If efficiency of bitcoin miners stays the same. That number will reach 1602 kg of CO2 by May 1st 2015.
comments in hackernews point out, to offset this, we'd have to plant 1.6 trees every 24 seconds in perpetuity, and keep every tree alive for at least 100 years.
In comparison, the ECB says producing Euros requires 27.6 MWatt×years. Unfortunately they don't cite the study they allude to - all I've been able to find are ELI5s like the linked ECB page - but I'm guessing they mean per year, since that seems like the most sensible way they could be expressing it. That gives us 27.6 MW as the amount of currency it takes to power Europe.
How can we compare this to mining costs? Well, 1 BTC is currently worth ~230 USD, according to Google's converter. Multiplying by 25 BTC reward per 10 minutes, that's 34500 $/hr total mining revenue. In China and India residential electricity averages 8¢/kWh (according to some website), so let's assume the major miners can get mining-quality power for 5¢. Assuming miners are free (they aren't, but I'll come back to this) and all costs go to energy, we get 790 MW as the current energy drain of mining.
It's a fair amount more than Euros, but Bitcoin is very young; how will this change over time? Well, as we've just seen, total energy usage is directly proportional to these variables:
- mining reward
- proportion of mining costs that is energy
- value of bitcoin
- (cheapness of energy)
Mining rewards are guaranteed to decrease exponentially, not counting transaction fees (which are currently a small fraction of total but will in year ~2140 be the entire reward). Proportion of mining costs that are energy we can also expect to continue decreasing exponentially as long as Koomey's law holds (like Moore's, but for energy; it's slightly faster, too). So we have two processes that will decrease exponentially for decades; in 2040 mining rewards (not counting tx fees) will decrease by a factor of more than 50, and energy usage per computation will decrease by a factor of 40,000. Price is harder to predict but if it goes up in the long run, then the number of people bitcoin is serving must also be increasing.
So, bitcoin is pretty energy inefficient in its infancy, when compared with banknotes. But even estimates more conservative than mine by orders of magnitude predict that in the long run, it'd save us a lot of trees to put away those billfolds and pull out our phones.