As the 'E' in P/E stands for 'Earnings,' no. P/E is a metric typically used to measure the valuation of businesses, primarily for pricing equity securities.

There are a variety of other metrics used to look at Bitcoin fundamentals, though at the end of the day a lot of the fundamental analysis of Bitcoin ends up being indirect, looking instead at fiat liquidity factors, and overall risk appetite given performance expectations of other sectors based on their overall backdrop. With bitcoin specific metrics people look at things like how much of the total supply has moved or hasn't moved recently, and of course, where we're at in the halving sequence when it comes to mining. Overall energy supply could play a factor as well, though to the best of my knowledge this is a smallerpart of things aside from massive events such as when China banned mining.

This is all more complicated than what a simple P/E is though. I like to often look at it in terms of fiat cost of bitcoin * 21 M/global population to give myself some perspective.

Right now, that's 21,000,000/8,200,000,000*$89,169.00, for a total of $228.36 for each person's equal share of the hardest money on the planet. Draw your own conclusions with that sort of data...

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That means there is no upper limit on bitcoin price ! .. unlike equities, it can grow for ever .. and yes , everyone should have way more than $228 of hard money :-) .. btw that's for this metric .. it is an awesome way to assess the potential of Bitcoin !

Growing forever is an interesting concept economically speaking. While of course there's an infinite amount of "stuff" to buy, arguably there could be an infinitely large (or at least indefinitely large) amount of services one could say no to in favor of Bitcoin, which would give it that indefinitely large if not infinite value potential. I would tend to say this is unlikely, if only because at some point base survival needs tend to kick in -- but hard money does tend to suck up extra value rather than encourage wasteful spending of resources in non-productive manners.

On the other hand, in fiat terms, while arguably in a mathematical sense inflation is multiplicative, it could perpetually approach while never arriving at zero. In practice, people tend to avoid fiat completely at some point, because it just gets too cumbersome to use (the paper is worth more as fire starter, or the cost to transport becomes worth more than the paper, or any other number of ways to visualize this possibility), so it does effectively reach zero due to friction.