Length × pool size = entropy
A randomly drawn password's strength is length × log2(pool size). Length is the multiplier you control, and it compounds: going from 8 to 16 characters does not double the attacker's work, it squares it. This table is generated from that formula — no copied figures.
| Length | Lowercase only (26) | Letters + digits (62) | All printable (94) |
|---|---|---|---|
| 8 characters | 37.6 bits | 47.6 bits | 52.4 bits |
| 10 characters | 47.0 bits | 59.5 bits | 65.5 bits |
| 12 characters | 56.4 bits | 71.5 bits | 78.7 bits |
| 14 characters | 65.8 bits | 83.4 bits | 91.8 bits |
| 16 characters | 75.2 bits | 95.3 bits | 104.9 bits |
| 18 characters | 84.6 bits | 107.2 bits | 118.0 bits |
| 20 characters | 94.0 bits | 119.1 bits | 131.1 bits |
What those bits mean in time
Under the model this site states everywhere — an attacker with a stolen fast hash trying 10 billion guesses per second — a 62-pool password of 12 characters (71.5 bits) lasts on average 5.1 thousand years, while 16 characters from the 94 pool (104.9 bits) lasts longer than the age of the universe, many times over. The jump from "a determined attacker with good hardware" to "not in the lifetime of the hardware, the vendor, or the sun" is about four characters. That is why the recommendation is 16, and why 20 costs you nothing when a password manager is doing the remembering.
Where length advice often goes wrong is treating human-chosen passwords as if they were random. A 20-character sentence you composed has far less entropy than a 20-character random draw, because cracking tools model human choices — words, dates, substitutions — first. The figures on this page apply to generated passwords and randomly drawn passphrases. If a person picked it, assume it is weaker than it looks and check it with the strength checker, which deducts for exactly those patterns.
Practical minimums
- Everyday accounts with a manager: 16 random characters, any pool that includes letters and digits (95.3 bits) — more than sufficient.
- Master password / device login (memorized): a 5–6 word generated passphrase, 51.8–62.2 bits from a 1,316-word list.
- High-value accounts (email, banking): 20 random characters or a 6-word passphrase, plus two-factor authentication — the password stops being the only lock.
- PINs and short codes: different threat model entirely (online, rate-limited); a random 6-digit PIN is 19.9 bits and acceptable only where the service locks attempts.
FAQ
Is 12 characters enough?
From the full 94 pool, 12 characters is 78.7 bits — safe against online guessing and respectable offline, though 16 is the better default now that managers make length free. From lowercase alone, 12 is only 56.4 bits; pool size matters too.
Do symbols actually help?
They widen the pool from 62 to 94, worth about 0.6 bits per character — real, but one extra character is worth more (≈6 bits). Take symbols when the site allows them; never trade length for them.
Why do some sites cap passwords at 12 or 16 characters?
Legacy systems and poor design. Use the maximum the site allows, and let your manager track each site's quirks. A capped site is also a hint its password storage may be old — two-factor authentication matters even more there.
Does changing my password every 90 days help?
Current guidance from standards bodies is no: forced rotation pushes people toward predictable variations. Change on evidence of compromise, not on a calendar.