How much gold is there in the Earth’s crust and how large could be the chunk of gold mined so far if we could collect it all into one large cube. To make these calculations, we need to know the following things.
Detrital gold nuggets from Tulameen River, British Columbia, Canada. In good old times diggers were looking for a tiny nuggets like this, but nowadays we are forced to extract gold directly from the rocks. Width of view 14 mm.
1. The crustal abundance of gold. It is 0.0031 ppm (parts per million). I took most of my numbers from Wikipedia.
2. The volume of the crust. This is a little tricky because there are two types of it. I assumed that the average thickness of the crust is 7 km for the oceanic and 40 km for the continental crust. Weighted average is therefore about 20 km if we assume that about 60% of the crust is oceanic. Now I only need to calculate the volume of the Earth (I assumed that the Earth is a spherical body) with and without the crust. The difference between these numbers is the volume of the crust. I found out it to be 1.02 x 1019 m3.
3. The mass of the crust. One m3 of the crust weighs about 2800 kg (this is average of both crustal types). So, the mass of the crust is 2.85 x 1022 kg. This is 0.48% of the total mass of the Earth.
The total mass of gold in the crust is therefore 8.83 x 1013 kg. Let’s try to illustrate now what this number means. So far we have extracted about 165,000 tonnes of gold (throughout history) from the crust. So, we have mined only about 1/5000th of the total gold available in the crust. Not much really. Perhaps we shouldn’t worry that we are running out of gold anytime soon?
Now you may say that this calculation is erroneous for several reasons. Yes, I know, it is far too simplistic. I’ll try to improve it. So far we are not desperate enough to mine gold underwater. So, we should remove the ocean basins from our calculations. We are also not able to go very deep. The deepest gold mine in the World is TauTona Mine in South Africa which reaches 3.9 kilometers below ground. This is impressive but nowhere close to the average thickness of the continental crust (40 km). Hence, I believe it is fair to say that we have extracted about 1% of the available gold.
But there is at least one more obvious problem: we do not attempt to extract gold from every rock. The concentration of gold needs to be at least 0.5 ppm for the mining to become economical. I don’t know what is the percentage of total gold that is found in such rocks, but there is no doubt that it further limits the availability of gold. The results are rather astonishing for me. I was not aware that we have already dug up so much of accessible gold. Especially when considering the fact that I assumed gold to be recoverable within 4 kilometers from the surface. This is a rather bold assumption because we normally won’t go that deep.
The mass of gold available in the crust is hard to visualize. So, it would be interesting to know how big would be the cube of gold if we could collect it all together. The density of gold is 19,300 kg/m3. The cube would be 1,660 meters on a side (here I did the calculations with the total mass of gold in the crust). The cube of gold mined so far would have only 20 meters on a side.
I was also interested about the monetary value of gold. One Troy ounce (31.1 grams) of gold costs about $1,660 (March 17th of 2012). So, one kilogram of gold costs $53,370. In every year, about 2,500 tons of gold is mined. Its monetary value is therefore more than 133 billion dollars. This is 0.21% of the GDP of the whole world.
Throughout most of history money had an intrinsic value because the coins were made of precious metals. Later we started using paper notes, but the amount of gold you could buy with these notes was fixed. Nowadays, gold standard, as we all know, is history. We have fiat money which is really guaranteed by nothing but our trust to the institution that issued it. Well, the trust may disappear, especially when governments start creating new money out of thin air which debases the value of the notes people have in their wallets. Because of that there seems to be a rising number of people who would prefer to see the gold standard coming back. I was interested to find out whether it is possible at all.
In 2008 the total amount of currency in circulation in the whole world was worth 4 trillion dollars. This number seems to be rising fast, it was only 2 trillion dollars in 2002. All the governments in the world are holding about 30,000 tons of gold. Its monetary value is only 1.64 trillion dollars or 41% of the value of all the money circulating in the world. So, the answer is quite clear: the gold standard is not likely to return and every year the difference between the value of circulating money and the value of gold held by the governments increases further.
It is interesting to calculate what is the percentage of gold mined so far that is held by the governments. It turns out that it is 18%. Exactly the same number is reported by the World Gold Council. I believe they also just divided the amount of gold held by the governments by the amount of gold mined so far. But there is one problem. Do we really assume that we have recycled all the gold that we have mined? It probably isn’t so, but this percentage may still be reasonably close to the correct number because humankind has been extraordinarily successful at recycling gold. I wish we could pay similar amount of attention to the recycling of all other resources. Gold shows that we can do it if we only want.