How Big is a Billion?

Counting is easy, right? When we were very young, we were taught to count in terms of apples or blocks or something like that: one apple, two apples, three apples, and so on. It is easy to imagine three apples. It doesn't require much effort to imagine ten apples. Imagining a hundred apples requires a bit more effort, but isn't too tough.

Now try to image a billion apples. What are you thinking of? A room filled with apples? A concert hall filled with apples? Let's be honest with ourselves, and admit that imagining a billion apples is hard. So, how do we go about imagining a billion apples?

How many is a billion?

The first thing we need to work out is what exactly a billion is, numerically speaking. You'd think this would be straight-forward, but there are actually 2 definitions for a billion.

The most common definition is the short-scale form. This states that a billion is a thousand million, and that a million is a thousand thousand. This makes sense as each new 'big number' is a thousand times bigger than the previous 'big number'. So a trillion would be a thousand billion and a quadrillion a thousand trillion. In other words we add 3 zeros to the end of each number.

The short-scale also makes sense in terms of SI prefixes. SI stands for Systéme Internationale and is an set of international standards. SI prefixes include milli-, kilo-, mega-, giga-, etc... A billion would use giga- as in gigabytes (1 billion bytes).

This scale is used in the US, the UK (since the 70s), and most English-speaking and Arabic countries.

In the short-scale form, a billion is written numerically as:

1,000,000,000

Using scientific notation it is written as:

10⁹ (that is 10x10 9 times)

 The long-scale form used to be used in the UK, and defines a billion as a million million. However, it makes little sense scientifically as it is pretty much incompatible with SI. In this form each new 'big number' is a million times bigger than the previous 'big number'. A thousand-million in the long-scale is called a 'milliard'.

The long-scale is used in many non-English speaking countries.

In the long-scale form, a billion is written numerically as:

1,000,000,000,000

Using scientific notation it is written as:

10¹² (that is 10x10 12 times)

You can get more information on the two scales on this rather comprehensive Wikipedia page.

For this post we are going to use the short-scale as it makes the most sense.

How many is a billion apples?

Let's think about apples for a minute. What kind of apple do we mean? I'm going to choose the Granny Smith apple. According to Tesco's nutritional information a typical apple is 133g. This seems a reasonable number and is pretty consistent with other figures. Feel free to redo these calculations with other apples or items and post your results in the comments below.

So, 1 billion apples would weigh:

1,000,000,000 x 133 = 133,000,000,000 g or 133,000,000 kg

So that's a hundred-and-thirty-three-billion grams or a  hundred-and-thirty-three-million kilograms.

They're still pretty big numbers, so that doesn't really help. How about the amount of space it would fill up. A common comparison you see in the media for big numbers is 'Olympic swimming pools'. An Olympic swimming pool is 2.5 million litres (2,500 m³).

How about the volume of an apple, though? Spheres don't perfectly stack, so there would be gaps. I couldn't find stats for Granny Smith specifically so I've gone down the middle and got the diameter for a medium sized apple. Apparently they have a diameter of around 7 cm. If we imagine a perfectly spherical apple in a perfectly sized box, each side would be 7 cm, making the volume 343 cm³.

"Boris bus front" by Andrew Davidson at en.wikipedia
Own work Transferred from en.wikipedia.
Licensed under CC BY-SA 3.0 via Wikimedia Commons.

Divide that into the 2.5 million litres and we get 7.289 million apples per Olympic swimming pool. Divide a billion by that number and we get 137.2. That means:

1 billion apples would fill approximately 137 Olympic swimming pools and would weigh as much as 10,514 double decker buses (specifically the New Routemaster, or Borisbus).

Maybe that will help visualise a billion a bit better!

Other billions

Let's quickly look at some other comparisons:

• 1 billion words ≈ 1782 War and Peace novels (561,093 words) ≈ 922 complete Harry Potter series (1,084,170 words)
• 1 billion ants ≈ 3 tonnes ≈ 0.43 African elephants
• 1 billion seconds = 31.69 years (in other words the year will be 2046 in a billion seconds time)
• 1 billion kg of gold ≈ £24,616,000,000,000 (24 trillion 616 billion pounds at £24616 per kg) ≈ 11 x the UK's total money supply (£2200 billion)
• 1 billion pieces of paper ≈ 100 km stack ≈ thickness of the Earth's atmosphere

So, now when you hear in 'billions' being thrown about in the media you have a better idea of what a billion is exactly. It is a 1 with 9 zeroes following it. It is the number of apples that would fill 137 Olympic swimming pools. There are around 7.2 billion (7,200,000,000) people on the planet. If they each put an apple in Olympic swimming pools we'd need over 986 pools. Alternatively, if we stacked each of the 7.2 billion apples up into a tower (each apple being roughly 7cm tall) it would be 1.3 x the distance between the earth and moon. Lay them in a line and they would go around the world 79 times taking light 1.7 seconds to travel the distance!

Have you got any fun comparisons for a billion? Or perhaps a curious fact about the number? If so let me know in the comments below or via social media. As always you can follow It Is All Science using the buttons on the right, and share this post using the buttons on the left and those under this post.

Remember, it is all science. So, let's be curious.