What a bit of entropy actually means

Every extra bit doubles the number of possibilities. That single fact settles most arguments about password strength.

Entropy measures unpredictability, in bits. One bit means two equally likely outcomes; ten bits means 1,024; fifty bits means about a thousand trillion. The doubling is the whole idea, and it is why small-sounding differences are not small.

Where the bits come from

• A coin — 1 bit.
• A six-sided die — about 2.6 bits.
• A random lower-case letter — about 4.7 bits.
• A character from the full keyboard — about 6.6 bits.
• A word from a 559-word list — about 9.13 bits.
• A random byte — exactly 8 bits.

Multiply by how many you draw, and that is your entropy — provided every draw is independent and random.

The condition that ruins everything

All of this assumes the choices are made at random. A password you invented has far less entropy than counting its characters suggests, because you did not choose uniformly: you chose something memorable, and memorable means predictable. Substituting 3 for E and adding a 1 at the end is a transformation every cracking tool has applied since the 1990s.

Entropy is a property of the process, not of the string. There is no way to measure the entropy of a password by looking at it, which is precisely what strength meters attempt.

Length or complexity?

Both add bits, and the tool computes the trade-off exactly. A larger alphabet adds bits per character; more characters add bits at the current rate. The break-even comes out at roughly two-fifths of the length — so at 16 characters, moving from lower-case only to the full keyboard is worth about the same as six more lower-case characters.

In practice length wins, because it is easier to add and does not interact badly with the sites that impose character rules. A long passphrase beats a short scramble on both strength and usability.

Frequently asked questions

How many bits is enough?

It depends on whether an attacker can guess offline. Against a service that rate-limits and stores passwords properly, over 40 bits is ample. Against something attacked offline — an encrypted disk, a password manager's master password — aim much higher, which is where passphrases become the practical answer.

Why do strength meters disagree with each other?

Because they are estimating something not visible in the string. They apply heuristics about patterns and dictionaries; entropy is a property of how the password was generated, which no meter can observe.

Does adding a symbol at the end help much?

Barely. It adds a few bits at most, and if an attacker knows the habit it adds close to nothing. Another random word or several more characters is worth far more.