Billions & Trillions

In order to understand a big, abstract number like one million or one billion, it helps to put it in terms of things we experience every day. But even then, big numbers stretch the imagination.

Big numbers can be really hard to understand. Whenever a word ends in “—illions,” it’s easy to just think of it as a whole lot of something, and nothing more. But there is a huge difference between one million and one trillion.

How much is one trillion?

How many millions are in one trillion? Are there one hundred millions in a trillion? One thousand millions?

There are one million millions in a trillion.

One trillion is 1,000,000,000,000. That is 12 zeros.

  • One trillion is more stars than there are in the entire Milky Way galaxy.[Prove it…]

    The Milky Way galaxy contains approximately 400 billion stars, but some estimates vary by as much as 200 billion stars.


Trillions in Time

  • One million seconds will pass in the next 12 days.One billion seconds will take 32 years.One trillion seconds will pass in 31,688 years.

    [Prove it…]

    One trillion is one million millions (1,000,000×1,000,000).

    Using time as an example, we will define one million, one billion, and one trillion using the passage of seconds. One million seconds in days is 11 days, 13 hours, and 40 minutes. (1,000,000)/[(60 seconds)x(60 minutes)x(24hours)] = 11 days, 13 hours, 40 minutes.

    On billion seconds in days is 11,574 days. (1,000,000,000)/[(60 seconds)x(60 minutes)x(24hours)] = 11,574 days. A year is approximately 365.2425 days. Therefore, a billion seconds in years is 31 years, 8 months. (11,574)/ 365.2425 = 31.6885 years = 31 years, 8 months.

    To convert a trillion seconds into years, we first find the number of days: 11,574,074. (1,000,000,000,000)/[(60 seconds)x(60 minutes)x(24hours)] = (11574074 days) Therefore, it will take 31,688 years to reach one trillion seconds. (11,574,074 days) / (365.2425 days) = (31,688 years)


  • Time is money, right? If you make one dollar every second, you will have a million dollars in twelve days. You will be a billionaire in 32 years, but it will take you more than 31,000 years to make a trillion dollars.
  • A trillion seconds ago, civilization didn’t exist. A billion minutes ago, Trajan was emperor in Rome. A million hours ago, it was 1895, and Grover Cleveland was President of the United States.[Prove it…]

    Civilization, as we understand it, is estimated to have begun between 12,000 and 14,000 years ago. “A trillion seconds ago” was more than 31,000 years ago. Using the current year as 2009.67, and subtracting 1901.32 years, we find that “one billion minutes ago” the year was 108.35 AD, during the reign of Emperor Trajan, who ruled from 98 AD to 117 AD [1,000,000,000 / {60 x 24 x365.2425 = 525,949.2} = 1901.32 years] [2009.67 – 1901.32 = 108.35] “A million hours ago” was 114.079 years ago. [1,000,000 / {24 x 365.2425 = 8765.82} = 114.079] Therefore, the year was 1895 when Grover Cleveland was President. [2009.67 – 114.079 = 1895.59]


How much money is a trillion dollars?

  • A trillion $10 bills, taped end to end, would wrap around the Earth more than 380 times.[Prove it…]

    The length of a $10 bill (6.14 in) divided into the equatorial circumference of Earth in inches (24,901 miles x 5,280 ft per mile x 12 inches per foot = 1,577,727,360) yields the number of $10 bills it takes to circle the Earth once (256,958,853.42 $10 bills). {[1577727360 / 6.140 (length of dollar bill)] = 256,958,853.42.}.

    This number of $10 bills is equal to $2,569,588,534.20 (around $2.57 billion). [10 x 256958853.4 = 2569588534] To find the number of ‘round-the-Earth trips needed to raise that amount of money to $1 trillion, divide the trillion by this number and the result is 389.167. [1,000,000,000,000/(2569588534.2) = 389.167]


  • That’s a ton of cash—actually 1.1 million tons of it.[Prove it…]

    There are approximately 907,185 grams in a ton [2000 x 453.59237 (grams in a pound) = 907,184.74 grams in a ton]. If one dollar bill weighs one gram, then 907,185 dollar bills equal one ton. Therefore, one trillion dollar bills equal 1,102,311 tons of cash. [1,000,000,000,000 / 907,185 = 1102310.99]


  • It would take more than 10,000 18-wheelers to transport one trillion $1 bills. Our national debt today would fill up 30 of the largest container ships ever constructed, each holding more than 4,100 containers full of cash.[Prove it…]

    Using the Department of Transportation’s standards for a 53-foot shipping container (8.0 feet wide, 8.5 feet high, 53 feet long), the volume of a shipping container is roughly 3604 cubic feet.

    Using the dimensions of a dollar bill (6.14 in. x 2.61 in. x .0043 in.), the volume of one dollar bill is .0000396 cubic feet. Therefore, one 53-foot container would hold roughly 91 million bills. [3604 cu. ft. / .000039 = 91,010,110]

    One trillion $1 bills would therefore fill more than 10,000 tractor trailers. [1,000,000,000,000 / 91,010,101 = 10,987.79]

    The world’s largest cargo ship, the Emma Maersk, can carry 11,000 “20-foot Equivalent Unit” shipping containers (TEUs), and a 53-foot container is considered 2.65 TEUs.

    Therefore roughly 4,151 53-foot containers [11,000 / 2.65 = 4150.94 53 ft containers] will fit on this cargo ship.

    10,987 shipping containers would fill two and one-half of the largest container ships ever made, or three average container ships. [10,987 / 4,151 = 2.64] Our national debt of $12 trillion would fill more than 30 such container ships. [12 x 2.65 = 31.8]


  • You could spend $10 million a day and it would still take you 273 years to spend $1 trillion.[Prove it…]

    At a rate of 10 million dollars a day, it would take a person 100,000 days to spend one trillion dollars. 100,000 days is 273 years. {[$1,000,000,000,000 / $10,000,000 = 100,000 days] / 365.2425 days = 273 years}


What is Innumeracy?

In his bestselling book, Innumeracy: Mathematical Illiteracy and its Consequences, John Allan Paulos defines innumeracy as “an inability to deal comfortably with the fundamental notions of number and chance.”

He tells the following story of how not intuitively understanding big numbers keeps us from getting the joke:

“An old married couple in their nineties contact a divorce lawyer, who pleads with them to stay together. “Why get divorced now after seventy years of marriage? Why not last it out? Why now?” The little old lady finally pipes up in a creaky voice: “We wanted to wait until the children were dead.”

A feeling for what quantities or time spans are appropriate in various contexts is essential to getting the joke. Slipping between millions and billions or between billions and trillions should be in this sense equally funny, but it isn’t, because we too often lack an intuitive feeling for these numbers. Many educated people have little grasp of these numbers and are even unaware that a million is 1,000,000; a billion is 1,000,000,000; and a trillion is 1,000,000,000,000.”

Driving up the debt:

  • How big is 15 trillion dollars? 15 trillion $1 bills, laid end to end, side to side, would pave every interstate, highway, and country road in America—twice.[Prove it…]

    A dollar bill is 6.14 inches x 2.61 inches. The total lane miles in the United States of America is estimated at 8,457,353. This means that each lane on a road is counted, regardless of how many lanes on the road. Therefore, there are approximately 44,654,823,840 feet of lanes in the country. [8,457,353x 5280 = 44,654,823,840] Most lanes are between 9 and 13 feet wide (Department of Transportation, Federal Highway Administration).

    For this example, we will use a lane width of 13 feet, which is above average and a recommended width for new roads, by the Texas Department of Transportation. Therefore, estimated surface area of US roadways is less than 580,512,709,920 sq. ft. [13 ft.x (44,654,823,840 ft.)= 580,512,709,920 sq. ft.] Using our earlier calculations regarding the length and width of a dollar bill, the square footage of a dollar bill is approximately .11 sq. ft. { [6.142.61 in.] / [144 in. sq.] = .11 sq. ft. }

    Therefore, the total surface area of US roadways divided by square footage of dollar bill equals the number of one dollar bills it would take to cover the surface area of US roadways. [580,512,709,920/.11 = 5,277,388,272,000 dollars bills] Our national debt is about $15 trillion, meaning that one trillion dollar bills would cover US roadways more than twice. [15,000,000,000,000 / 5,277,388,272,000 = 2.84


Social Insecurity

  • Estimates from the Congressional Budget Office suggest that by 2016, we will begin regularly running a Social Security deficit, with more benefits being paid out than revenue coming in. Social Security will begin to contribute to our national debt and annual deficits by the billions.[Prove it…]