What Entropy Actually Measures
Entropy is the number of bits needed to describe how many equally likely passwords could have been produced by the process that made yours. Each additional bit doubles the number of possibilities.
Formula
Passphrase = words × log₂(word list size)
The crucial qualifier is the process that made yours. This formula describes a password generated by picking each character uniformly at random. It does not describe the password a person invented, and the gap between the two is the single most misunderstood point in password security.
Why Human-Chosen Passwords Score Far Lower
Take P@ssw0rd1. Nine characters across a 95-character set gives a theoretical 59 bits. Its real strength is close to zero, because a cracking tool does not iterate blindly through the keyspace — it works through leaked password lists and known substitution patterns first.
Attackers exploit the structure people reliably produce: a capital at the start, a digit or two at the end, an exclamation mark last, @ for a, 0 for o, a year, a name, a keyboard run. Every one of those choices removes bits, because it collapses a huge random space into a small predictable one.
This is why the figure above should be read as an upper bound. It is what your password would be worth if a random process had produced it. If you chose it yourself, assume substantially less.
Entropy Is Not the Whole Threat Model
A 120-bit password offers no protection at all if it has been reused on a site that was breached. Credential stuffing does not attack your password’s strength; it takes a known working pair and tries it elsewhere. Strength is irrelevant once the password is already in a list.
In practice, three things matter more than squeezing out extra bits: a unique password per account, so one breach cannot spread; two-factor authentication, which defeats a stolen password entirely; and a password manager, which is what makes the first two realistic. Manager-generated passwords are also genuinely random, which means the entropy figure above finally describes them accurately.
Why Cracking Speeds Vary So Widely
The times above depend enormously on how the site stored your password. A fast general-purpose hash such as unsalted MD5 or SHA-1 can be attacked at billions of guesses per second on consumer hardware. A deliberately slow, memory-hard function such as bcrypt, scrypt or Argon2 is designed to resist exactly that, cutting the rate to thousands per second — a difference of six orders of magnitude for the same password. You cannot control which a site uses, which is another reason uniqueness and 2FA carry more weight than length alone.