What is password entropy?

A measure of unpredictability, in bits. Each bit doubles the number of guesses an attacker needs: 40 bits means ~1 trillion possibilities. For randomly generated passwords, entropy = length × log₂(character-pool size).

How many bits of entropy is enough?

Rough guidance: 60+ bits for everyday accounts, 80+ bits for anything important, 128 bits for cryptographic keys. A 12-character random password from upper/lower/digits/symbols gives ~78 bits — comfortably strong.

Is a long passphrase better than a complex password?

Usually yes, if both are random. A 6-word random passphrase (~77 bits) matches a 12-character complex password — and it's far easier to type and remember. The catch is "random": human-picked phrases ("correct horse…") have much less entropy than the math suggests.

How long does it take to crack an 8-character password?

A truly random 8-character password (mixed case + digits + symbols, ~52 bits) resists online attacks effectively but falls to a well-funded offline attack in hours to days. That's why 12+ characters is the modern minimum for generated passwords.

Does adding symbols help much?

Less than you'd think: symbols expand the pool from 62 to ~94 characters, adding about 0.6 bits per character. Adding two extra characters beats adding symbols to a short password. Length first, complexity second.

What does NIST recommend for passwords?

NIST SP 800-63B: minimum 8 characters (but encourage 64+), check new passwords against known-compromised lists, no forced periodic changes, and no mandatory complexity rules — because "P@ssw0rd1!"-style rules produce predictable passwords, not strong ones.

Are password strength meters accurate?

Only roughly. Most meters estimate entropy from character classes and length, but they can't know if your password is in a breach dictionary or follows a predictable pattern ("Spring2026!"). Treat green meters as necessary, not sufficient.

Password Entropy Explained: Bits, Length & Real Security

September 26, 2026 · Security

"This password has 52 bits of entropy." What does that actually mean — and how long does 52 bits survive against a real attacker? Password entropy is the one number that honestly measures password strength. Here's the formula, the crack-time math with stated assumptions, and why length beats complexity almost every time.

What entropy means: each bit doubles the guesses

Entropy measures unpredictability in bits. One bit = 2 possibilities (a coin flip). Ten bits = 2¹⁰ = 1,024 possibilities. Each additional bit doubles the attacker's work: 40 bits ≈ 1 trillion guesses, 50 bits ≈ 1 quadrillion, 60 bits ≈ 1 quintillion. This exponential scaling is why small differences in bits mean enormous differences in crack time — 10 extra bits makes a password roughly a thousand times harder to brute-force.

The one formula

For a randomly generated password:

entropy = length × log₂(pool size)

Worked example: 12 characters drawn randomly from uppercase + lowercase + digits + 32 symbols (94 characters total). log₂(94) ≈ 6.55 bits per character, so 12 × 6.55 ≈ 78.6 bits — about 2⁷⁸ ≈ 3.8 × 10²³ possibilities. The two levers are obvious: make it longer, or draw from a bigger pool. Length is the cheaper lever.

Bits translated to crack time

Crack time = 2^(bits−1) ÷ guesses-per-second (the −1 because on average the attacker finds it halfway through). Assumptions matter enormously, so here are two scenarios:

Entropy	Example	Online attack (10 guesses/sec)	Offline attack (10 billion/sec)
40 bits	6-char random (a–z, 0–9)	~1,700 years	~55 seconds
52 bits	8-char mixed + symbols	~7 million years	~5 days
60 bits	9-char mixed + symbols	~1.8 billion years	~3.6 years
78 bits	12-char mixed + symbols	Longer than the universe	~480,000 years
128 bits	22-char mixed + symbols	Forget it	Forget it

The gap between columns is the point: rate-limiting is doing most of the work for online attacks, while offline attacks (stolen hash database, no rate limit, GPUs) are brutally fast. Always evaluate against the offline column — breaches happen.

Check yours: generate a password and see its entropy in bits plus a crack-time estimate in our free Password Generator — the assumptions are stated right next to the numbers.

Length beats complexity: the worked math

Compare Tr0ub4dor&3 (11 chars, full 94-char pool ≈ 72 bits) with a 25-character all-lowercase random string (25 × log₂(26) ≈ 117 bits). The "simple" lowercase password is ~2⁴⁵ times stronger — and infinitely easier to type correctly. Or symbols vs length directly: adding symbols to an 8-char password gains ~5 bits; adding 2 characters gains ~13 bits. When choosing, add length first. Complexity rules mostly just annoy users into predictable patterns (P@ssw0rd!), which is why NIST dropped them.

The human problem: dictionary attacks

Everything above assumes random generation. Human-chosen passwords collapse the math: attackers don't brute-force — they try breach dictionaries, common patterns, and mangling rules ("Password" → "P@ssw0rd2026!") first. A human "complex" 10-character password often falls in seconds to a dictionary attack that would never touch a random 10-character string. Entropy formulas describe the generator, not the guessability of your specific choice. If a human picked it, assume less entropy than the formula says.

Passphrases vs random strings

A random 6-word passphrase from a 7,776-word list (the classic Diceware size): 6 × log₂(7776) ≈ 77.6 bits — matching a 12-character complex password, while being typable and memorable. The trade-off is length on screen and entry time on mobile. Either is fine; the rule is random words, not clever sentences — "correct horse battery staple" as a human invention has far less entropy than 4 dice-rolled words.

Practical rules

Generate, don't invent: 12+ random characters (upper/lower/digits/symbols) or 6+ random words.
Unique per site: reuse is the #1 real-world failure — one breach becomes all breaches.
Use a password manager: it's the only way "unique 78-bit passwords everywhere" is humanly possible.
Minimum 8 characters for anything human-memorable (NIST floor), but treat 8 as the basement, not the target.
Check against breach lists: a 60-bit password that's already leaked has effectively zero bits.

Frequently asked questions

What is password entropy?: A measure of unpredictability, in bits. Each bit doubles the number of guesses an attacker needs: 40 bits means ~1 trillion possibilities. For randomly generated passwords, entropy = length × log₂(character-pool size).
How many bits of entropy is enough?: Rough guidance: 60+ bits for everyday accounts, 80+ bits for anything important, 128 bits for cryptographic keys. A 12-character random password from upper/lower/digits/symbols gives ~78 bits — comfortably strong.
Is a long passphrase better than a complex password?: Usually yes, if both are random. A 6-word random passphrase (~77 bits) matches a 12-character complex password — and it's far easier to type and remember. The catch is "random": human-picked phrases ("correct horse…") have much less entropy than the math suggests.
How long does it take to crack an 8-character password?: A truly random 8-character password (mixed case + digits + symbols, ~52 bits) resists online attacks effectively but falls to a well-funded offline attack in hours to days. That's why 12+ characters is the modern minimum for generated passwords.
Does adding symbols help much?: Less than you'd think: symbols expand the pool from 62 to ~94 characters, adding about 0.6 bits per character. Adding two extra characters beats adding symbols to a short password. Length first, complexity second.
What does NIST recommend for passwords?: NIST SP 800-63B: minimum 8 characters (but encourage 64+), check new passwords against known-compromised lists, no forced periodic changes, and no mandatory complexity rules — because "P@ssw0rd1!"-style rules produce predictable passwords, not strong ones.
Are password strength meters accurate?: Only roughly. Most meters estimate entropy from character classes and length, but they can't know if your password is in a breach dictionary or follows a predictable pattern ("Spring2026!"). Treat green meters as necessary, not sufficient.