Password Entropy Calculator

Measuring Password Strength the Right Way: Shannon Entropy

When a website tells you your password is "strong" because it contains a symbol and a number, that's a heuristic, not a measurement. Real password strength is measured in bits of entropy, and the math is unambiguous. This calculator implements the same formula used in NIST guidelines and academic cryptography: entropy = length × log2(character pool size).

The Math, Briefly

A random password is one of pool_size ^ length possible strings. Taking log2 of that gives you the number of binary decisions an attacker has to make to enumerate every possibility:

• 8 lowercase letters → 8 × log2(26) ≈ 37.6 bits → 200 billion possibilities
• 8 mixed alphanumeric → 8 × log2(62) ≈ 47.6 bits → 218 trillion possibilities
• 12 ASCII printable → 12 × log2(94) ≈ 78.6 bits → 5 × 10^23 possibilities
• 20 ASCII printable → 20 × log2(94) ≈ 131 bits → 2.7 × 10^39 possibilities

Each extra bit doubles the keyspace. Each extra random character adds 4–7 bits depending on the pool. This compounds dramatically, length is the single most powerful lever.

Translating Bits to Crack Time

The bit count is the size of the search space. To translate it to a time-to-crack, divide by the attacker's guess rate. Realistic rates depend on the threat:

• Online attack against a login form, rate-limited, maybe 10–100 guesses/second. A 40-bit password is effectively safe.
• Offline attack on a stolen bcrypt hash, ~10,000 guesses/second per GPU. A 50-bit password lasts months.
• Offline attack on an MD5 hash, ~100 billion guesses/second per modern GPU. A 60-bit password falls in under a minute.
• Offline attack on a fast hash + GPU cluster, up to 10^12 guesses/second. You want 80+ bits to be safe.

The calculator shows crack time at common rates so you can pick a threshold that matches the threat model you actually care about.

Why Entropy Math Assumes True Randomness

The formula above assumes every character is chosen uniformly at random from the full pool. If your password is Password123!, the entropy formula says 12 × log2(94) ≈ 79 bits, but the effective entropy against a real attacker is much lower because attackers run dictionary attacks: capitalize-first-letter + common word + year + symbol is one of the first patterns tried.

For human-chosen passwords, real entropy is often 10–30 bits lower than the formula suggests. This is why password managers, which generate truly random passwords, produce dramatically stronger credentials than what humans pick.

Passphrase Entropy

A passphrase like correct horse battery staple is famously memorable. Its entropy is measured per-word, not per-character. Using the EFF's Diceware list of 7,776 words: log2(7776) ≈ 12.92 bits per word. So:

• 4 words → ~52 bits, fine for low-risk accounts
• 5 words → ~65 bits, solid for most uses
• 6 words → ~78 bits, strong
• 7 words → ~90 bits, very strong, and still memorable

Use a real random source (a six-sided die, a Diceware tool, or a password manager), don't pick the words yourself, because human "random" is biased.

Practical Recommendations

1. Never reuse passwords. Even a strong one becomes useless if it's reused on a site that gets breached.
2. Use a password manager. Random 20+ character passwords are unbeatable, and a manager makes them effortless.
3. Enable 2FA. Even an 80-bit password can be phished. A second factor (TOTP, WebAuthn) is the real defense.
4. Reserve high-entropy passwords for high-value accounts. Your email and password manager master are the keys to the kingdom, make them 100+ bits.

Local-First Calculation

This calculator runs entirely in your browser. Open the network tab and you'll see no requests during calculation. You can paste production passwords without exposing them, though best practice is to test sample passwords with the same shape, not real ones.