We normally measure the coin value in USD, which is the most well known and liquid money on the world scale.
But that is only the relative price to some other money, which also varies in value. The dollar index itself is just the a relative dollar price to a few other well known money types, weighed by a more or less random "importance" factor.
So how to do it? Obviously it has to be a form of buying power, buying real value. Real value is different from money value. Real things have value because it supports life, if you have no real things to consume in your life you can not continue to live. Money doesn't help you if there is nothing to buy.
The obvious answer is the consumer price index (cpi), when you invert the consumer price index you get the money's power for buying consumables. But there are some difficulties in measurement. You have to weigh the prices by what people tend to buy. You can not include any kind of stuff people buy, it has to be the things that most people buy. Normal food, normal clothes and other things almost everybody use. The basket with weights has to be changed from time to time, as the economy and the products develop and consumer preferences change. A new (10-20 years) complication is that the government calculated cpi (yes it is calculated now, there is no one walking around shopping the "basket" any more), is totally doctored for the purpose of showing lower prices (and higher money value). That serves the government. AFAIK there is no one else trying to create a competing cpi.
Then there are other important prices. There are some commodities that are traded world wide, that does not change much (although the relative amounts can change, difficult to track). I think of oil, copper, steel, cement, maize, wheat, beans, coffe. These have been traded for hundreds of years and are relatively fungible. Those products are capital goods, not consumer goods, but changes will necessarily flow to consumer goods in months. Still some problems, geographical price differences, and qualities. Problem with oil is that the most well known world prices are futures, not spot. But still useful, because it can track prices and indirectly the money value over great leaps of time.
It is still not good enough, to find the money value you have start with the amount of money (in coins) for all money types, and divide it by all prices of all goods on the market, mutiply it by amounts, and that is obviously impossible.
The most common simple way to measure change in the value, is to use the year over year change in percent. There are also formulas to compute volatility as a positive number, but no standard, so the way is to choose one formula and stick to it. Stability is then the inverse of the volatility.
TLDR: If you want to find the money value, and its stability, you need to find a price index for relevant real stuff, and the degree of change. The inverse of the price index is the money value, and the inverse of the degree of change is the stability.
Edits 2021-11-05
Starting point for looking into volatility: https://www.investopedia.com/terms/v/volatility.asp
Some prices measured in gold (gold money is more stable than cryptos, but not completely stable: http://pricedingold.com/
Alternative to government consumer price indes: http://www.shadowstats.com/alternate_data/inflation-charts
Federal Reserve consumer price indexes: https://fred.stlouisfed.org/categories/9
Money is getting its value reassesed everyday now, and it will only get worse. I've said it elsewhere too, but right now value is highly shifting to commodities like food, and of course energy resources. Think the big thing is going to be Uranium soon, buying some as of now. Going DCA little by little.