 1,000,000 = Million 1,000,000,000 = Billion 1,000,000,000,000 = Trillion 1,000,000,000,000,000 = Quadrillion

OK, so what does a trillion look like? The problem with most answers to questions like this is that they try to it into perspective by relating it to things normal people have no perspective for. For instance, did you know that,

One trillion dollars would stretch nearly from the earth to the sun. It would take a military jet flying at the speed of sound, reeling out a roll of dollar bills behind it, 14 years before it reeled out one trillion dollar bills. I don’t know when the last time you traveled from the earth to the sun, much less traveled at the speed of sound in a jet, but for me those comparisons are just as mind-boggling as the concept of a trillion of something. One Million Pennies The Megapenny project uses something a lot more common to most of us, a penny. Most people have a few in their pockets or in a jar on the bookshelf and it provides a much better sense of scale. Round up 16 of them, stack them on top of each other into a little pile and it’s one inch tall. Place them side by side in a line and they stretch out one foot. So much for what’s in your pockets, now break open your piggy banks and gather up one million pennies, that’s only $10,000 of course. One million pennies creates a wall four feet wide, five feet tall and one foot thick. This wall weighs nearly 6,300 pounds, or just over three tons! One Billion Pennies Stepping up to a billion, things start to change as we start imagining stacks of pennies the size of a typical school bus. Five school buses to be exact. As an interesting side-note, most European countries use a slightly different naming convention for large numbers and refer to our trillion, as a “thousand billion” they reserve the word trillion for a million billion or 1,000,000,000,000,000,000. Add another three zeros and we begin to enter into the realm of the age of the universe (in years) and the national debt (in dollars – not pennies). One trillion pennies would create a mind boggling cube with edges nearly as long as a football field. If only there were that many pennies in existence! One Trillion Pennies Current estimates by the U.S. Mint place the number of pennies in circulation at around 140 billion. Others have estimated as many as 200 billion currently circulating. Since the first penny was minted in 1787, until present-day, over 300 billion pennies have been minted in the United States. Of course the final step here is to image fourteen (14) of these cubes of pennies. Each penny representing one dollar of the national debt. The physical representation of large numbers is an interesting way to wrap your head around what it means to say something is in the billions or trillions, and beyond. Of course, if pennies stacked up are just not doing it for you, head over to Global Researcher where they use 100 dollar bills in tidy little stacks to make the same point. I found it interesting how small a package one million dollars turns out to be when made of bundles of $100 bills. It could fit in plastic grocery bag with ease!

From 1 to 1,000,000

Look. I don’t know what you’re over there thinking about. It could be simple or sophisticated, mundane or whimsical, practical or creepy.

But I’m over here thinking about numbers. Again.

I’ve never been especially impressed by words. They’re mushy and sometimes pleasant and sometimes annoying. They’re subtle and subjective and rambly and flowy. Words are okay. Whatever.

But numbers. Numbers are fascinating and precise and satisfying and delicious and whatever it is you’re thinking about at any given time, there’s at least a 60% chance that I’m over here thinking about numbers.

So I’ve decided to do not one, but two consecutive posts on numbers, during which we’ll start at 1 and end up in a very scary place. Today, we’ll keep things in the realm of the ordinary and the conceivable, capping ourselves at a million.

The numbers between 1 and 1,000,000 are everywhere in daily life. 1, 10, 100, 1,000, 10,000, and 100,000 are our friends—we get them, they get us, and in this post, we’re basically gonna just hang out with them and catch up, since you probably haven’t been good at keeping in touch.

Let’s start at the beginning—

One-Digit Numbers

We’ll lead off with the extraordinarily dull 1.

1 likes to masquerade as this poetic and profound thing, getting used in sentences I don’t really understand, like “the oneness of all” or something annoying like that. But then anytime you actually spend time with 1, you end up bored.

1 is also no fun to play with. Multiplying or dividing things by it is an incredibly underwhelming experience, and it manages to be such a dud that somehow, it’s not a prime number even though it only has one factor.

Let’s move on.

Two-Digit Numbers

Getting to the two-digit numbers, interesting things finally start happening. 10 itself is a big one, because our entire base ten existence stems from it. Why did we end up in base ten (instead of something like base 8, which would go 1, 2, 3, 4, 5, 6, 7, 10, 11, 12, 13, 14, 15, 16, 17, 20, etc.)? Because we have 10 fingers. It seems intuitive that only with base 10 could you multiply and divide so easily and simply add zeros or move a decimal point when shifting by multiples of 10, but that would be the case with any number system. 3 Let’s look at some bigger numbers—

12 has the dozen thing going which is something, as well as factors up the dick. It’s also the number of people who have been on the moon .

Let’s pause for a second to acknowledge how ridiculously impressive it is that humans got humans onto the moon and safely back. And how lucky are those 12 guys? Could any life experience be more desirable than getting to bounce around the moon while looking at the Earth hovering out there in space?

Continuing along, I don’t know whose sister 13 slept with, but somewhere along the way it pissed off the wrong person and managed to become the only number with a legitimately bad reputation.

33 is relevant because of Larry Bird and because that’s what I turned on Wednesday thanks for wishing me a happy birthday none of you.

You might be surprised to know that only 1/43 Americans openly identifies as gay, lesbian, or bisexual , but that when asked in an anonymous and veiled survey , that number jumps to 8/43:

There are 41 Disney princesses and 48 real-life princesses , none of whom is Kate Middleton .

Not much else happening with the two-digit numbers until we arrive at sleazy 99, the price tag whore who’s made its whole living being the guy next to 100.

Three-Digit Numbers

100 is a big deal and clearly knows it, but that’s fair. It’s the first three-digit number, but in our world, 100’s main role is being the overlord of the one and two-digit groups—it’s a century of years, the official “okay you win” age to reach, and the whole concept of percent is just comparing a part of 100 to all of 100. 100 is also a perfect square of another one of these fundamental numbers (i.e. 10, 100, 1,000, etc.), which is satisfying.

Being in the top 100th of a group in some way is also a thing. It looks like this:

If you’re in the red dot when it comes to wealth, you’re the notorious 1 percent and a lot of people will make signs that are mean to you. To be in the red dot among Americans, you need to make almost $400,000/year , but only about a tenth of that ( $39,000 in 2011) to be in the red dot worldwide.

After 100, we’re about to get into superbly random number territory, but first we hit 101, a C-list number celebrity for a handful of small claims to fame, like 101 Dalmations and beginner courses and the West Coast US highway.

Continuing along, while about exactly 1 out of every 100 dots speaks sign language ( 70 million people worldwide), 6 1 of every 179 living humans ( 39 million ) is blind:

There are 444 Apple retail stores in the world:

If you deal five cards 508 times, you’ll average one flush:

And there are 12 million US dollar millionaires in the world, or 1 out of every 583 people. If your total assets (in excess of your total liabilities) add up to over $1,000,000, you’re the red dot in this diagram:

Four Digit Numbers

1,000 is also a huge deal in our world and has a bunch of nicknames, like a grand, a G, a kilo, and k. It’s also part of the elite chain of numbers in the “order-of-magnitude” chain, which we know as million, billion, trillion, etc. Million is actually the third number in that chain, with the dud 1 as the first number and 1,000 as the second number. And 1,000 is the key multiplier that defines the whole chain.

Anyway, let’s look at some four-digit numbers and odds:

Here’s how many times a neutron star spins around every second :

And here’s how many minutes there are in each day:

A genius-level IQ of 150 will earn you red dot status on the thousand-dot intelligence diagram, but that doesn’t mean you got a perfect 1600 on the SAT—only the red dot in a 1,489-dot sample aces the SAT:

There are 1,811 large US corporations (over 10,000 employees), and astronomers have identified 1,849 planets outside our solar system :

On a perfectly clear night, we can see about 2,500 stars in the night sky:

And there may be only 2,800 living people over 7 feet tall (213cm), but they each have a 17% chance of making the NBA.

Here are all the seconds in an hour:

And here’s the number of religions in the world:

So there are more religions than the stars we see in the night sky, and you could name a religion every second and it would take you over an hour to name them all.

We’ve identified over 400,000 species of beetle in the world, but only 5,416 mammal species .

And here’s how many living languages there are in the world:

Finally, this is how many medium-sized (.5mm in diameter) grains of sand you could fit in a cubic centimeter box:

Five-Digit Numbers

If 1,000 is a little overrated, 10,000 is underrated. No one talks about 10,000, but unlike the square rootless 1,000, 10,000 a perfect square of 100 100s, and 1% of a million.

Stephen Hawking’s IQ is supposedly 160, which would just qualify him to be the red dot in a 10,000 dot average sample of human intelligence. And just so you know, in an average group of 17,000 people, one will be an albino .

This is how many people fit in a sold-out Fenway Park :

Larger than the number of people in Fenway are both the 41,821 airports in the world and the number of buildings in Manhattan :

The 55,030 Google employees would fill up a large stadium, as would Apple’s 50,250 . Facebook is considerably smaller , with a staff of 8,348, while Wikipedia is running with only 208 people . You could fit the Craigslist team in a small bus:

And here’s how many seconds tick by every day:

Six-Digit Numbers

Equal to the capacity of the world’s largest stadium is the number of abortions that happen in the world every day , on average:

That’s about 1/3 the amount of worldwide births per day , meaning a quarter of all pregnancies that don’t end in miscarriage end in abortion. That’s about the same as the rate in the US , but in New York City, 41 of every 100 non-miscarried pregnancies are aborted. And no, this isn’t meant to be a political statement of any kind, just an interesting (and to me, surprising) statistic, so just settle down.

One Million

Good luck. See you at the bottom—

Sorry. A million dots is a lot of dots.

And how small are one-in-a-million odds? How much of a long shot is one-in-a-million? Just try to find the red dot in the million dots above.

This image is the only way I can think of to visualize what a million or what one-in-a million actually means.

A million is interesting because it’s huge— but it’s also the smallest of the big boys, just small enough that you can still picture it or depict it on a diagram. It’s right on the border between the world we can wrap our heads around and the world of the totally inconceivable.

That red dot, if you found it, is a good thing to keep in mind next time you buy a 1-in-146 million Powerball ticket, or anytime you hear facts like one out of every 11 million airplane flights crashes. A one-in-a-million long shot is the same as rolling three 100-sided dice and trying to hit the number 63 with all three of them in one roll .

If you want to play around with taking a one-in-a-million shot at something, pick a number between 1 and 1,000,000, say it out loud, and then click Generate below and try to hit it (or two other ways to do it: 1) Change the max number to 1,000 and try to hit the number you say with the next two clicks; 2) Change the max number to 100 and try to hit a chosen number three times in a row):

The Million-Dot Poster

I like both the number 1,000,000 and the number 1/1,000,000, and I love any chance to visualize them. A blog post that can only fit 200 dots horizontally isn’t an ideal way to visualize a million because it makes a 1 x 25 rectangle you have to scroll down for an hour to see all of. So we’ve made a million-dot poster .

The poster is, satisfyingly, a square. A 24″ x 24″ (61cm x 61cm) poster with a 1,000 dot x 1,000 dot square of a million total dots. This allows you to most effectively visualize the number one million (it also helps to visualize 5 or 10 or 100 million, or even a billion, by picturing multiple posters next to each other).

And, of course, one of the dots is red. It takes a hunt to find it, 9 but once you do, you can understand exactly what 1/1,000,000 means. So one poster, two extreme numbers to visualize. You can check it out here .

Here’s what the plain one looks like:

Full poster:

A closer shot, showing the red dot in the middle:

And a close-up shot, showing the red dot:

Numbers post #2: From 1,000,000 to Graham’s Number

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The difference between a million and a billion dollars [with graphic]

When reading over earnings reports, doing valuation assessments, trying to visualize someone’s wealth accumulation, or running any other financial analysis, it’s sometimes hard to conceptualize the difference between two very large financial sums.

To that end, here’s a helpful visual on the massive difference between $1 million and $1 billion, from Abu Amin on Quora:

One million vs. one billion

A billion dollars looks like this in $100 dollar bills. You’d need ten forklift rides to cart it around:

For comparison, a million dollars in $100 dollar bills looks like this… a backpack would do:

So, when Apple announces it did $39 billion in revenue last quarter, and has over $110 billion in cash reserves … you can get a better sense of what that’s all about.

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All of the World’s Money and Markets in One Visualization

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All of the World's Money and Markets in One Visualization, 2020 Edition

In the current economic circumstances, there are some pretty large numbers being thrown around by both governments and the financial media.

The U.S. budget deficit this year, for example, is projected to hit $3.8 trillion , which would be more than double the previous record set during the financial crisis ($1.41 trillion in FY2009). Meanwhile, the Fed has announced “open-ended” asset-buying programs to support the economy, which will add even more to its current $7 trillion balance sheet.

Given the scale of these new numbers—how can we relate them back to the more conventional numbers and figures that we may be more familiar with?

Introducing the $100 Billion Square

In the above data visualization, we even the playing field by using a common denominator to put the world’s money and markets all on the same scale and canvas.

Each black square on the chart is worth $100 billion , and is not a number to be trifled with:

In fact, the entire annual GDP of Cuba could fit in one square ($97 billion), and the Greek economy would be roughly two squares ($203 billion).

Alternatively, if you’re contrasting this unit to numbers found within Corporate America, there are useful comparisons there as well. For example, the annual revenues of Wells Fargo ($103.9 billion) would just exceed one square, while Facebook’s would squeeze in with room to spare ($70.7 billion).

Billions, Trillions, or Quadrillions?

Here’s our full list, which sums up all of the world’s money and markets, from the smallest to the biggest, along with sources used:

Category	Value ($ Billions, USD)	Source
Silver	$44	World Silver Survey 2019
Cryptocurrencies	$244	CoinMarketCap
Global Military Spending	$1,782	World Bank
U.S. Federal Deficit (FY 2020)	$3,800	U.S. CBO (Projected, as of April 2020)
Coins & Bank Notes	$6,662	BIS
Fed's Balance Sheet	$7,037	U.S. Federal Reserve
The World's Billionaires	$8,000	Forbes
Gold	$10,891	World Gold Council (2020)
The Fortune 500	$22,600	Fortune 500 (2019 list)
Stock Markets	$89,475	WFE (April 2020)
Narrow Money Supply	$35,183	CIA Factbook
Broad Money Supply	$95,698	CIA Factbook
Global Debt	$252,600	IIF Debt Monitor
Global Real Estate	$280,600	Savills Global Research (2018 est.)
Global Wealth	$360,603	Credit Suisse
Derivatives (Market Value)	$11,600	BIS (Dec 2019)
Derivatives (Notional Value)	$558,500	BIS (Dec 2019)
Derivatives (Notional Value - High end)	$1,000,000	Various sources (Unofficial)

Derivatives top the list, estimated at $1 quadrillion or more in notional value according to a variety of unofficial sources.

However, it’s worth mentioning that because of their non-tangible nature, the value of financial derivatives are measured in two very different ways. Notional value represents the position or obligation of the contract (i.e. a call to buy 100 shares at the price of $50 per share), while gross market value measures the price of the derivative security itself (i.e. $1.00 per call option, multiplied by 100 shares).

It’s a subtle difference that manifests itself in a big way numerically.

Correction: Graphic updated to reflect the average value of an NBA team.