Diceware Words to Entropy Bits

Calculate ideal word-passphrase entropy from independent uniform choices in a caller-supplied Diceware-style word list.

Description

A Diceware-style passphrase gains ideal entropy from independent uniform selections in a word list.

A Diceware-style passphrase gains ideal entropy from independent uniform selections in a word list. Word count alone is insufficient unless the effective list size and selection process are known.^[1]

Calculate ideal word-passphrase entropy from independent uniform choices in a caller-supplied Diceware-style word list.

When to use Diceware Words to Entropy Bits

Use this tool to calculate ideal word-passphrase entropy from independent uniform choices in a caller-supplied Diceware-style word list.

Choose the text, counts, explicit reference time or format parameters requested by this tool. Follow the stated byte, epoch-time and randomness assumptions.

How to use Diceware Words to Entropy Bits and understand its results

Choose the text, counts, explicit reference time or format parameters requested by this tool. Follow the stated byte, epoch-time and randomness assumptions.
Enter wordListSize, wordCount using the field table and calculation rules, then run the tool.
Read bits. The explanation below defines the units, signs, ordering and any flags or placeholder values.
If the tool reports an input issue, correct the values and run it again. Apply the stated assumptions when interpreting a successfully returned result.

Input field	Meaning	Value type; see rules below	Requirement
wordListSize	Word list size	integer; minimum: 1; maximum: 9007199254740991	Required
wordCount	Independent word count	integer; minimum: 0; maximum: 9007199254740991	Required

Enter a positive safe-integer list size and a nonnegative safe-integer word count. The tool calculates the ideal bits per choice and multiplies by the count. One available word or zero selections gives zero bits; the result is a numeric estimate and can be fractional.

bits = wordCount × log₂(wordListSize)

Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.

Output field	Meaning	Value type
bits	Ideal entropy	number; minimum: 0

json

{
  "input": {
    "wordListSize": 4096,
    "wordCount": 5
  },
  "output": {
    "bits": 60
  }
}

Limitations and assumptions

It does not choose words, load a particular Diceware list or inspect a passphrase. Duplicate entries, biased dice/mapping, manual word selection and correlated choices can reduce entropy. Spaces and spelling length are not modeled as additional random choices.

Numeric inputs must be finite. Follow the calculation-specific rules for overflow, underflow and exceptional cases. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors.

Alternative or Complementary methods

Use Passphrase Word-Count Minimum Check: Check the minimum number of independently uniform word choices needed to meet a supplied ideal entropy target. For a complementary task, use Mnemonic Checksum Bits For Word Count: Return the entropy and checksum bit counts prescribed for a valid BIP39 mnemonic word count.

References

Diceware Words to Entropy Bits — tool.io

Similar or alternative tools

Passphrase Word-Count Minimum Check
Check the minimum number of independently uniform word choices needed to meet a supplied ideal entropy target.
Mnemonic Checksum Bits For Word Count
Return the entropy and checksum bit counts prescribed for a valid BIP39 mnemonic word count.