Diceware Passphrase Entropy Calculator

Understanding the Diceware passphrase entropy calculator — concept and principle

A Diceware passphrase is a string of words chosen truly at random from a fixed list, traditionally by rolling dice. Because the selection is random, its strength can be calculated exactly from just two numbers: how many words you use and how many words are on the list. This calculator gives the entropy in bits and the total number of possible passphrases.

Each dice-chosen word adds the same 12.9 bits, so length is what makes it strong.

How it is calculated

Entropy (bits) = words × log₂(list size)
Combinations = list size ^ words

With the EFF large word list of 7,776 words (6^5, one word per five dice rolls), each word adds log₂ 7,776 ≈ 12.925 bits. Spaces, capitalisation or separators are not counted, which keeps the figure conservative.

The principle

Entropy measures the size of the space an attacker must search, assuming they know your method and your word list. If every word is equally likely and chosen independently, the number of passphrases is L^n, and the base-2 logarithm turns that into bits: n × log₂ L. Every additional word multiplies the attacker's work by the list size. The word list can be public; the secret is which words the dice picked. That is why this estimate is trustworthy, unlike scores for passwords people invent.

Worked example

Inputs: 6 words, list of 7,776 words.
Bits per word: log₂ 7,776 = 12.92481250.
Entropy: 6 × 12.92481250 = 77.54887502 bits.
Combinations: 7,776^6 = 221,073,919,720,733,357,899,776 ≈ 2.210739e+23.
Even at 10 billion guesses per second, searching half the space takes about 1.1 × 10^13 seconds, roughly 350,000 years.

Each point is the calculator re-run with only “Words” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Words	Entropy (bits)
1.5	19.38721876
3	38.77443751
4.5	58.16165627
6	77.54887502
7.5	96.93609378
9	116.3233125
12	155.09775

How to read the result

Each word adds about 12.9 bits. Four words (about 52 bits) are fine where guessing is rate-limited; five or six words (65–78 bits) are a common recommendation for a password-manager master password or disk encryption. Compare the figure with the hash the passphrase protects: slow hashes such as Argon2id make each bit far more expensive to attack.

Common mistakes

Picking the words yourself or rerolling until you like them; that breaks the randomness the formula assumes.
Counting the list size of a short list as 7,776; the EFF short lists have 1,296 words (about 10.3 bits each).
Adding a famous quote or lyric; those are guessed as single units.

Keep in mind: The result is exact only if every word is selected uniformly at random with physical dice or a cryptographically secure generator. It says nothing about phishing, malware or reuse of the passphrase on several sites.

Frequently asked questions

How many Diceware words do I need?

Six words (about 77.5 bits) is a widely used choice for high-value secrets; fewer can be enough for rate-limited online logins.

Do capital letters or a separator help?

Slightly, but adding another random word gives about 12.9 bits and is easier to remember.

Why 7,776 words?

Five rolls of a six-sided die give 6^5 = 7,776 possible outcomes, one per word.

Sources: Arnold G. Reinhold, The Diceware Passphrase (diceware.com), 1995 · Electronic Frontier Foundation, "Deep Dive: EFF's New Wordlists for Random Passphrases", 2016

Checked 8 Nov 2026. Standard formulas and RFC/IEEE definitions, computed locally in your browser — nothing you type is sent anywhere.

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