Password Strength & Entropy Calculator

Understanding the password strength and entropy calculator — concept and principle

This calculator estimates how hard a password is to crack, as bits of entropy and as an average cracking time at a chosen guessing speed. It shows two figures: the entropy if every character were random, and a realistic estimate that discounts dictionary words, common passwords, repeats and sequences.

How it is calculated

• Character pool = 26 if the password contains a lowercase letter, + 26 for an uppercase letter, + 10 for a digit, + 33 for any other character (symbols and spaces).
• Entropy if random (bits) = length × log₂(pool)
• Realistic estimate: a password made only of words counts 12.9 bits per word (log₂ 7,776, a random pick from a diceware list); a very common password counts about 10 bits; each repeated or sequential character counts as nothing.
• Average time = 2^(realistic bits − 1) ÷ guesses per second, as an attacker searches half the space on average.
• Rating (from the realistic estimate): under 28 bits very weak, under 36 weak, under 60 reasonable, under 128 strong, 128 or more very strong.

Speed presets: 1,000/s (throttled online login), 100,000/s (offline bcrypt or Argon2) and 10 billion/s (offline fast hash).

The principle

If each of L characters is drawn uniformly from a pool of N symbols, there are N^L equally likely passwords, which is L × log₂ N bits. Length therefore adds strength much faster than a slightly larger pool: one extra character adds log₂ N bits, while adding symbols to a lowercase pool raises each character only from 4.7 to about 6.6 bits.

Worked example

1. Password: "k7#Qm2!vRx9p", 12 random characters; guessing speed 10 billion per second.
2. Pool: lowercase, uppercase, digits and symbols, 26 + 26 + 10 + 33 = 95.
3. Entropy: 12 × log₂ 95 = 12 × 6.5699 = 78.8382673 bits. The pattern check finds none, so the realistic estimate is the same.
4. Time: 2^77.838 ÷ 10^10 s ≈ 856,000 years, rating strong.
5. Compare "correct horse battery staple": 164.7 bits if random, but as 4 words only 4 × 12.9 = 51.7 bits, about 2.12 days at that speed (reasonable).

How to read the result

Use the realistic estimate, and treat even that as a best case: a known phrase or a leaked password is far weaker than its word count suggests. As a rough guide, 60 bits or more resists offline attacks only when the password is truly random, and 128 bits is beyond any foreseeable brute force.

Common mistakes

• Trusting the score for names, dates or keyboard patterns the check may miss.
• Assuming substitutions like "P@ssw0rd" add strength; crackers try them first.
• Forgetting that a leaked password is weak whatever its score.

Frequently asked questions

How many bits of entropy is a good password?

For a randomly generated password, around 70 to 80 bits is a comfortable target for most accounts; 128 bits is used for cryptographic keys.

Is my password sent anywhere?

No. The calculation happens locally and nothing is transmitted.

Sources: NIST SP 800-63B, Digital Identity Guidelines: Authentication and Lifecycle Management · OWASP Authentication Cheat Sheet