Password Entropy Calculator
Complete Guide
Master password entropy calculation and understand the mathematical foundation of password security. Learn how to analyze password strength using entropy metrics.
📋 Table of Contents
🔐 What is Password Entropy?
Password entropy is a measure of the unpredictability or randomness of a password. It quantifies how difficult it would be for an attacker to guess your password through brute force attacks.
Key Concept
Entropy is measured in bits. Higher entropy means more secure passwords. Each additional bit of entropy doubles the number of possible combinations an attacker must try.
✅ High Entropy
- • Random character selection
- • Multiple character types
- • Longer length
- • No patterns or words
❌ Low Entropy
- • Dictionary words
- • Predictable patterns
- • Personal information
- • Short length
🧮 Entropy Formula & Calculation
The Entropy Formula
Where:
E = Entropy in bits
R = Size of character set
L = Length of password
Character Sets
- • Lowercase: 26 chars
- • Uppercase: 26 chars
- • Numbers: 10 chars
- • Symbols: 32+ chars
Example Calculation
Password: "Abc123!"
Length: 7
Character set: 26+26+10+32 = 94
Entropy: log₂(94⁷) ≈ 46 bits
Security Level
46 bits = Very Strong
Time to crack: ~2,000 years
(at 1 billion guesses/sec)
🔤 Character Sets & Complexity
| Character Set | Characters | Count | Example |
|---|---|---|---|
| Lowercase letters | a-z | 26 | abcdefghijklmnopqrstuvwxyz |
| Uppercase letters | A-Z | 26 | ABCDEFGHIJKLMNOPQRSTUVWXYZ |
| Numbers | 0-9 | 10 | 0123456789 |
| Common symbols | !@#$%^&* | 32 | !@#$%^&*()_+-=[]{}|;:,.<>? |
💡 Pro Tip
Using all four character sets (lowercase, uppercase, numbers, symbols) gives you 94 possible characters. This dramatically increases entropy compared to using only lowercase letters (26 characters).
📊 Entropy Levels & Security
🔴 Weak (0-30 bits)
Crackable in seconds to hours
- • 0-20 bits: Instant cracking
- • 21-30 bits: Minutes to hours
- • Examples: "password", "123456", "qwerty"
🟡 Moderate (31-50 bits)
Crackable in days to years
- • 31-40 bits: Days to months
- • 41-50 bits: Months to years
- • Examples: "MyPass123", "Secure2024!"
🟢 Strong (51-70 bits)
Crackable in years to centuries
- • 51-60 bits: Years to decades
- • 61-70 bits: Decades to centuries
- • Examples: "Kx9#mP2$vL8!", "Tr0ub4dor&3"
🔵 Very Strong (71+ bits)
Practically uncrackable
- • 71+ bits: Centuries to millennia
- • Recommended for high-security applications
- • Examples: "X7#kL9$mP2&vN4!qR6@wE8"
💡 Practical Examples
Example 1: Simple Password
Password: "password123"
Example 2: Complex Password
Password: "Kx9#mP2$vL8!"
Example 3: Passphrase
Password: "CorrectHorseBatteryStaple"
✅ Best Practices
🎯 For High Entropy
- ✓Use all character types (lowercase, uppercase, numbers, symbols)
- ✓Make passwords at least 12 characters long
- ✓Use random character selection
- ✓Avoid dictionary words and patterns
- ✓Consider passphrases for better memorability
🚫 Avoid These
- ✗Personal information (names, birthdays)
- ✗Common patterns (123, abc, qwerty)
- ✗Dictionary words without modification
- ✗Repeating characters (aaa, 111)
- ✗Keyboard patterns (asdf, zxcv)
⚠️ Common Mistakes
Mistake 1: Overestimating Entropy
Many people think "MyPassword123!" is very secure, but it's actually only moderate entropy.
"MyPassword123!" → ~65 bits (Strong, but not exceptional)
Mistake 2: Ignoring Character Set Size
Using only lowercase letters severely limits entropy, even with long passwords.
"verylongpassword" → ~75 bits (but only 26 character set)
"V3ryL0ngP@ssw0rd!" → ~95 bits (94 character set)
Mistake 3: Focusing Only on Length
Length is important, but character diversity is equally crucial for high entropy.
"aaaaaaaaaaaa" (12 chars) → ~56 bits
"Kx9#mP2$vL8!" (12 chars) → ~79 bits
🔬 Advanced Concepts
Password Entropy vs. Password Strength
While entropy measures randomness, password strength also considers:
- Dictionary attacks and common patterns
- Social engineering vulnerabilities
- Implementation weaknesses
- Attack sophistication
Entropy in Different Contexts
Online Attacks
Rate-limited attempts (3-5 per second). Even 30-bit entropy can be sufficient.
Offline Attacks
Unlimited attempts (billions per second). Need 60+ bits for security.
Future-Proofing
As computing power increases, entropy requirements should also increase:
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