Just how big is a trillion?

Media interest has recently focussed on the effects of the credit crunch. The UK’s stalled metric changeover is all but forgotten. John Frewen-Lord has, perhaps tongue-in-cheek, succeeded in linking these issues while providing another example of the superiority of metric measures.

In the UK, several of the banks, as well as various other entities, have had to be bailed out by the government. A figure commonly quoted by the media is that these organisations have received around £1 trillion of government ‘funding’ (a trillion here is defined as the now commonly accepted 10^12).  Can you imagine just how much money that is?

Setting aside the fact that most of that money is simply zeros on a computer screen, and most of the physical money that’s left is of the paper variety, it would still be interesting if that £1 trillion could be visualised in terms of £1 coins.  Just how big would the pile be?

A pound coin is specified as being 22.50 mm in diameter, 3.15 mm thick, and has a mass of 9.50 g.  The coin will therefore occupy a cube 22.5 x 22.5 x 3.15 mm deep.  The volume of that cube is 22.5 x 22.5 x 3.15 = 1595 mm³ (working to four significant figures).  Now, as we have one trillion of these, we’d better convert to cubic metres, which we can do by moving the decimal point nine places to the left (another way is to move the decimal point three places to the left for each of these millimetre values to convert them straight into metres – the end result is the same).  This gives us a figure of 0.000 001 595 m³. Don’t worry about all the zeros – we are now going to multiply this by 10^12, again by just moving the decimal point, this time 12 places to the right.  This gives us a total of 1 595 000 m³ (we could even express it as 1 595 000 000 litres, such is the simplicity of the metric system).

That’s a lot of cubic metres.  Imagine these coins in a warehouse stacked 10 metres high (approximately the topmost ceiling level of a four-storey house).  To find the floor area of this warehouse, simply divide by the height of 10 m – and we have an area of 159 500 m² (which can also be expressed as 15.95 ha again, more metric simplicity).  If this warehouse was say 60 m wide, it would be 2 658 m long 2.658 km!  It would take the average person a full half hour to walk from one end to the other.

As for how much these 1 trillion coins weigh – well, 9.50 g = 0.0095 kg x 10^12 = 9 500 000 000 kg, or 9 500 000 t (tonnes).  You certainly won’t want that landing on your toes.

Note that the ONLY calculations have been to multiply 22.5 by 22.5 by 3.15, and to divide the volume of the warehouse by its height and then its width a total of four calculations.  Everything else is simply moving decimal points around.

Now for all those who say Imperial is easier/better/more ‘human’, etc., let us show these same calculations using Imperial measures.  Pay attention at the back!

The first thing we have to do is find all the necessary Imperial conversion factors  conversion factors that are simply not required in metric.  So we have 12 inches in a foot, 3 feet in a yard, 1760 yards in a mile, 9 square feet in a square yard, 4840 square yards in an acre, 1728 cubic inches in a cubic foot, 27 cubic feet in a cubic yard, 0.1605 cubic feet in an imperial gallon, 16 ounces (the avoirdupois kind) in a pound, and 2240 pounds in a long ton.  One of the claimed advantages of the Imperial system is the use of base 12 (to facilitate division by 2, 3, 4, and 6, as opposed to base 10 which permits division by only 2 and 5), so we will initially use fractions rather than decimals.

Now comes the easy bit.  Converting from the official metric values, the pound coin is approximately 7/8 diameter by 1/8 thick and weighs about 1/3 of an ounce.  The volume of the cube that the coin fits into is therefore 7/8 x 7/8 x 1/8  That works out to 49/512ths of a cubic inch (with normally four calculations, two for the numerator and two for the denominator).  49/512 is not exactly an easy number to work with, so let’s cheat and convert it into decimals 0.09570 cubic inch (working again to four significant figures).  Multiply by 10^12, and we get 95,700,000,000 cubic inches.  Divide by 1728, and we get 55,380,000 cubic feet.  Divide again by 27, and we end up with 2,051,000 cubic yards. If we take the cubic feet and divide by 0.1605, we have the equivalent of 345,100,000 imperial gallons.

So far, eight calculations where we had just two with metric (other than moving decimal points around).  None of the answers bears any relationship to the others.

And the size of the warehouse that this £1 trillion of coins will fit into?  Well, let’s say the stack is 33 feet high, then the area is 55,380,000 cu. ft. divided by 33 = 1,678,000 square feet.  Divide by 9 to give its area as 186,500 square yards, and divide again by 4840 to express its area as 38.53 acres.  If the warehouse is 200 feet wide, then it would be 8,390 feet long.  Divide by 3 and divide again by 1760, and it calculates out to 1.589 miles long.  Another six calculations where we had just two in metric.

As for the weight of these 1 trillion pound coins well, 1/3 oz x 10^12 = 333,300,000,000 ounces.  Divide by 16, and we get 20,830,000,000 pounds, and divide again by 2240, and we get 9,300,000 long tons. Another two calculations where we had NONE in metric (other than moving the decimal point).

All this has involved no fewer than sixteen separate calculations (not to mention getting all the conversion factors right, what if we used the wrong one, or multiplied when we should have divided?), whereas in metric we had just four calculations and no conversion factors.

Of course, this example has been chosen to illustrate the issue. But until the 1970s in Commonwealth countries, including the UK, it was the misfortune of many working in, for example, the construction industry to carry out similar calculations on a daily basis. It is still so in the US.

By any standards, this was and is idiotic, particularly when there is an alternative.  So why do the Imperialists want to stay with these measures, for example on the roads and in the street markets?  Sounds like self-inflicted torture.  If your eyes sort of glazed over when looking at the imperial calculations well, hardly surprising, but it really does beg the question: Why do some of us still want to use this irrational and complex system?

Now, if I go onto Google Earth, I should be able to locate that big warehouse….

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20 Responses to Just how big is a trillion?

  1. lee kelly says:

    I just read this and I have to say I can't wait till this country goes metric completely, I mean the imperial bit was so confusing I had to look at it twice. I know that a lot of imperial supporters will say it's more human and natural, but if you have learning difficulties it can be a serious problem. And in this fast-paced world where people want results fast, metric wins all the time.

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  2. Bill says:

    Now, since I live in the U.S., I would have to convert several units in this story to the U.S. version of the units even though the story will unnecessarily grow in length and the readers confusion will grow.

    Here are the adjustments for the U.S. reader:
    - you already had to specify that you were speaking of the short trillion (10^12) instead of the long trillion (10^18),
    - you already specified that you are using the avoirdupois ounce (but I missed that on the first read-through; it might be better if you say "avoirdupois ounce" each time).
    - we would need to convert from long tons (2240 lb = 1 long ton) to short tons (2000 lb = 1 short ton) since the short ton is the ton used in common speech in the U.S. We should also call it the U.S. ton so that U.S. readers know which ton they're supposed to be familiar with,
    - we would need to compare £ (GBP) to $ (USD) to show the value of the currency in this warehouse,
    - we might want to consider illustrating the size of the warehouse in acres (38.52 acres) for U.S. readers,
    - we would need to convert to BOTH kinds of U.S. gallons, the U.S. liquid gallon and the U.S. dry gallon (we are talking about a dry substance but most of us in the U.S. are familiar with the U.S. liquid gallon since the U.S. liquid gallon is a common milk packaging size).

    Imagine how much messier the story would be with these additional units for readers in a different country who speak the same basic language. The Imperial and US Traditional systems of measurement are a complete disaster, especially when relating to each other. It really is time the the UK and the US to go metric.

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  3. Martin Vlietstra says:

    Many apologists for the imperial system say that the imperial system is simpler. They are right, when it comes to simple things. After all, saying that you weight 11 stone is probably simpler than saying that you weight 70 kg.

    You can even refine the use of stones by going down to half-stones _ “I put on half a stone, and I now weigh 11½ stone�. It is now marginal whether the introduction of half stones is easier than saying “I put on 3 kg – I now weight 73 kg�.

    Now try refining stones a little further – people don’t use quarter stones, but they make the awkward conversion to stones and pounds. In my book, kilograms now have the edge.

    The next step is to manipulate stones and pounds – how much do the eight men in a rugby scrum weigh? A bit of a problem using pencil and paper. Now try doing is on a spreadsheet. Kilograms win in a rather one-sided contest.

    Is it any wonder that as a nation our numeracy levels are dropping – by continuing to use archaic units of measure and not teaching our young people how to manipulate them, we are doing ourselves as a nation a grave disservice.

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  4. Crooked Miles says:

    How big is a trillion used to raise a different question. The UK has shifted (officially in 1974) from a trillion of a million million million to one of a million million (with the billion similarly downsizing), therefore the words have different meanings to their counterparts in French and other European languages. By comparison the SI prefixes of giga, kilo and so on are the same in any language, thereby avoiding similar confusion.

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  5. Richard Birkby says:

    I was one of those at the back trying to pay attention on how to do the imperial calculations but I'm afraid I lost it somewhere along the line. Guess I'm in for detention.

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  6. Matthew says:

    Good piece. I note that 9.3 Mt of pound coins would require (if Yahoo answers figure of 70% copper is correct) about 6.5 Mt of copper, more than 1/3rd the world's annual supply as well as a lot of its zinc and copper.

    Now what's a trillion in £50 bank notes (20 billion of them)?

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  7. Michael Glass says:

    Metric Honey Bun

    Here’s South Pacific’s saucy song “Honey Bun� in a metric version.

    My doll is as dainty as a sparrow,
    Her figure is somethin' to applaud.
    Where she's narrow she's as narrow an arrow,
    And she's broad where a broad should be broad.

    Just fifty-one kilos of fun,
    That's my little honey bun!
    Get a load of honey bun tonight.

    I'm speakin' of my Sweetie Pie,
    Just one metre fifty-five,
    Ev'ry millimetre’s dynamite!

    Her hair is blond and curly,
    Her curls are hurly-burly.
    Her lips are pips!
    I call her hips 'Twirly' and 'Whirly.'

    She's my baby, I'm her pap!
    I'm her booby, she's my trap!
    I am caught and I don't wanna run,
    'Cause I'm havin' so much fun with honey bun!

    I am caught and I don't wanna run,
    'Cause I'm havin' so much fun with honey bun!

    Believe me sonny!
    She a cookie who can cook you 'till you're done,
    Ain't bein' funny!
    Sonny, put your money on my honey bun!

    So what has been gained – and lost – in the translation? Well, Sweetie-Pie has been beefed up a little. Her body mass Index has risen from a scrawny 19.7 to a well-rounded 21.2. With that little extra padding, she really can be broad where a broad should be broad. However, she’s still well within the acceptable weight range. Also, at 155 cm, she’s also 2.4 cm taller than she was. However, she’s still on the petite side, as the average 20 year old woman stands at about 164 cm. The biggest transformation in the song is to change the inch packed with dynamite to every millimetre. So Honey Bun packs an even bigger punch!

    The original can be found at http://www.stlyrics.com/lyrics/southpacific/honeybun.htm

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  8. Michael Glass says:

    If your tastes go more to Peter, Paul and Mary perhaps you would prefer 800 ks:

    Eight Hundred ‘K’s

    If you miss the train I’m on, you will know that I am gone
    You can hear the whistle blow a hundred k’s,
    A hundred ‘k’s, a hundred ‘k’s, a hundred ‘k’s, a hundred ‘k’s,
    You can hear the whistle blow a hundred ‘k’s.

    Lord I’m two, lord I’m four, lord I’m six, lord I’m eight,
    Yes, I’m 800 ‘k’s from my home.
    Far away, far away far away far away
    Lord I’m eight hundred ‘k’s from my home.

    Not a shirt on my back, not a penny to my name
    Lord I can’t go a-home this a-way
    This a-away, this a-way, this a-way, this a-way,
    Lord I can’t go a-home this a-way.

    If you miss the train I’m on you will know that I am gone
    You can hear the whistle blow a hundred ‘k’s.

    A translation of 500 miles
    The original is at
    http://www.lyricsfreak.com/p/peter%2C+paul+%26+mary/500+miles_20107665.html

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  9. Michael Glass says:

    If you think my translations are flat, try out the German version of the Stonecutters Song:

    http://www.youtube.com/watch?v=NcV-SC6ha2I&feature=related

    We do! (The Stonecutters Song)

    All: Who controls the British crown?
    Who keeps the metric system down?
    We do! We do!

    Enjoy!

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  10. Martin Vlietstra says:

    If we assume that £50 bank notes are printed on ordinary (80 g/m²) computer paper, the calculation goes like this:

    One ream (500 sheets) of computer print-out paper is 55 mm thick (I measured it). Thus one sheet of paper is 0.11 mm thick.

    A £50 bank note is 156 mm long and 85 mm high (Bank of England website).

    Thus a £50 Bank of England bank note has a volume of 1.458E-6 m³.
    Multiply this by 10^12 (one trillion) and divide by 50, giving a volume of 29172 m³.

    Assume a rectangle with a base of hectare (10000 m²). The pile of banknotes will then be 2.92 m high.

    To put this into perspective, both Trafalgar Square and an international rugby field (such as Twickenham) have areas of approximately one hectare.

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  11. Michael Glass says:

    Maybe you would prefer to watch Deirdre Flint expostulating about the great Metric threat of the 1970s

    http://www.youtube.com/watch?v=83e3n83Re5s

    we went through the streets willing and running
    metric is coming
    metric is coming

    for all the lyrics, go to

    http://www.metrication.us/content/deirdre-flint-metric-lyrics

    enjoy

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  12. John Frewen-Lord says:

    If we're talking about metric in popular songs, some of us older types may remember a group from the '50s/early '60s called The Four Preps. They had a huge hit (at least in the UK) with the song Twenty Six Miles.

    Buried in the words of that song is a line that goes: "Forty kilo-meters in a leaky old boat...". The full lyrics can be found at http://www.lyricstime.com/four-preps-26-miles-santa-catalina-lyrics.html

    I wonder if there are any other pop songs that contain some metric references?

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  13. David King says:

    I do not know if your imperial calculations are correct, they are just so horrendously complex - which illustrates your point well. The metric numbers are so easy to use, moving the decimal point around is much easier than having all those unusual conversions to do - if someone were to set out to invent the Imperial system from scratch, I doubt if they would come up with the current conversion factors (e.g. 3 feet in 1 yard, etc.). They would surely come up with something much easier.
    So why do people hang on to Imperial? Maybe they feel superior in doing so, a kind of "I must be clever because I use Imperial with all its complex conversions and long-winded maths"? Maybe metric is too easy for them.
    But for the masses, metric is ideal. It just needs a little more nudging in the right direction to get people using metric without feeling its foreign or strange.
    I think showing calculations like this in metric, shows us how easy it is to use.
    Of course £1 trillion could also be expressed at 1 tera Pound, 1 T£, using metric prefixes. The media already uses things like £5k to represent £5000.
    These metric prefixes should be used more and people should eventually get used to them and the metric units that use metric prefixes, such as kg and km.

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  14. Richard Birkby says:

    David King is absolutely right to note that "if someone were to set out to invent the Imperial system from scratch, I doubt if they would come up with the current conversion factors". This is, of course, exactly what happened when the metric system was invented - they decided on a conversion factor of ten!

    He also asks "why do people hang on to Imperial?". I think it is for two principal reasons - firstly because the issue of metrication has become linked to scepticism over the political direction of Europe, which is an erroneous position to take but nevertheless difficult to shift, and secondly very simply because they can, a situation which could very swiftly be sorted by a spot of legislation!

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  15. Martin Vlietstra says:

    The reasons that people hang onto the Imperial system as I see it are two-fold.

    Firstly, there is the "I can't be bothered to change" attitude. I was aware of this attitude by certain local government officials in South Africa when that country was undergoing their metrication process. That protest was not politically motivated - the local authority concerned was a staunch support of the Apartheid Government.

    Secondly there is the "luggage" that is associated with being the leader in any process. You make all the investment, but others pick up the profits. This is particularly true in business. That is why Goverment must take the lead and ensure that all of business has a level playing field

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  16. Keith Atkin says:

    The pound coin mentioned occupies a CUBOID - not a cube!
    (All the sides of a cube are equal!)

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  17. lee kelly says:

    It's not change the British are affraid of it's being told to change, i've notice since the European commision said that the U.K could keep imperial measures along side metric there has been a lot more use of metric on television. We will one day change & say what where we scared of, if they can do it in commonwealth countries. I can only hope, as evolution teaches adapt or die ( no offense I mean through industry )

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  18. J Gabrielczyk says:

    I happen to be one of those people who really, really, really do believe that the Imperial system is human. It has evolved over the ceturies to arrive at some units of measurement that come in very handy in day to day life.

    The decimal base of the metric system is very simple to understand, but when using mental arithmetic I sometimes find it easier to use the Imperial system because I can break large numbers down into different units and find products using nothing more than well memorised multiplication tables.

    People hang on to Imperial because a) they are used to it, b) they dont like being forced to do things, c) they regard the metric system as 'foreign' and therefore to be viewed with suspicion, c) they have a certain amount of inertia and the view 'if it ain't broke don't fix it' and finally d) they think it is better.

    Merely because you can see nothing but advantages in the UK going metric without delay, do not assume everyone who doesn't think the same is in some way flawed.

    I agree with Lee Kelly that people do not like being told to change. I do not agree with Lee Kelly that evolution teaches "adapt or die". I understand it it would be more likely to teach "cooperate or fail".

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  19. Marc says:

    To visualize (very) large sums of money, a great artist has imaged piles of copper pennies, starting at $10 up to Two hundred billion (hint: it fits on a football field 🙂
    http://www.kokogiak.com/megapenny/default.asp

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  20. John Steele says:

    I recognize the first calculation is fanciful. However, in a real world application, the US has been trying to push the dollar coin over the dollar bill and minted the coin far in excess of demand. They have accumulated $1.4 billion in unwanted coins returned to the Mint, but kept minting coins at a rate determined by law (each year with a new past President depicted). The US dollar coin is 26.5 mm dia x 2 mm, and a weight of 8.1 g.

    The "bone pile" is 11.34 Gg (11340 metric tons). There are enough that calculation of the volume in hexagonal close pack is warranted (there are half coin problems at the edge of a rectangular array which I have ignored). The volume of the (circumscribed)
    hexagonal prism occupied by the coin in hex pack is 1216.3 mm³ and the bone pile occupies 1703 m³.

    They have recently decided to cut production to the rate demanded by collectors and charge a premium for collector grade coins. The bone pile will satisfy currency demand for 1-2 decades. Unfortunately, this pile of coin is not fanciful. (I refuse to calculate it in either Customary or Imperial)

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