Free · Security arithmetic

Password Character-Pool Information Bound

Compute the captured uniform character-pool bound from counts and up to three custom alphabets.

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

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Formula and method

Eight uniform lowercase draws give approximately 37.60 bits under the stated combined-pool model.

entropy = (((lowercase_letters>0 ? 26:0)+(uppercase_letters>0 ? 26:0)+(digits>0 ? 10:0)+(special_characters>0 ? special_characters_pool:0)+(custom_characters_1>0 ? custom_pool_1:0)+(custom_characters_2>0 ? custom_pool_2:0)+(custom_characters_3>0 ? custom_pool_3:0))>0 ? (lowercase_letters+uppercase_letters+digits+special_characters+custom_characters_1+custom_characters_2+custom_characters_3)*log(((lowercase_letters>0 ? 26:0)+(uppercase_letters>0 ? 26:0)+(digits>0 ? 10:0)+(special_characters>0 ? special_characters_pool:0)+(custom_characters_1>0 ? custom_pool_1:0)+(custom_characters_2>0 ? custom_pool_2:0)+(custom_characters_3>0 ? custom_pool_3:0)))/log(2) : 0)

Worked example

Enter these known values and leave the other values blank.

Lower case Latin letters
8
Upper case Latin letters
0
Digits
0
Special characters
0
Special characters pool size
0
Pool size #1
0
Characters from pool #1
0
Pool size #2
0
Characters from pool #2
0
Pool size #3
0
Characters from pool #3
0
Uniform combined-pool information bound
37.6 bits

Assumptions and limitations

  • This bound is total length × log2(combined selected pool). It assumes independent uniform draws from a disjoint combined alphabet; entered character-category counts only select pools and total length. Fixed per-category composition, predictable human choices and overlapping custom alphabets reduce actual uncertainty. This is not a password-strength certification or a cracking-time estimate.
  • All original editable controls remain available. Clear one unknown and provide sufficient independent inputs to solve a supported inverse; outputs marked read-only cannot be entered.

Common questions

Does this rate a real password?

This bound is total length × log2(combined selected pool). It assumes independent uniform draws from a disjoint combined alphabet; entered character-category counts only select pools and total length. Fixed per-category composition, predictable human choices and overlapping custom alphabets reduce actual uncertainty. This is not a password-strength certification or a cracking-time estimate.

How do custom alphabets affect the result?

A custom alphabet contributes its pool size when its character count is positive. Used alphabets must contain at least one character. The combined-pool model assumes alphabets do not overlap; duplicated characters would overstate this bound.

References

Translate the captured eleven-input character-pool helper as the same piecewise total-length logarithm. Preserve every custom pool and count, empty-input behavior and read-only result. Decimal arithmetic removes binary rounding; author notes state this combined-pool bound cannot certify the strength of a chosen password. A character category with a positive count requires a nonempty alphabet; otherwise the captured combined-pool model can report a finite bound for an impossible category.

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