# Is it valid to compare cryptocurrencies by using their smallest divisible unit?

I'd like to compare the relative value (in USD) of three cryptocurrencies: Bitcoin, Ethereum, and IOTA. (See spreadsheet below.) Specifically, I'm comparing the price of each currency's smallest unit of division. And I'm taking that a step further to compare the "unit price" and the "smallest unit price" over the current circulating supply.

(Note, although these currencies have big differences with respect to their feature sets and target markets, and I don't want to consider that for the purposes of this question.)

# The Problem: Currency Differences

## Unit Subdivision

These three cryptocurrencies vary dramatically by the amount a single unit can be subdivided. A single bitcoin (BTC) can be divided by 1/10^8. That is the smallest unit that can be recorded on the blockchain and is sometimes called a Satoshi. A single Ethereum unit is called an ether. It can be divided by 1/10^18 and this smallest unit is called a Wei. A single IOTA cannot be subdivided, unlike the BTC and Ether units, which were chosen to give sub-unit precision rather than large whole numbers.

## Circulating Supply

Also, the current circulating supply of each currency is dramatically different. At the time of this writing there are 16,451,325 BTC in circulation, 93,329,609 Ether in circulation, and approximately 2.8E+15 IOTA in circulation (which unlike BTC and Ether, is fixed and will never increase.)

# Solution Premises

### Use Smallest Unit of Currency for Price Comparison

The first premise of my question, which may be incorrect, is that we can get closer to an apples-to-apples comparison of price by calculating the price of the small unit of currency. For example, I don't think it would be accurate to compare the price of BTC (\$1,918.41 at the time of this writing) and the circulating supply of 16,451,325 BTC against the price of an IOTA (0.17) and it's circulating supply of 2,779,530,283,000,000.

### Use Price over Supply to Show Value

The second premise, which may be also be incorrect, is that after we have a price-per-smallest-unit for each currency, we can further estimate value by dividing that number by the existing circulating supply.

For example, if a baker slices a single pie into 4 slices and sells each for two dollars apiece, and a second baker slices a pie into three slices and also sells for each for two dollars apiece, I can see that I can more "value," for my money by dividing the cost of a single slice by the number of total slices. In the case, a value of .5 for the quarter slices and a value of .67 for the pie sliced in thirds.

I'm considering the available supply in this case to be fixed, which is true with IOTA. The circulation of Bitcoin and Ethereum will increase to give a slow inflationary rate, but I don't think I want to consider that in the context of this question.

# Summary

This is a screenshot of a spreadsheet where I've done the above calculations (click to enlarge):

• In the last three columns we see very different results. In column G, the price of the smallest unit for the currency, the Ethereum unit "Wei" is cheapest by far.
• However, in column I--which takes the price of the smallest unit of currency divided by the circulating supply of that smallest unit--the IOTA (larger numbers are better here) seems to be a better value.
• And finally, in column H, we abandon the idea that using the smallest possible unit is important and simply divide the unit price by its circulating supply. That result suggest that bitcoin is a better value.

I feel that the calculation in column H, where we don't reduce the currency price/circulation to it's smallest possibly unit is wrong, especially if we're considering IOTA in the set. But I'm also unsure, due to my lack of economics knowledge, that the degree to which the currency can be subdivided is important.

In the end, a stock (or cryptocurrency) is just worth what someone is willing to pay for it. And value is more than just price. But are the above calculations a valid way to compare cost of these currencies?

• Perhaps your question would be easier to answer if you explained the motivation for your comparison. Comparing the 'cost' of a penny and a dollar in a third currency is possible, but it is doubtful that information is useful in any reasoning. Commented Jul 17, 2017 at 6:25
• Very interesting points. One non-crypto-friendly gets easily confused by the idea that 1 bitcoin is now (October 2017) worth 5'000 USD. Does it mean you "can buy more" if you earn you salary in Bitcoin rather than in Ethereum for instance? This raises a lot more questions. Very much like when in Europe there still was one currency per country: people would get so confused, everyone claiming to know better, and in the end having exchanges making the most of the situation. I doubt it is much different in the crypto world. Commented Oct 17, 2017 at 14:13