Password Strength Calculator

entropy (bits) = password length × log₂(pool size), and the number of combinations is 2^entropy

password length

How many characters the password has

pool size

How many distinct characters are available: 26 lowercase, 26 uppercase, 10 digits, 32 symbols

log₂

Base-2 logarithm, so the result is counted in bits

Use it to compare two password policies before you write one, or to check whether a password you already have is worth keeping. It is exact for a password generated at random from a known character set, and only an upper bound for one a human invented — people pick patterns, so a 12-character password someone made up has far less entropy than 12 random characters. Brute force is also not the only attack: a password reused across sites is compromised by the other site's breach, and no amount of length helps there.

1. 16 characters, letters and digits

   1. Pool: 26 + 26 + 10 = 62 characters
   2. Entropy per character: log₂(62) = 5.95 bits
   3. Total entropy: 16 × 5.95 = 95.3 bits
   4. Combinations: 10^28 — the tool reports the power of ten rather than all 29 digits

   95.3 bits clears the 60-bit band by a wide margin and lands in the top band normally reserved for 128. Turning on symbols as well would take the pool to 94 and the entropy to 104.6 bits — worth 9.3 bits, which is the same as adding about 1.6 characters.

2. 8 characters, lowercase only

   1. Pool: 26 characters
   2. Entropy per character: log₂(26) = 4.70 bits
   3. Total entropy: 8 × 4.70 = 37.6 bits
   4. Combinations: 2^37.6 ≈ 2.1 × 10^11, so 10^11

   37.6 bits lands in the fair band — roughly seven seconds of work for a fast hash on one card. Doubling the length to 16 characters takes it to 75.2 bits, while leaving the length at 8 and switching every character set on only reaches 52.5 bits. Length does more per keystroke than variety does.

The entropy figure assumes the password was generated uniformly at random from the character set you selected. Any password a person chose by hand has less, often far less, because people reach for words, dates and keyboard patterns that a cracking tool tries first. This page therefore measures the policy, not the password. The crack times are order-of-magnitude estimates from a single modern GPU, not a measurement of any particular machine: a determined attacker with a cluster, or simply a newer card, beats them by a large factor, and a stolen hash database can be attacked offline for as long as the attacker likes. Nothing here accounts for whether the password is reused, phished, keylogged or reset through a support desk — those are how passwords actually fall, and none of them are affected by entropy. Finally, the page will not generate a password for you, for the reason in the first paragraph of this file: a secure generator needs a cryptographic random source, which a pure calculation cannot be.

How is password entropy calculated?

Entropy is the password length multiplied by the base-2 logarithm of the pool size. Choosing lowercase letters, uppercase letters and digits gives a pool of 62 characters, log₂(62) is 5.95 bits per character, and a 16-character password from that pool therefore carries 95.3 bits. The number of possible combinations is 2 raised to the entropy, which is why entropy is the useful unit: it adds up when the password gets longer.

Is 60 bits of entropy enough, and how do I read the crack time?

It depends entirely on how the site stores your password. At 10^10 guesses per second — one modern card against an unsalted fast hash — 60 bits is about three years of continuous work. Against bcrypt at cost 12 the same card manages around 10^4 guesses per second and the same password takes millions of years. So 60 bits is enough against a competent site and marginal against a careless one; 80 bits is enough against both.

Should I use symbols and mixed case, or just make it longer?

Longer is usually the better trade, and always the easier one to remember. Going from an 8-character lowercase password to 16 characters is worth 37.6 bits; keeping it at 8 characters but switching on every character set is worth 15 bits. The pool only multiplies once when you widen it, while every added character multiplies again. Use symbols when a site demands them, not because they are the efficient way to add strength.

Why will this page not generate a password for me?

A password is only as unpredictable as the source of randomness behind it, and a page that computes a displayed number cannot also draw from a cryptographically secure random source — that source is exactly what makes a generator different from a calculator. Use your password manager's generator or your operating system's, both of which do have one, and then use this page to check that the length and character sets you chose there are worth it.

Does a longer password always mean a stronger one?

Only if it was generated at random. Length is what the arithmetic rewards, and the arithmetic is why a four-word passphrase can beat a short jumble of symbols — but a 20-character password built from a song lyric, a birthday and a name is crackable with a dictionary, and its real strength is nothing like the 20 random characters this page measures. This page gives you the ceiling for a password policy; a password a person invented sits well below it.

• NIST Special Publication 800-63B: Digital Identity Guidelines — Authentication and Lifecycle Management — National Institute of Standards and Technology
• NIST Special Publication 800-57 Part 1 Revision 5: Recommendation for Key Management — National Institute of Standards and Technology
• Password Storage Cheat Sheet — OWASP Foundation