Is a short password with symbols better than a long password with just letters? The answer lies in mathematics, specifically a concept called Information Entropy.
The Formula
Entropy (E) is calculated using the pool of available characters (R) and the length of the password (L). The formula is:
E = log₂(Rᴸ)
Where R is the range of characters (e.g., 26 for lowercase, 62 for alphanumeric) and L is the number of characters in the password.
Length vs. Complexity
- Scenario A: An 8-character password using all symbols, numbers, and cases (R=94). Entropy ≈ 52 bits.
- Scenario B: A 15-character password using only lowercase letters (R=26). Entropy ≈ 70 bits.
Surprisingly, Scenario B is stronger. Every bit of entropy doubles the effort required to crack the password. A 70-bit password is not just twice as strong as a 52-bit one; it is 2¹⁸ times stronger (that's 262,000 times harder to crack).
The Magic Number: 60 Bits
For general internet security, you should aim for at least 60 bits of entropy. For banking and critical infrastructure, aim for 80+ bits. Our tool helps you visualize this strength instantly.
Calculate Your Strength
Use our calculator to see the bit-strength of random passwords.
Conclusion
Don't rely on gut feeling. Rely on math. Increasing your password length by just a few characters offers significantly more protection than replacing an 'e' with a '3'.