Let's take a different crack from a monetary perspective instead of a physics perspective. Skylar Nagao at Peerio stated that:
In a 2014
research paper on password memorability, security researchers Joseph
Bonneau (Stanford) and Stuart Schechter (Microsoft) estimated the cost
of an attack based on the total annual payout to bitcoin miners in
"In 2013, Bitcoin miners collectively performed ≈ 275 SHA-256 hashes in exchange for bitcoin rewards worth ≈ US$257M… this is the
only publicly known operation performing in excess of 264
cryptographic operations and hence provides the best estimate
available. Even assuming a centralized effort could be an order of
magnitude more efficient, this still leaves us with an estimate of
US$1M to perform a 270 SHA-256 evaluations and around US$1B for 280
Here we have the billion dollar password
estimate — even for a centralized state attacker, it would cost about
$1 billion US dollars to compute 280 SHA-256 hash functions over the
course of a year. This is like saying it would cost $1 billion USD to
try 280 lock combinations over a year. Since an attacker would be
‘likely’ to guess correctly with just one guess after the halfway
point, Peerio uses an 81-bit (280 times two) minimum standard for our
computer generated passphrases. We chose this standard because we
wanted to make sure even a state level attacker would need to drop $1
billion US dollars to have even a coin’s toss chance of cracking a
An 81-bit password is estimated to cost 1 billion to be likely to crack and so is considered by Peerio to be "uncrackable". In layman's terms 81-bits would work out to 17 random lower-case letters, 13 random characters from a US keyboard, or 7-8 words randomly chosen from a dictionary.
There are admittedly a lot of technical details like prices, risk levels, and hashing algorithms. Perhaps the passwords are hashed much, much more strongly with bcrypt. Perhaps these figures are out of date and more modern mining costs or the latest mining revenue data puts the hashes/dollar as high as 1016 hashes/dollar. Maybe Bitcoin isn't the best comparison due to market differences or hardware differences. At the end of the day we still have an order of magnitude for the lowest cost of hashing at scale.
Even if some nation-state or millionaire put together a hash-breaking farm the size of Bitmain's Ordos mine, they'd still take months to have a good chance of finding your 80-bit password password from an insecure hash, and throw away millions or even billions of dollars of cost and lost potential revenue. If any government could hit a billion terahashes per second, I bet they have better things to do with that money-making machine than crack your 81-bit password.
If we're talking about guarantees and defense against incredibly powerful adversaries, it's important to note that there are plenty of ways to get around an uncrackable password. Methods include session hijacking, MITM attacks, password reset exploits, keyloggers, asking the website/admin for access, and phishing. Although some threats like physically tampering with your computer may seem absurd, they're more reasonable than a billion dollar password cracking effort (relevant xkcd).