What actually makes a passphrase hard to guess

Password rules have trained a whole industry to do the wrong thing. Take a word you can remember, capitalise the first letter, swap a vowel for a digit, put an exclamation mark on the end, and the form accepts it. The rule has been satisfied. Almost nothing has been gained.

The quantity that matters is how many equally likely possibilities your secret was drawn from. That is what people mean by entropy, and it is a property of the process that produced the secret, not of how complicated the result looks.

Why the punctuation does so little

Adding a symbol widens the set of characters, which sounds valuable and is, slightly. Adding characters multiplies the number of possibilities for each one you add, which is a completely different order of improvement. Length compounds; character variety decorates.

But there is a condition attached, and it is the whole game: those possibilities only count if each character was actually unpredictable. A mangled dictionary word is not unpredictable. Substituting digits for letters, capitalising the front and hanging punctuation off the back are conventions — the same conventions everybody was taught. A predictable transformation of a predictable word gives a predictable result, however jagged it looks on screen.

Passphrase arithmetic, with the assumption stated

Here is a calculation you can follow all the way through, because the assumption is written down. This site's passphrase generator draws words from a fixed list of 100 short words, and picks each word independently.

If each of 4 words is one of 100, the number of possible passphrases is 100 × 100 × 100 × 100 = 100,000,000. In bits that is 4 × log₂(100) = 4 × 6.64 = 26.6 bits. The generator also appends a two-digit number from 10 to 99, which is 90 further possibilities, or log₂(90) = 6.49 bits, giving about 33.1 bits in total.

Now look at what each extra word buys. Every additional word multiplies the count by 100 and adds 6.64 bits. Eight words give 8 × 6.64 = 53.2 bits before the number, twelve words give 12 × 6.64 = 79.7. That is the entire lesson in one line: with a short list, the fix is more words. The generator accepts three to twenty-four for exactly that reason, and the default of four is a starting point rather than a recommendation.

Two honest caveats about those figures. They assume the words were chosen by the generator, uniformly and independently — pick four words yourself from the same list and the arithmetic no longer describes what you did, because your choices are not uniform. And bits are a way of comparing sizes of haystacks, not a promise about any particular outcome. This page gives no elapsed-time claim, because that depends on hardware nobody here can see and it changes.

What a strength meter can and cannot know

A meter is an estimate, and it is worth knowing which estimate. This site's checker looks at the length of what you typed and at which character sets appear in it — lowercase, uppercase, digits, anything else — adds up an alphabet size from those, and reports length times the log of that alphabet as a bit figure, plus a rough time figure derived from an assumed guessing rate.

That model assumes every character was chosen at random from the alphabet it detected. Where that assumption does not hold, the estimate is generous. The meter has no idea that your word is a common one, that it appears in the site name, that it is the name of a family member, that the digits are a birth year, that the pattern is one everybody uses, or that the same secret is already protecting four other accounts. It reads shape, not history.

So read it as a floor on how bad a guessable choice looks, never as a verdict. A high reading on something you invented yourself is the estimate being polite. The number is only meaningful when the thing it measured was genuinely produced at random.

What to do with all that

Let something else make the choice. The Password Strength checker on this site runs locally and stores nothing, and it sits next to a password generator and a passphrase generator that both run the same way — the point of using one is that the result is not a choice you made. The generator leaves look-alike glyphs such as O, 0, l and 1 out of its alphabets, which trades a sliver of variety for never misreading a character, and length is the lever that more than covers the difference.

Then the two things that outrank strength entirely: use a different secret for every account, so that one exposure stays one exposure, and keep them somewhere built for it rather than in your head, so that using long random ones is actually practical. A strong secret reused everywhere is a single point of failure wearing a good disguise.