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I'm trying to understand how a bitcoin is valued. In my mind, it seems like it can be broken down with some basic math. For instance, if there is $50 trillion worth of "money" in the world and 1% of that money is in bitcoin, and there are 12 million bitcoins in existance, that would make a bitcoin 'worth' $41,666.67 in the physical world.
Is that a correct approach to identifying its value if I wanted to convert to/from dollars? Or, am I missing something?
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There is no mathematical way to determine the value of Bitcoins (or shares of real companies, currencies and similar). It's value is how much people that use it value it. The best indicator what the price is is its exchange rate on various exchanges on the internet like BTC-e, mtGox, Bitstamp and many more. Bitcoins can more or less be related to more traditional currencies when it comes to theoretical background, valuing and more, but take in account Bitcoins are not backed nor managed by anyone or anything. It's all virtual. To look at the price and maybe analyse it you can hop over to bitcoincharts and take a look.
You are missing a source for the fraction you assumed to be one percent. Why not 0.00000000001 percent instead, or maybe 99.99999 percent? – pyramids – 2013-11-29T16:19:05.837
It's speculation, based on computational costs and eminent scarcety, it is expected to valuate at $0.01 USD per uBTC, or $100,000 USD per BTC. The only requirement is that BTC become a de facto currency for 5-8% of global trade to have that much value.
On the subject of determining a currencies value, you have to consider how much the world depends on it. Right now the value of BTC isn't based on demand, it's based on speculation. I still wish I had bought a few thousand when they were still < $10 USD per BTC, I could have bought a house. – Shaun Wilson – 2015-02-12T13:50:02.617