Entropy is measured in bits, and each bit doubles the work an attacker must do. For a randomly generated secret it is simply the length multiplied by the base-two logarithm of the alphabet size — which makes the trade-off between "longer" and "more character types" straightforward to settle rather than argue about.
Take a twenty-character password using lowercase, uppercase and digits: an alphabet of sixty-two, worth about 119 bits. Add the full symbol set and the alphabet reaches eighty-six, taking you to about 129 bits — an extra ten. Now instead keep the original alphabet and add four characters: twenty-four bits, more than twice the gain, and the result is easier to type.
This is why composition rules demanding one of everything are the wrong instinct. They add a little entropy, push people toward predictable substitutions like P@ssw0rd1, and give the impression that a short password has been made safe. A long password from a small alphabet beats a short one from a large alphabet comfortably.
Where the numbers sit
- Under 40 bits — falls to an offline attack quickly. Not adequate for anything.
- 60 to 70 bits — sound for ordinary accounts behind a proper password hash.
- 80 bits and above — beyond brute force for the foreseeable future.
- 128 bits — the default here, and more than any password realistically needs.
Worth remembering that none of this protects you if the password is reused. Entropy defends against guessing; uniqueness defends against a breach elsewhere. To check something you already use, the strength checker looks for the patterns that make a password far weaker than its length suggests.