Imagine you are on a game show, and you’ve just won the grand prize. The prize is your own weight in coins!

The host gives you ten seconds to select what kind of coin you want your prize to be measured in. *(Insert game show music here …)*

Do you want to go home with your own weight in pennies? Do you want to go home with your own weight in nickels? How about dimes, quarters or dollar coins? What about half-dollars? |

Quick, what do you select? (We’re assuming that your goal is to select the option that maximizes the prize money you take home). Obviously quarters are more valuable than dimes, but does their extra weight work against you since you since you’ll get less of them?
Let's work it out … |

To answer the prize question, we need to work out how many of each coin we get per pound (or kg, or Stone …), and then we can multiple this by the value of each coin.

There are six types of coin currently in US circulation. These are: the penny, nickel, dime, quarter, half-dollar, and the dollar coin. Here they are:

*(Whilst there is more than one version of the dollar coin, they all have the same mass).*

Below is a table showing each of these coins and their respective weights.

Next we can calculate how many of each of these coins there are in one Kilogram (To my non-metric friends, one **kg** is approximately 2.2 lbs, though it does not really matter what weight we select when comparing the coins as we are really only looking at the ratio – as long as we use the same for each coin it does not matter).

Penny^{*} |
Nickel | Dime | Quarter | Half-Dollar | Dollar | |
---|---|---|---|---|---|---|

Weight (g) |
2.500 | 5.000 | 2.268 | 5.670 | 11.340 | 8.100 |

Coins/kg |
400.000 | 200.000 | 440.917 | 176.367 | 88.183 | 123.457 |

^{*} The Penny changed in 1982 from 3.11g when the Copper content was reduced.

Next we multiply the number of coins per **kg** by the value of each coin to give the result of *Value per kg*.

Penny | Nickel | Dime | Quarter | Half-Dollar | Dollar | |
---|---|---|---|---|---|---|

Weight (g) |
2.500 | 5.000 | 2.268 | 5.670 | 11.340 | 8.100 |

Coins/kg |
400.000 | 200.000 | 440.917 | 176.367 | 88.183 | 123.457 |

Value |
$0.01 | $0.05 | $0.10 | $0.25 | $0.50 | $1.00 |

Value/kg |
$4.000 | $10.000 | $44.092 | $44.092 | $44.092 | $123.457 |

There are some very interesting results. Firstly, the correct answer is The next interesting thing is the equivalence of dimes, quarters and half-dollars. The ratio of their masses is This means that it would not matter which of these coins you selected, if you elected to be paid in these coins; your prize would be the same. |

In fact we can go further, since these coins have exactly the same value density, if we used just these three coins it does not matter the mix of the coins. Any random combination of these coins that weigh the same has the same value. That’s right – if you were handed a bucket of coins containing a random mixture of dimes, quarters and half-dollars you could determine the total value of money simply by weighing them, and would not need to count or sort the coins! (After subtracting the weight of the bucket, obviously!) |

Why does this happen? Well, It goes back to the days when a coin’s value was simply the value of the metal that the coin was made out of. When coins were made out of Silver, the value of the Silver in the coin was the value of the coin. It makes sense that a coin containing twice as much Silver would be worth twice as much!

In North America, the average body weight is 80.7 kg, which would be a prize of just less than $10k if you selected dollar coins ( If you are interested in another random way a body can be valued check out this article about splitting the body into elemental components. |

We can perform similar calculations for the coinage of other countries and regions.

Below is a table showing similar calculations for the UK.

One Pence | Two Pence | Five Pence | Ten Pence | Twenty Pence | Fifty Pence | One Pound | Two Pound | Five Pound | |
---|---|---|---|---|---|---|---|---|---|

Weight (g) |
3.560 | 7.130 | 3.250 | 6.500 | 5.000 | 8.000 | 9.500 | 12.000 | 28.280 |

Coins/kg |
280.899 | 140.252 | 307.692 | 153.846 | 200.000 | 125.000 | 105.263 | 83.333 | 35.361 |

Value |
£0.01 | £0.02 | £0.05 | £0.10 | £0.20 | £0.50 | £1.00 | £2.00 | £5.00 |

Value/kg |
£2.809 | £2.805 | £15.385 | £15.385 | £40.000 | £62.500 | £105.263 | £166.667 | £176.803 |

Here is a table for the coins used in connection with the Euro.

One Centime | Two Centime | Five Centime | Ten Centime | Twenty Centime | Fifty Centime | One Euro | Two Euro | |
---|---|---|---|---|---|---|---|---|

Weight (g) |
2.300 | 3.000 | 3.900 | 4.100 | 5.700 | 7.800 | 7.500 | 8.500 |

Coins/kg |
434.783 | 333.333 | 256.410 | 243.902 | 175.439 | 128.205 | 133.333 | 117.647 |

Value |
€0.01 | €0.02 | €0.05 | €0.10 | €0.20 | €0.50 | €1.00 | €2.00 |

Value/kg |
€4.348 | €6.667 | €12.821 | €24.390 | €35.088 | €64.103 | €133.333 | €235.294 |

My final example is coins used in Switzerland.

Five Centime | Ten Centime | Twenty Centime | Fifty Centime | One Franc | Two Franc | Five Franc | |
---|---|---|---|---|---|---|---|

Weight (g) |
1.800 | 3.000 | 4.000 | 2.200 | 4.400 | 8.800 | 13.200 |

Coins/kg |
555.556 | 333.333 | 250.000 | 454.545 | 227.273 | 113.636 | 75.758 |

Value |
SFr 0.05 | SFr 0.10 | SFr 0.20 | SFr 0.50 | SFr 1.00 | SFr 2.00 | SFr 5.00 |

Value/kg |
SFr 27.778 | SFr 33.333 | SFr 50.000 | SFr 227.273 | SFr 227.273 | SFr 227.273 | SFr 378.788 |

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