Password Entropy Calculator

TL;DR

This guide shows you how to calculate the entropy of a password – basically, how strong it is. We’ll use Python for an example, but the principles apply to any language or even manual calculation.

Calculating Password Entropy

1. Understand Entropy: Entropy measures randomness. A higher entropy means more possible combinations and a stronger password. It’s calculated using logarithms (base 2 is common) and probabilities of each character appearing in the password.
   • A simple password like “123456” has very low entropy because it’s easy to guess.
   • A complex password with mixed case letters, numbers, and symbols will have high entropy.
2. Determine the Character Set: First, you need to know what characters are allowed in your passwords.
   • Lowercase letters (a-z): 26 characters
   • Uppercase letters (A-Z): 26 characters
   • Numbers (0-9): 10 characters
   • Symbols: Varies, but let’s assume 32 for common symbols.
3. Calculate the Total Possible Characters: Add up all the characters in your character set.

   For example, lowercase + uppercase + numbers + symbols = 26 + 26 + 10 + 32 = 94

4. Determine Password Length: The length of the password is crucial. Longer passwords have exponentially more combinations.

   Let’s assume a password length of 8 characters.

5. Calculate Total Possible Combinations: Raise the total number of possible characters to the power of the password length.

   94 ** 8

   This gives you approximately 5.96 x 10¹³ (almost 60 trillion) combinations.

6. Calculate Entropy: Use the following formula:

   Entropy = log₂(Total Possible Combinations)

   import math
   
   combinations = 94 ** 8
   
   entropy = math.log2(combinations)
   
   print(f"Password Entropy: {entropy}")

   This will output approximately 27.56 bits of entropy.

7. Consider Character Frequency (Advanced): The above calculation assumes each character is equally likely. In reality, people tend to use certain characters more often.
   • If you know the frequency of each character in your passwords, you can refine the calculation for a more accurate result.
   • This involves calculating the probability of each character and using that in the entropy formula (Shannon Entropy). It’s more complex but provides a better estimate.
8. Interpreting Entropy Values:
   • < 30 bits: Weak password – easily crackable.
   • 30-50 bits: Moderate password – requires more effort to crack.
   • > 50 bits: Strong password – very difficult to crack.