How many possible passwords are there?
With the 95 printable ASCII characters, an eight-character password has 95^8 = 6,634,204,312,890,625 possibilities. That sounds large and is not: a purpose-built cracking rig testing a fast hash at 100 billion guesses a second exhausts the entire space in under a day. Add four characters and 95^12 = 5.4 × 10^23 takes the same rig around 170,000 years. Length beats complexity by an enormous margin, which is why modern guidance dropped the mandatory-symbol rules and raised the minimum length instead.
How the figure is arrived at
c^n, where c is the character set size and n the length: each extra character multiplies the space by 95, while each extra symbol class multiplies it far less. Real attacks never search the space uniformly — they try leaked password lists, dictionary words with predictable substitutions, and keyboard patterns first, which is why an eight-character password chosen by a person is usually broken in minutes rather than a day.
Other numbers and possibilities counts
- How many combinations does a Rubik's Cube have? 43,252,003,274,489,856,000 — about 43 quintillion
- How many ways can you shuffle a deck of cards? about 8 × 10^67
- How many possible chess games are there? about 10^120 games; about 4.8 × 10^44 legal positions
- How many combinations are there in the lottery? 292,201,338 for Powerball
- How many digits of pi have been calculated? about 202 trillion
- How many Sudoku puzzles are there? 6,670,903,752,021,072,936,960 completed grids
- How many prime numbers are there under a million? exactly 78,498
- How many possible positions are there in Go? about 2.08 × 10^170
Common questions
- How many possible passwords are there?
- 6.6 quadrillion for eight characters — 540 sextillion for twelve
- How is that estimated?
- c^n, where c is the character set size and n the length: each extra character multiplies the space by 95, while each extra symbol class multiplies it far less. Real attacks never search the space uniformly — they try leaked password lists, dictionary words with predictable substitutions, and keyboard patterns first, which is why an eight-character password chosen by a person is usually broken in minutes rather than a day.
Related pages
- How many combinations does a Rubik's Cube have? 43,252,003,274,489,856,000 — about 43 quintillion
- How many ways can you shuffle a deck of cards? about 8 × 10^67
- How many possible chess games are there? about 10^120 games; about 4.8 × 10^44 legal positions
- How many combinations are there in the lottery? 292,201,338 for Powerball
- How many digits of pi have been calculated? about 202 trillion
- How many Sudoku puzzles are there? 6,670,903,752,021,072,936,960 completed grids
- How many prime numbers are there under a million? exactly 78,498
- How many possible positions are there in Go? about 2.08 × 10^170
- How many people are there in the world? Living things and the natural world
- How many stars are there in the universe? Space and the universe
- How many countries are there in the world? Things people built
- How many bones are in the human body? The human body
- How many grains of sand are there on Earth? Living things and the natural world
- How many ants are there in the world? Living things and the natural world
Sources
- Calculated on this page — At One Place