A/B Testing Password Strength (Annual) Calculator Examples
Worked examples comparing password designs by search space, annual brute-force likelihood, and average exhaustive-search time.
These worked examples use theoretical random-password designs and an effective attacker guessing rate. They demonstrate why length, character set size, and the attack environment all matter when comparing Password A with Password B.
Longer password with the same character set
A team is deciding whether to require 12 or 16 randomly generated characters for a sensitive account.
Input Summary
Password A
12 characters from 94 possible characters
Password B
16 characters from 94 possible characters
Effective guess rate
1,000 guesses per second
Calculation Breakdown
- 1Annual guess budget1,000 × 31,536,00031,536,000,000 guesses
- 2Password A search space94^12approximately 4.76 × 10^23
- 3Password B search space94^16approximately 3.72 × 10^31
- 4Relative search space94^16 ÷ 94^1278,074,896×
Result Summary
Relative search space
78,074,896×
A/B Testing Password Strength (Annual) Calculator
Password B has about 78 million times the search space of Password A, with a correspondingly lower modeled annual brute-force likelihood.
Letters and digits versus a longer lowercase password
A product team is comparing a 10-character letters-and-digits requirement with a 16-character lowercase random token.
Input Summary
Password A
10 characters from 62 possible characters
Password B
16 characters from 26 possible characters
Effective guess rate
100 guesses per second
Calculation Breakdown
- 1Annual guess budget100 × 31,536,0003,153,600,000 guesses
- 2Password A search space62^10approximately 8.39 × 10^17
- 3Password B search space26^16approximately 4.36 × 10^22
- 4Relative search space26^16 ÷ 62^10approximately 51,950×
Result Summary
Relative search space
approximately 51,950×
A/B Testing Password Strength (Annual) Calculator
The 16-character lowercase random design has roughly 52,000 times the theoretical search space of the 10-character letters-and-digits design.
Online login with a tightly constrained guess rate
An online service uses throttling and lockouts, so the effective attacker rate is estimated at 1 guess per second.
Input Summary
Password A
8 characters from 62 possible characters
Password B
12 characters from 62 possible characters
Effective guess rate
1 guess per second
Calculation Breakdown
- 1Annual guess budget1 × 31,536,00031,536,000 guesses
- 2Password A search space62^8approximately 2.18 × 10^14
- 3Password B search space62^12approximately 3.23 × 10^21
- 4Relative search space62^12 ÷ 62^8 = 62^414,776,336×
Result Summary
Relative search space
14,776,336×
A/B Testing Password Strength (Annual) Calculator
At a heavily constrained online guess rate, both random designs receive more protection, but Password B remains far stronger in the brute-force model.
Higher-rate offline-style comparison
A security review wants to see how two designs differ under a hypothetical 1 billion guesses per second effective rate.
Input Summary
Password A
10 characters from 94 possible characters
Password B
14 characters from 94 possible characters
Effective guess rate
1,000,000,000 guesses per second
Calculation Breakdown
- 1Annual guess budget1,000,000,000 × 31,536,0003.1536 × 10^16 guesses
- 2Password A search space94^10approximately 5.39 × 10^19
- 3Password B search space94^14approximately 4.21 × 10^27
- 4Relative search space94^14 ÷ 94^10 = 94^478,074,896×
Result Summary
Relative search space
78,074,896×
A/B Testing Password Strength (Annual) Calculator
Password B has about 78 million times more combinations and retains much lower modeled annual brute-force likelihood under the higher assumed attack rate.
How to Read Your Results
A search-space ratio above 1 means Password B has more theoretical combinations than Password A.
A lower annual compromise likelihood is better in this brute-force-only model.
Expected crack time is an average exhaustive-search estimate, not a guaranteed time to compromise an account.
Very small displayed percentages may be rounded; compare their relative scale as well as the formatted value.
Results apply best to randomly generated passwords, not phrases or predictable human-created patterns.
Assumptions & Important Notes
- All password characters are independently and uniformly selected from the stated character set.
- The same attacker guess rate applies to both password designs within an example.
- The attacker guesses continuously for 365 days without repeating guesses.
- The modeled rate reflects the practical environment, including any relevant technical controls.
Related Examples
Frequently Asked Questions
Why do the examples use an effective guess rate?
The effective rate is meant to reflect the real attack environment after factors such as hashing cost, throttling, lockouts, and available access are considered.
Can a lowercase-only password be stronger than a shorter complex password?
Yes, if it is substantially longer and randomly generated. The examples show that length can create more combinations than a shorter password with a larger character set.
Are these examples suitable for passphrases?
Only if the words or characters are selected randomly from a defined set. Familiar phrases and predictable word choices need a different model.
Does a high search-space ratio eliminate all password risk?
No. Search space addresses brute-force guessing only. Reuse, phishing, malware, and credential leaks can still lead to compromise.
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