Assumptions
Every number here uses the same formula as this site’s password strength checker.
- Possibilities per character: the total for the character types used — 10 digits, 26 lowercase, 26 uppercase, 32 symbols
- Strength (entropy) = length × log₂(possibilities) bits
- Time to brute-force = 2entropy ÷ guesses per second
We assume 10 billion guesses a second, roughly what powerful hardware manages against a leaked password hash (the scrambled form services store). Times in the tables are for trying every combination; on average a password falls in half that time.
Quick reference: length and character types
Time to brute-force a randomly generated password.
| Length | Digits only (10) | Lowercase only (26) | Letters + digits (62) | Letters, digits, symbols (94) |
|---|---|---|---|---|
| 6 | Instant | Instant | 6 s | ~1 min |
| 8 | Instant | 21 s | 6 h | 7 days |
| 10 | 1 s | 4 h | 2.7 years | 171 years |
| 12 | 2 min | 110 days | 10,000 years | 1.5 million years |
| 14 | 2.8 h | 205 years | 39 million years | 13 billion years |
| 16 | 12 days | 138,000 years | 151 billion years | over 100 trillion years |
| 20 | 317 years | 63 billion years | over 100 trillion years | over 100 trillion years |
What this shows
- Length beats variety: 14 lowercase letters (205 years) outlast 10 characters using all four types (171 years). Each extra character multiplies the time by the number of possibilities — 26 for lowercase, 94 for everything.
- Eight characters falls in a week even with every type: the old “at least 8 characters” advice does not hold up once a hash has leaked.
- Past 12 characters it becomes impractical: 12 characters of every type take 1.5 million years, and 16 take over 100 trillion.
- Numeric PINs rely on attempt limits: four digits allow only 10,000 combinations. Short bank-card and phone PINs work because the device locks after a few wrong tries.
Attack speed changes everything
The same password holds out for very different times depending on how fast the attacker can guess.
| Attack | 8 characters (94) | 12 characters (94) |
|---|---|---|
| Through a login page (assumed 1,000/s) | 190,000 years | 15 trillion years |
| Leaked hash, brute force (10 billion/s) | 7 days | 1.5 million years |
| 100 times faster (1 trillion/s) | 1.7 h | 15,000 years |
Guessing through a login page is slow, and most services lock the account after repeated failures. The real danger is a service leaking its password hashes, which attackers can then test as fast as their hardware allows. That is where length makes the difference.
Passwords the formula gets wrong
The tables above assume random passwords. Passwords people make up fall much faster. Running a few through the strength checker exposed its weak spots.
| Password | Before | After | Comment |
|---|---|---|---|
P@ssw0rd | 52.4 bit 7 days | 24.0 bit Instant | Just "password" with look-alike swaps |
Password1! | 65.5 bit 171 years | 24.0 bit Instant | The classic word + digit + symbol shape |
Tokyo2020! | 65.5 bit 171 years | 24.0 bit Instant | Place name + year + symbol |
tanaka1985 | 51.7 bit 4 days | 51.7 bit 4 days | Surname + birth year; the formula cannot tell (see below) |
correct horse battery staple | 164.0 bit over 100 trillion years | 164.0 bit over 100 trillion years | A string of words; the formula overrates it (see below) |
k7#Qm2!xR9vB | 78.7 bit 1.5 million years | 78.7 bit 1.5 million years | An example of 12 random characters; the formula holds |
The weakness we found, and the fix
At first the checker rated P@ssw0rd at “7 days” and Password1! at “171 years”. Yet both are classic shapes near the top of leaked-password lists. Before any random brute force, attackers try common words with look-alike swaps (a→@, o→0) and a number or symbol tacked on.
We improved the checker: it now undoes look-alike swaps, strips leading and trailing digits and symbols, and if what remains is a common word it caps the strength at 24 bits (cracked instantly) (19 September 2026). We ran 200,000 random passwords through it to confirm none are flagged by mistake.
What no formula can catch
- Names, birthdays and phone numbers:
tanaka1985scores “4 days”, but anyone who knows you — or an attacker who gathers your social media details — can guess it far faster. Personal information cannot be judged by a formula. - Passphrases of words:
correct horse battery stapleis long, so the formula calls it extremely strong. But an attacker who knows the shape is “four words” tries combinations of words, not characters. Four words chosen at random from a 2,048-word list give 44 bits, cracked in about 29 minutes at 10 billion guesses a second. If you use a passphrase, choose six words from a 7,776-word list with dice (Diceware): about 77.5 bits, or roughly 700,000 years.
The site’s password generator uses 18 symbols, while the strength checker counts symbols as 32, so it rates generated passwords slightly higher than they are. For example, 12 characters of letters, digits and symbols from the generator are really about 75.9 bits (about 220,000 years).
Summary
- Passwords you do not need to remember: generate 16 or more random characters with the password generator and keep them in a password manager.
- Passwords you must remember: use a passphrase of six or more randomly chosen words. Avoid sentences you made up and letter swaps.
- Never reuse passwords: however strong, a password leaked from another service will be tried as is.
- Turn on two-factor authentication: even if your password becomes known, it is not enough on its own to log in.