Password Entropy Calculator

How this is calculated

ENTROPY IS LENGTH TIMES THE BITS EACH CHARACTER ADDS. A character drawn at random from a pool of 95 printable symbols carries about 6.57 bits; one drawn from the 26 lowercase letters carries about 4.70. Multiply by the length and you have the total. Every extra character adds the SAME amount, which is why length beats complexity so reliably - going from 8 to 16 characters doubles the entropy, while adding symbols to an 8-character password adds under 15 bits. ⚠️ THIS ONLY DESCRIBES A PASSWORD CHOSEN AT RANDOM, AND THAT IS THE WHOLE CATCH. The arithmetic assumes every character was picked independently and uniformly from the pool. A password a person invented does not work like that: it is built from words, names, dates, keyboard runs and predictable substitutions, so a cracker guesses those patterns first rather than working through the space. 'P@ssw0rd123!' uses all four character classes and twelve characters and this tool would score it at about 79 bits - its real strength against a modern cracking wordlist is a tiny fraction of that. THE NUMBER HERE IS AN UPPER BOUND, AND IT ONLY EQUALS THE REAL STRENGTH IF A MACHINE CHOSE THE PASSWORD. THE ATTACK RATE IS AN ASSUMPTION, NOT A FACT, WHICH IS WHY IT IS A CHOICE HERE. The same password can be uncrackable or trivial depending on how the attacker gets to guess. A rate-limited login lets someone try a handful per second; a stolen database hashed with bcrypt might allow a hundred thousand a second; the same database hashed with an unsalted fast algorithm allows a hundred billion or more on rented hardware. That range is roughly TWELVE ORDERS OF MAGNITUDE, and it dwarfs any realistic difference in password choice. Pick the row that matches the threat you care about. THE TIME SHOWN IS THE AVERAGE, ASSUMING HALF THE SPACE IS SEARCHED. An unlucky password is found early and a lucky one late; only the average is meaningful, and the difference is a factor of two, which is nothing next to the other uncertainties. ⚠️ CRACKING RATES ONLY EVER GO UP. Hardware improves and the numbers here are a snapshot, so treat a result of a few decades as weak rather than adequate - it is protecting against today's attacker, not the one who has your stolen hash in ten years. Anything that has to survive long-term should be well clear. THE POWERS-OF-TEN OUTPUT IS THE ONE TO READ ON STRONG PASSWORDS. Once a figure passes a few billion years the exact number stops meaning anything, and its exponent is easier to compare. Negative means the password falls in under a second. A PASSWORD MANAGER MAKES THIS TOOL DESCRIPTIVE RATHER THAN ASPIRATIONAL. It generates genuinely random strings, so the calculated entropy is the real entropy - which is the only situation in which these numbers can be taken at face value. Our password generator does this in your browser.

Common questions

Does this tell me if my actual password is strong?

Only if a machine chose it. The arithmetic assumes every character was picked independently and uniformly from the pool, and a password a person invented is nothing like that - it is made of words, names, dates, keyboard runs and predictable substitutions, all of which a cracker tries long before working through the space at random. 'P@ssw0rd123!' scores about 79 bits here and would fall almost immediately to a modern wordlist with rules applied. Treat the figure as an UPPER BOUND on strength: the most the password could possibly be worth, reached only when it was generated randomly.

Why does length matter more than adding symbols?

Because every extra character adds the same number of bits, while changing the alphabet only changes how much each one adds - and that change is small. Going from letters and digits to letters, digits and symbols takes a character from 5.95 bits to 6.57, a gain of 0.62 bits each. On an eight-character password that is under five bits in total. Adding four more characters at the smaller alphabet adds nearly twenty-four. This is why a long passphrase beats a short cryptic string, and why the advice to add punctuation to a short password was always the weaker half of the guidance.

Why is the attack rate a dropdown instead of a fact?

Because it is an assumption, and it moves the answer more than anything about the password does. A rate-limited login allows a handful of attempts a second. A stolen database hashed with bcrypt might allow a hundred thousand a second. The same database hashed with an unsalted fast algorithm allows a hundred billion or more on rented hardware. That is around twelve orders of magnitude, which dwarfs any realistic difference in password choice - the same password can be effectively uncrackable in one scenario and gone in seconds in another. Choosing the row is choosing which threat you are reasoning about, and pretending there is one right number would hide that.

How many bits should I aim for?

Eighty is a reasonable floor for an ordinary account, and 128 is the usual target for anything long-lived or high-value - a password manager master password, a backup encryption key, anything protecting other credentials. The characters-needed output works backwards from whatever you set: 80 bits takes 13 characters from the full symbol alphabet, or 18 from lowercase letters alone. That second figure is worth noticing, because a longer password from a smaller alphabet is usually far easier to type and remember than a shorter cryptic one of equal strength.

Why show powers of ten?

Because once a crack time passes a few billion years the exact figure stops carrying any meaning, and the exponent is much easier to compare. A jump from 10 to 16 in that output is six orders of magnitude - a million times harder - which is far clearer than reading two enormous numbers side by side. It also behaves sensibly at the weak end, where it goes negative: a value of -3 means the password falls in about a thousandth of a second. One number that stays readable across the entire range beats a figure that is unreadable at both ends.

Should I trust a crack time of a few decades?

No - treat that as weak rather than adequate. Cracking rates only ever go up, and the numbers here are a snapshot of hardware that will look slow before long. A password protecting something that matters is not defending against today's attacker but against whoever holds your stolen hash in five or ten years, with hardware nobody has yet. That is why the recommendation is to be comfortably clear of the threshold rather than just past it, and why 128 bits is the target for anything long-lived: it leaves room for decades of improvement without any recalculation.

Why is the average half the search space?

Because an attacker working through possibilities finds the right one after searching half of them on average - sometimes early, sometimes late. The figure here is that average rather than the worst case, which would be twice as long. It is worth knowing the assumption is there, but it is also the least important uncertainty in the whole calculation: a factor of two is nothing beside the twelve orders of magnitude between attack scenarios, or the enormous gap between a random password and one a person thought up.

Take it further with AI

Copy this into ChatGPT or Claude with your own numbers filled in. It hands over the figures this calculator worked out, so the answer is built on real arithmetic instead of a guess.

I used the Password Entropy Calculator at https://www.bfcbrilliance.com/tools/password-entropy-calculator.

What I entered:
- Password length (characters): ___
- Characters drawn from: ___
- What the attacker can try: ___
- Strength you are aiming for (bits): ___

What it calculated:
- Entropy: ___
- Powers of ten in the crack time (years): ___
- Average time to crack: ___
- That time in seconds: ___
- Characters in the pool: ___

Use those figures as given — they are already worked out, so please don't recalculate or estimate your own. Help me turn them into a plan: what to buy or do, in what order, roughly what it should cost, and the mistakes people most often make with this job.

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