When a website says “strong password”, it usually checked the length and the presence of a digit. That says nothing about real strength. The proper measure is called entropy, it is counted in bits, and it is exactly what the dial on our pages shows.
What a bit of entropy is
Entropy is the base-two logarithm of the number of equally likely options. One bit means a choice between two, ten bits a choice among 1024, twenty bits roughly a million. Every added bit doubles the cracking work.
For a random password the formula is simple:
entropy = length × log₂(alphabet size)
An alphabet of lowercase and uppercase letters, digits and symbols holds 94 characters, and log₂(94) ≈ 6.55 bits per character. A 16-character password therefore carries about 105 bits.
A farm testing 10¹⁴ candidates per second would need longer than the universe has existed. That is not a figure of speech but the result of a division: 2¹⁰⁴ over 10¹⁴ lands on the order of 10¹⁷ years.
How many bits are enough
| Bits | Verdict | Appropriate for |
|---|---|---|
| under 40 | weak | nothing beyond throwaway forms |
| 40–60 | fair | forums and services without personal data |
| 60–80 | good | shops, social media, subscriptions |
| 80–100 | strong | email, banking, work systems |
| 100+ | fortress | master passwords, encryption keys |
Turning bits into years
On average an attacker has to cover half the space, that is 2(bits−1) guesses. Divide that by the guessing rate and you get the time. The rates we use:
- 100 guesses per second — attacking a login form with delays and lockouts.
- 10¹⁰ per second — offline cracking of a stolen hash database on a few GPUs.
- 10¹⁴ per second — a dedicated rig at the scale of a large organisation.
One caveat matters: the figures hold only if the service stores passwords properly, with a slow function such as bcrypt or Argon2 and a salt. If the hashes are plain MD5, the rates jump by orders of magnitude.
How the formula works, if you are curious
Entropy equals log₂(N) × L, where N is the alphabet size and L the length. The base-two logarithm answers “how many doublings fit into this alphabet”: for 26 lowercase letters that is 4.7 bits per character, for 94 printable characters 6.55.
Multiplying by length works because each character is chosen independently: the search space is N to the power of L, and the logarithm turns the power into multiplication.
Hence a practical conclusion: adding a character beats widening the alphabet. Going from 26 characters to 94 gains 1.85 bits per character, while every extra character adds the full 6.55.
Why filters lower strength
Every restriction shrinks the alphabet. The “drop look-alikes” switch removes 13 characters out of 94 and the price of a character falls from 6.55 to 6.34 bits. Over 20 characters that is four bits lost — an acceptable trade for readability, but worth knowing about.
The “no repeats” mode bites harder: there the alphabet shrinks with every character, so entropy is a sum of logarithms. Our calculator does exactly that instead of multiplying by the original alphabet size the way many generators do.
Why invented passwords have no entropy
The formula only works for a uniformly random choice. If a human invented the password, the number of options is formally the same but the probabilities are wildly uneven: words from an active vocabulary, a birth date, a favourite team. The attacker walks the likely options first, and real strength drops thousands of times.
That is precisely why a passphrase must be drawn by lot: six random words from a 2048-word list give exactly 66 bits, while six words a person came up with are worth 25 at best.
Working out your own password
Identify the alphabet you actually used, multiply log₂ of its size by the length, and you have an upper bound. Then subtract for dictionary words, dates and keyboard runs. The strength checker does the whole calculation for you.