Character generators use alphabet size
For length L and alphabet size N, the ideal estimate is L × log2(N).
Passphrases use word-list size
For W independently chosen words from a list of N words, the ideal estimate is W × log2(N). Separators add little if predictable.
Uniform selection is required
Modulo bias and non-cryptographic random sources reduce the quality of the estimate. Rejection sampling avoids favoring some choices.
Compromise bypasses guessing
Phishing, malware, password reuse, server breaches, and insecure recovery can defeat a high-entropy secret without brute force.
Rejection sampling keeps choices even
A cryptographic random integer covers a fixed numeric range. Taking a simple remainder can favor some outcomes when the alphabet size does not divide that range. This generator discards values above the largest evenly divisible boundary and draws again, then uses the same bounded selection while shuffling required character groups. That control supports the uniform-choice assumption behind the displayed estimate; it does not certify the security of the browser, device, account provider, or recovery process.
Interpret the number as a model
The displayed bits multiply password length by the logarithm of the active character pool, or word-pair count by the logarithm of the available adjective–noun combinations. Requirements that force at least one character from each group, user edits, banned strings, leaked account rules, and attacker knowledge can change the effective distribution. Use the estimate to compare generator settings, not to predict a breach time. Uniqueness, secure storage, rate limits, multifactor authentication, and recovery controls remain separate defenses.