Estimate character-pool entropy and brute-force search time under a random-character model, or generate reproducible sample passwords for learning.
By AdminDrafted with AI writing toolsUpdated Checked examples: 6
This password has 11 characters from a modeled pool of 95: theoretical entropy 72.3 bits. At 10,000,000,000 guesses per second, an exhaustive search of that modeled space averages 9,010 years. This is not a prediction of actual crack time.
| Attacker | Guesses per second | Average time |
|---|---|---|
| Online, rate-limited | 10 | 9.01 × 10¹² years |
| Online, no rate limit | 1,000 | 9.01 × 10¹⁰ years |
| Offline, slow hash | 10,000 | 9.01 × 10⁹ years |
| Offline, fast hash | 10,000,000,000 | 9,010 years |
| Offline, large cluster | 1,000,000,000,000 | 90.1 years |
26 lowercase; 26 uppercase; 10 digits; 33 symbols and space
On average an exhaustive search finds the password halfway through the space.
About 9,010 years.
Entropy counts how many guesses a randomly chosen password could take: H = L × log2 N bits, where L is the length and N the size of the character pool (26 lowercase, 26 uppercase, 10 digits and 33 symbols including space). A brute-force search finds the password after N^L ÷ 2 guesses on average, so the crack time is that number divided by the attacker's guesses per second.
The default, Tr0ub4dor&3 from the xkcd comic 936, draws on all 95 printable ASCII characters across 11 positions, which gives 72.3 bits; at 10 billion guesses per second an exhaustive search would average 9,010 years.
This is a theoretical model for the displayed character pool, not a measurement of how a password was chosen. Tr0ub4dor&3 is a dictionary word with common substitutions, which the comic puts at about 28 bits. Generated samples use non-cryptographic xoshiro256** and a 64-bit seed. They are educational examples and must not be used for real accounts.
For a password chosen at random, entropy is H = L × log₂ N bits, where L is the length and N the number of possible characters. Eight random lowercase letters give 8 × log₂ 26 = 37.6 bits, and 16 characters drawn from the 94 printable ASCII symbols give 104.9 bits. The formula holds only when every character was picked at random.
Each character adds log₂ N bits: 4.7 for lowercase, 6.6 for the full 95-symbol pool. Four more lowercase letters add 18.8 bits, more than switching an 8-character password from lowercase to all 95 symbols, which adds 15.0.
An exhaustive search finds a random password after N^L ÷ 2 guesses on average. Divide that by the attacker's guessing rate:
The rate matters as much as the password. A rate-limited login allows about 10 guesses per second, while an offline attack on a leaked fast hash runs near 10¹⁰, a billion times faster. Slow password hashes such as bcrypt and Argon2 exist to shrink that gap.
The formula rates the method, not the string. Tr0ub4dor&3 spans all four character classes across 11 positions, so the model gives 72.3 bits, but it is a dictionary word with common substitutions, which attackers try first.
password gets 37.6 bits from the model, yet it sits near the top of common-password lists, so a dictionary attack tries it almost immediately.
For words drawn at random from a list, use the list size as N and the word count as L. EFF's dice method picks each word from 7,776 by rolling five dice: four words give 4 × log₂ 7,776 = 51.7 bits, and six give 77.5 bits.
Counting characters overrates a passphrase. correct horse battery staple scores 164.7 bits as 28 characters from a 59-symbol pool, but as four random words from a 7,776-word list it would carry 51.7.
| Scenario | Length | Pool | Modeled entropy bits |
|---|---|---|---|
| Default | 11 | 95 | 72.27 |
| Check password | 8 | 26 | 37.60 |
| Six digit sample | 6 | 10 | 19.93 |
| No lookalikes | 12 | 88 | 77.51 |
| Check éé | 2 | 1 | 0.00 |
Default is Tr0ub4dor&3, and Check password is password. Six digit sample is generated from seed 0 with digits only, giving 028278.
No lookalikes is a 12-character sample from seed 18446744073709551615 without I l 1 O 0 o, giving SP}R=Pykuu3K. éé scores zero because its pool is the single distinct character it uses.
NIST SP 800-63B-4 requires at least 15 characters for a password used alone and 8 when it is paired with a second factor.
The same guidelines reject composition rules such as "one digit and one symbol" and require checking new passwords against a blocklist of common and breached ones.
Samples come from xoshiro256** seeded through SplitMix64 (reference code), so the same seed and settings always give the same password. That suits examples and tests.
It also makes the samples unsafe: anyone with the seed has the password, and a 64-bit seed caps the uncertainty at 64 bits. For real accounts, use a password manager's generator, never one of these samples.
For why stored passwords need a slow, salted hash, see the hash and checksum calculator.
Checked against: Independent calculation
Checked against: / 1e10 = 10.4414 s
Checked against: 26 / 2 = 13 guesses; 13 / 10 = 1.3 s
Checked against: Independent calculation
NIST SP 800-63B-4 (2025) requires at least 15 characters for single-factor passwords and at least 8 for passwords used with another factor. It recommends allowing a maximum length of at least 64 characters, prohibits composition rules and arbitrary periodic changes, and requires checking new passwords against a blocklist. A change is required when there is evidence of compromise.
It depends on the pool, the length and the attacker's speed. A random 8-letter lowercase password has 26^8 ≈ 2.1 × 10^11 combinations and falls in about 10 seconds on average at 10 billion guesses per second, a fast offline attack on a leaked hash. A random 16-character password from 94 printable symbols would take about 5.9 × 10^13 years at the same speed.
Password entropy is the base-2 logarithm of the number of equally likely passwords the choosing method could produce, in bits; each extra bit doubles the guesses needed. A random password of length L from N symbols has L × log2 N bits, so 8 lowercase letters give 37.6 bits. It rates how the password was chosen, not how it looks, which is why human-picked words score far lower.
Usually, if the words are chosen at random. Four words drawn from the EFF's 7,776-word dice list give 4 × log2 7,776 ≈ 51.7 bits, and six give 77.5 bits, more than a random 11-character password from all 95 printable characters (72.3 bits), while being easier to type and remember. Words a person picks, or a known quote, are far weaker.
No. This generator makes reproducible educational samples with xoshiro256**, which is not cryptographically secure. A secret seed does not change that. Anyone with the same seed and settings gets the same sample. For real accounts, use a password manager with a cryptographically secure generator.
This calculator includes 6 worked examples with independently sourced answers. They run in the test suite, and you can run them here too.