What’s a trillion?


Trillion.

It’s such a pretty word, so easy to say.  And, recently, so common, especially when it comes to talking about government debt and deficits. A deficit is the difference between income and expenses in a particular year. The total deficit of the U.S. government  in 2009 was $1.42 trillion.  And successive deficits breed debt: the total U.S. public debt in March 2011 was $14.26 trillion.

But just how much is a trillion dollars? Oh, it’s straightforward to write down. In words, a trillion is a thousand billion. In numbers, 1,000,000,000,000. That’s 1 followed by 12 zeros. And if you want to be really slick, write it in scientific notation, which simply counts zeros: 1012 . That’s 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10.

(Here, I am using the so-called short-scale method of classifying large numbers, which is used in most English-speaking countries. Some countries use the long-scale classification in which 1012 is called a billion and a trillion is a million times that — 1018.)

Are there ways to make this immense number more accessible to our small human perceptions? It’s a temptation I cannot resist to come up with some.

How long is a trillion seconds? In days, weeks, months or years. Roughly. Guess. Right now. Without looking ahead or reaching for your calculator.  Jot down your guess.

Now get out your calculator, or just follow along with me. Since there are 60 seconds in a minute, a trillion seconds is 1,000,000,000,000/60 minutes. That’s 16,666,666,667 minutes. Sixteen billion, 666  million, 666 thousand, 667 minutes. (I have rounded the number off to the nearest  minute.)

Now, there are 60 minutes in an hour, so a trillion seconds is 16,666,666,667/60 hours. Rounded, that’s 277,777,778 hours. Two hundred and seventy-seven  million and change.

You can see where we are going, can’t you? A trillion seconds is approximately 277,777,778/24 = 11,574,074 days.  Ignoring leap years (be my guest if you want to count them, but your time may be better spent getting treatment for your obsessive-compulsive disorder), that’s 11,547,074/365 = 31,710 years.

In other words, if you were being paid at a dollar a second, $3600 an hour, day and night, it would take you almost 32 thousand years to accumulate a trillion dollars.

The total US debt is $14.26 trillion, so if you tried to pay it off at a dollar a second it would take you 14.26 x 31710 =  452,185 years.  Fortunately, the US debt is shared by about 300 million people. If each of them chipped in a dollar a second, the debt would be paid off in 452,185/300,000,000 = 0.001507 years. That’s 0.5502 days or 13 hours 12 minutes. That does not sound too bad, until you realise that each person has coughed up about 47,500 dollars.

There’s another way to conceive of a trillion dollars. If you stacked up a trillion US dollar bills, how high would the stack be?

The modern US dollar bill is 0.11 mm thick.

(I could do the following calculation in the old, ramshackle British system of weights and measures to which Americans, old people and the hard-of-thinking seem addicted. But since I don’t want to get weighed down in feet, furlongs and fortnights, I stick to standard units, which do everything in multiples of 10. If you are stuck with the British system, remember that a millimetre (mm) is the width of a fingernail pairing; a centimetre (cm) is 10 mm — the width of the finger; a metre (m) is 100 centimetres — a bit more than a yard; and a kilometre (km) is 1000 metres — about six tenths of a  mile. Now sit back and watch how calculations in the standard system amount to shifting the decimal point and tossing zeros about.)

Ten dollars make a stack 1.1 mm high. A hundred dollars is 11 mm or 1.1 cm high. Best to put this into a table.

Number of dollars

Height of pile in …

Centimetres (cm)

Metres (m)

Kilometres (km)

1 = 100 0.11 mm = 0.011 cm 0.00011 m 0.00000011 km
10 = 101 1.1 mm = 0.11 cm 0.0011 m 0.0000011 km
100 = 102 1.1 cm 0.011 m 0.000011 km
1000 = 103 11 cm 0.11 m 0.00011 km
10,000 = 104 110 cm 1.1 m 0.0011 km
100,000 = 105 1100 cm 11 m 0.011 km
1 million = 106 11,000 cm 110 m 0.11 km
10 million = 107 110,000 cm 1100 m 1.1 km
100 million = 108 1.1 million cm 11,000 m 11 km
1 billion = 109 11 million cm 110,000 m 110 km
10 billion = 1010 110 million cm 1.1 million m 1100 km
100 billion = 1011 1.1 billion cm 11 million m 11,000 km
1 trillion = 1012 11 billion cm 110 million m 110,000 km

So the stack of a trillion dollar bills would be 110,000 km (about 68,000 miles) high. Laid horizontally (with the bills still face to face, not edge to edge), this stack would stretch coast to coast in North America (a distance of 5000 km) 22 times. Driving day and night at 100 km/h (60 mph), it would take you 1100 hours or nearly 46 days to pass the trillion dollars.

If you laid the entire US debt ($14.26 trillion) out like this, it would take you 1100 x 14.26 or 15,686 hours to drive past the horizontal stack. That’s 654 days — nearly a year and 10 months of constant driving.

The U.S. obsession with the paper dollar has always baffled me. At least three other English-speaking countries use dollar-based currency ditched paper dollars 25 years ago soon after they said goodbye to the English “system” of weights and measures. This makes operating candy machines, parking meters and toll roads much easier.

So here’s an exercise for residents of those countries. How high would a trillion Australian, Canadian or New Zealand dollar coins be? And how long would it take to drive (at 100 km/h) past the stack if it were laid along the side of a road? To save you looking it up, the thicknesses of the three dollar coins are:  Australia, 3 mm; Canada, 1.75 mm; New Zealand, 2.74 mm. Each of the three currencies are valued within eight cents of the U.S. dollar. And the external national debts of each (in local currencies) are: Australian A$1.090 trillion; Canada, C$0.971 trillion; New Zealand, NZ$0.077 trillion. Hm. New Zealand, with less than one tenth the debt of the other two, seems to be doing something right.

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About aharmlessdrudge

Way back during the late Bronze age -- actually it was the 1950s -- all of us in high school had to take a vocational test to determine our interests and, supposedly, our future careers. I cannot remember the outcome, but I do recall one question that gave me pause. "If you were to win a Nobel prize, would it be in literature or in physics?" I hesitated over the question: although I enjoyed mathematics and science more than English class, I did have a couple of unfinished (and very bad) novels hidden away at home. I cannot remember what I chose back then, but the dilemma followed me to university, where I switched from mathematics to English and -- after a five-year stint in journalism -- back to mathematics. I recently retired as a professor of statistics. Retirement. What a good chance to revive my literary ambitions. I have finished a novel -- more about that in good time -- and a rubble of drafts of articles about mathematics and statistics is taking up space on my hard disk.
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