Tag Archives: coins

A More Logical System of Coinage

(Please note: I didn’t say this was necessarily a better system, just that it is more logical. I still can’t believe I spent this much time on this total non-issue.)

There are many, many currency redesigns on the internet. But everybody always concentrates on redesigning the paper currency; very rarely does someone look at redesigning the coins. I’m far from a  graphic designer, but what I can do is look at the size and shape of the coins.

Here is what current UK coinage looks like:*

Coin Diameter /mm Thickness /mm Mass /g Material
1p 20.3 1.65 3.56 Copper-plated steel
2p 25.9 2.03 7.12 Copper-plated steel
5p 18.0 1.7 3.25 Nickel-plated steel
10p 24.5 1.85 6.5 Nickel-plated steel
20p 21.4 1.7 5.0 Cupro-nickel (84:16)
50p 27.3 1.78 8.0 Cupro-nickel (75:25)
£1 22.5 3.15 9.5 Nickel-Brass
£2 28.4 2.50 12.0 Cupro-nickel and

Clearly this makes no sense at all. The 1p and 2p coins are both bigger than the 5p, and the 10p is bigger than the 20p. The 2p coin is heavier than the 1p, 5p, 10p and 20p coins. There are four different materials used, and even though both the 20p and 50p coins are made out of cupro-nickel, the copper-to-nickel ratio is different, which must make manufacturing them more difficult.

Step 1: Get rid of the 1p and 2p

There are a number of reasons for doing this. The 1p and 2p coins are now essentially useless for actually buying anything (which is why many countries have got rid of their 1p/2p equivalents), and the UK 2p coin is particularly big and heavy. Also, it will help when we want to scale the sizes of coins logically.

Step 2: Make coins from the same material

Since we have a fiat money system, we don’t need coins to be made out of different materials, and visual appearance isn’t important, as people will be able differentiate between our new coins using other factors. We should just use the cheapest material, which is nickel-plated steel.

Step 3: Make the sizes more logical

As demonstrated above, the sizes of UK coins currently makes no sense. We want the size of our coins to be proportional to their value, so that the £2 is larger than the £1, and the £1 is larger than the 50p and so on. (This has the useful side effect of making less “powerful” or less “useful” coins smaller and lighter, so that they take up less space in your wallet.)

However, given that we don’t want our new coins to be significantly smaller or larger, or lighter or heavier than our existing coins, we cannot vary size linearly with value. If we did this then the £2 coin would be forty times bigger than the 5p coin, and one of them would have to be either unmanageably small or unmanageably big.

We will therefore have to use a logarithmic system to calculate the new sizes (this makes sense because people’s cognition of numbers is naturally logarithmic). Thus a £2 coin will be bigger than a £1 coin, but not twice the size; and a 50p coin will be bigger than a 10p coin, but not five times bigger.

We don’t want any coin to be smaller than the 5p (the coin with the lowest diameter) or the 1p (the coin with the lowest thickness), or to be larger than the £2 (the coin with the highest diameter) or the £1 (the coin with the highest thickness). Thus we will take the measurements of these coins to be our limits: our new coins must have diameters between 18.0 and 28.4 mm, and thicknesses between 1.65 and 3.15 mm.

After some relatively simple calculations, we end up with the following:

Coin Diameter /mm Thickness /mm Mass /g
5p 18.0 1.65 3.13
10p 20.0 1.93 4.50
20p 21.9 2.21 6.22
50p 24.5 2.59 9.08
£1 26.4 2.87 11.74
£2 28.4 3.15 14.87


Old £1 coin shown above for scale.


Most of the coins are similar in size (the 5p and £2 have exactly the same diameters), but there are a couple of notable differences.


The change in properties are easier to understand via graphs.

As you can see, the proposed diameter and thickness increase sensibly, whereas the existing diameters and thicknesses do not. The same is also true for the proposed masses.


As you can see, the proposed masses are higher than the existing masses for all but the 5p and 10p coins. However, considering the removal of the 1p and 2p coins and after running some extensive Monte Carlo testing, I can confidently say that your average pocket full of change will now weigh less. (It would not be difficult to use a less dense material than nickel-plated steel if weight proved to be a problem. We could also reduce the thicknesses of the coins, making the 2.5 mm thickness of the £2 coin our maximum.)

The logic of using a logarithmic system is further demonstrated when considering adding the £5 coin (which is really only a collectors’ item) into our system. The existing £5 coin is enormous: 39 mm in diameter and 28 grams in mass; in our new system it is a svelte 31 mm and only 19.8 grams. We could therefore replace some of our paper money, which requires frequent costly replacement, with longer-lasting coins.

Existing £1 and £2 coins shown for scale.

Known Issues

Use by the blind

Unlike the current system, our new proposed system uses only circular coins: we do not use shapes of equal width as with the current 20p and 50p coins. This could make them more difficult for blind users to deal with.

Our new coins have a greater variation in mass than the existing coins, and this should make differentiating between them by feel easier. Also, the diameter:thickness ratio changes more noticeably (and of course, more consistently) than existing coins: coins become “fatter” relative to their diameter as their value increases.


The problem of blind users is easily fixed by using different edges on our coins, as is currently done with Euro coins: the 2¢ coin has a groove around its edge, the 10¢ coin has fine “scallops” on its edge, the 20¢ coin uses a “Spanish Flower” design, the €1 coin uses interrupted milling and the €2 uses a fine-milled edge with lettering. There are more than enough different options for blind users to easily differentiate between coins.


My choice would be for every second coin (i.e. 10p, 50p and £2) to use a scalloped edge, as the remaining coins would then different enough either by size or by feel (the scallops are easier to feel than fine milling) to differentiate between. Obviously, extensive testing with blind users would be necessary to iron-out any problems.

Other Issues

None. This is clearly a brilliant idea.

* The difference in the number of significant figures should correspond to different tolerances, but I wouldn’t be surprised if it’s a mistake by the Royal Mint.

Shapes of equal width

Circular objects roll because a circle is a shape of equal width. No matter where you measure from, the distance from one side to the other (through the centre) is the same. But circles aren’t the only shape with this property.

Two British coins are shapes of equal width: the 20p (21.4 mm) and 50p (27.3 mm) coin. Having an equal width makes the coins able to roll and prevents them from getting stuck in machinery. Shapes of equal width also make good manhole covers; because no “side” is any shorter than any other, it is impossible for the cover to fall down the manhole. Circles are easiest to make which is why most manhole covers are circular.

The cost of coins

It used to be the case that coins used as currency had value because of the material from which they were made: a solid gold coin weighing one ounce had the same value as one ounce of gold. The introduction of fiat currencies, issued by central banks, that only have value because a government decrees by law that they do, allowed governments to move away from this dependence on rare metals.

UK coins come in four “flavours”: the “copper” 1p and 2p coins, the “silver” 5p, 10p, 20p and 50p coins and the larger and heavier £1 and two-tone £2 coins. Before 1992 the “copper” 1p and 2p coins really did contain copper, being made from a bronze containing 97% copper, 2.5% zinc and 0.5% tin. With a mass of 3.56 and 7.12 grams respectively the pre-1992 coins contained 3.54 and 6.91 grams of copper; at the current bulk price and the current USD-GBP exchange rate this makes a 1p coin worth 1.66 pence and a 2p coin worth 3.23 pence (those links will take you to automatically calculated values using current values for spot price and exchange rate).

If you were able to buy pre-1992 1p and 2p coins in bulk for their face value you could make a profit by melting them down and selling the resulting copper as scrap (though this is illegal under the 1971 Coinage Act). This increasing price of copper in the early lead to a change from bronze to copper-plated steel and this makes it very easy to differentiate between the old and new 1p/2p coins: pre-1992 coins are not magnetic and post-1992 coins are.

The “silver” coins have previously been made from cupro-nickel, an alloy of copper and nickel in a 75:25 ratio. In terms of its raw metal, a 3.25 gram five pence coin, containing 2.44 grams of copper and 0.81 grams of nickel is currently worth 3.08 pence (1.14p for the copper and 1.94p for the nickel). A 6½ gram ten pence coin is worth 6.16p, a five gram twenty pence coin is worth 4.74p and an eight gram fifty pence coin is worth 7.58p.

From January 2012 the “silver” coins will be made from nickel-plated steel (making them magnetic), a change driven probably by the rising cost of both copper and nickel. (In May 2007, when the price of nickel was at a peak, a five pence coin was worth more than six pence as scrap copper and nickel).

The high value of the £1 coin (current value), composed of 70% copper, 24.5% zinc, and 5.5% nickel and the £2 coin, with a cupro-nickel core surrounded by a ring of 76% copper, 20% zinc, and 4% nickel, makes them unlikely to ever approach a situation in which they are worth more than their face value.