How the bits are counted
For a randomly generated password, entropy is the length times the base-2 logarithm of the pool size. The pool is the set of characters each position can take. Each bit is one yes or no choice, so every extra bit doubles the number of passwords an attacker has to try.
With every class switched on, the Password Generator draws from a pool of 91 characters. Each character adds 6.5 bits. A 12-character password has 78 bits, and a 16-character one has 104. A six-digit PIN, from a pool of only 10, has 20.
Length beats variety. Sixteen lowercase letters give 75 bits, more than the 52 bits of eight characters from every class. Widening the pool from lowercase letters to all 91 characters adds 1.8 bits to each position. Each added position gives 6.5.
From bits to crack time
Bits turn into time once you pick a guess rate. The Password Generator's crack times assume 100 billion guesses per second. That models an attacker who has stolen a list of password hashes and tests them offline on fast hardware. On average the attacker finds the password after trying half of all combinations.
Here's the average time at that rate for passwords built from all 91 characters:
- 8 characters, 52 bits: 7 hours
- 10 characters, 65 bits: 6 years
- 12 characters, 78 bits: 51,000 years
- 16 characters, 104 bits: 3,500,000,000,000 years
Four more characters make the search 69 million times bigger, which is why the times climb so fast. Real attacks vary. A login form that locks you out after a few tries limits an attacker to a tiny fraction of that rate. A site that stores passwords with a deliberately slow hash makes every offline guess cost more, and a fast hash does the opposite. How password hashing works explains the difference.
When the formula doesn't apply
The formula only holds when every character is chosen at random. Entropy describes the process that made a password, not the string you see. Summer2026! has 11 characters from a pool of 91, which the formula would score at 72 bits. It's a word, a year and a symbol, a pattern attackers try early, so its real strength is far lower. Judging passwords that people choose is hard for this reason, and a reused password has no strength at all against someone holding the breached copy.
Words work as well as characters if they're picked at random. The EFF's long dice wordlist has 7,776 words, so one word adds 12.9 bits. Six words, the EFF's suggestion for most uses, give 77.5 bits. That's only about 0.5 bits short of 12 random characters from the full pool, and a lot easier to type. The passphrase comparison goes through the tradeoffs.
What the number depends on
The count assumes real randomness. The Password Generator draws each character with the browser's CSPRNG, so its numbers hold. A password you made up and then padded with symbols doesn't earn the same credit.
Two settings change the count. Leaving out look-alike characters (0, O, 1, l, I and the pipe) shrinks the pool to 85 and costs 1.6 bits at 16 characters. One extra character adds 6.4 bits, so adding one wins that back.
A long random password stops brute force. It doesn't stop phishing, reuse or a breach at the site, so pair it with a second factor.