A/B Testing Password Strength Formula
Learn how the calculator estimates and compares the effective entropy of two password designs.
This calculator estimates each password design's effective entropy from its length, estimated character variety, and a predictability penalty. It is useful for comparing proposed structures without entering an actual password.
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Estimated Effective Password Entropy
Where:
Multiply password length by estimated bits per character, then reduce that theoretical estimate by the percentage assigned for predictable content.
Variables Explained
| Variable | What It Means | Unit |
|---|---|---|
| E - Estimated effective entropy | The comparative entropy estimate after the predictability adjustment. | bits |
| L - Password length | The number of characters in the password design. | characters |
| B - Estimated bits per character | The calculator's approximation for the selected character variety. | bits per character |
| P - Predictability penalty | The percentage reduction used for words, patterns, dates, repeated structures, or familiar information. | percent |
Step-by-Step Calculation
Choose a password length
Use the number of characters in the design, not the password text itself.
L = passwordLength
Set the character-variety estimate
Select the estimate matching lowercase only, mixed letters, letters and numbers, or letters, numbers, and symbols.
B = bitsPerCharacter
Calculate theoretical entropy
This gives an estimated character-space value before considering predictable content.
theoreticalEntropy = L * B
Convert the penalty to a remaining fraction
A 20% predictability penalty leaves 80% of the theoretical estimate.
remainingFraction = 1 - P / 100
Calculate Password A entropy
This produces the adjusted estimate for option A.
passwordAEntropy = passwordALength * passwordACharacterPoolBits * (1 - passwordAPredictabilityPenalty / 100)
Calculate Password B entropy and compare
A positive difference favors Password B; a negative difference favors Password A.
entropyDifference = passwordBEntropy - passwordAEntropy
Compare a 12-character design with a 16-character design
Password A theoretical entropy
12 × 5.95
71.4 bits
Password A remaining fraction
1 − 20 / 100
0.80
Password A effective entropy
71.4 × 0.80
57.1 bits
Password B theoretical entropy
16 × 6.55
104.8 bits
Password B effective entropy
104.8 × (1 − 5 / 100)
99.6 bits
Difference and relative change
99.56 − 57.12; (99.56 − 57.12) / 57.12 × 100
42.4 bits; 74.3%
Final Result
Password A is estimated at 57.1 bits and Password B at 99.6 bits. Password B is higher by 42.4 estimated bits, or 74.3% relative to Password A.
Assumptions
- ✓The selected bits-per-character value reasonably represents the intended character variety.
- ✓The predictability penalty is a practical estimate of how much familiar structure reduces effective resistance to guessing.
- ✓Both options are compared using the same simplified method.
- ✓Higher estimated entropy represents a larger estimated guessing search space, not guaranteed security.
Limitations
- !The calculator does not inspect a real password or detect specific dictionary words, leaks, keyboard patterns, or substitutions.
- !Actual attack resistance depends on password hashing, rate limits, account recovery processes, and attacker capabilities.
- !A user-selected predictability penalty is subjective and can materially change the result.
- !Entropy estimates do not address password reuse, phishing, malware, or credential theft.
Common Mistakes to Avoid
Entering a real, current, or sensitive password instead of only design details.
Using a 0% penalty for a design built from a familiar word, date, phrase, or keyboard sequence.
Treating symbols as fully random when they are used in predictable positions or substitutions.
Comparing designs with different penalty assumptions without considering why the penalties differ.
Assuming a higher estimate makes password reuse safe.
Reading a positive B-minus-A result as a guarantee rather than a comparative estimate.
Related Formulas
Frequently Asked Questions
What is the password entropy formula used by this calculator?
For each option, it uses length × estimated bits per character × (1 − predictability penalty ÷ 100).
How is the entropy difference calculated?
The calculator subtracts Password A's estimated entropy from Password B's estimated entropy. Positive results favor B.
Why does the formula include a predictability penalty?
Length and character variety can overstate resistance when a design contains easily guessed words, dates, patterns, or repeated structure.
What do bits per character mean in this calculation?
They are fixed estimates representing the selected character pool, rather than a direct analysis of the password text.
Can a longer password have a lower estimate?
Yes. A longer design can have a lower adjusted estimate if it uses a smaller character pool or receives a much larger predictability penalty.
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