The password entropy bits calculator determines the raw informational strength of passwords by computing Shannon entropy bits and average brute-force search space traversal times across configurable attacker hardware setups. Rather than checking simple arbitrary rules, informational entropy measures the total number of trial guesses required to exhaust a given keyspace.

### Keyspace & Shannon Entropy Formulas

Character pool size ($R$) is determined by enabled character sets: - Lowercase ($a-z$): 26 characters - Uppercase ($A-Z$): 26 characters - Digits ($0-9$): 10 characters - Symbols ($!@#$): 33 characters

Key calculation formulas: - **Total Pool Size:** $R = \sum R_i$ (defaults to 26 if all sets disabled) - **Shannon Entropy (Bits):** $E = L \times \log_2(R)$ - **Average Brute-Force Seconds:** $T = \frac{R^L}{2 \times \text{Hash Rate}}$

### Attacker Rig Speeds

Cracking duration scales against attack throughput settings: - **Single Fast GPU (NTLM):** $10^{11}$ hashes per second (100 Billion H/s) - **8x RTX 4090 GPU Cluster:** $10^{12}$ hashes per second (1 Trillion H/s) - **Slow Hash / Key Derivation:** $10^5$ hashes per second (100,000 H/s for Argon2/Bcrypt)

### Worked Numeric Example

Evaluating a 14-character passphrase with all 4 character sets enabled ($L=14, R=95$) against an 8x RTX 4090 cluster ($10^{12}\text{ H/s}$): 1. Shannon Entropy: $14 \times \log_2(95) = 14 \times 6.56985 = \mathbf{92.0\text{ bits}}$. 2. Total combinations: $95^{14} \approx 4.79 \times 10^{27}$ permutations. 3. Average seconds to solve (50% keyspace): $\frac{4.79 \times 10^{27}}{2 \times 10^{12}} \approx 2.4 \times 10^{15}\text{ seconds}$. 4. In years: $2.4 \times 10^{15} / 31{,}536{,}000 \approx \mathbf{76\text{ Million Years}}$.

### Client-Side Processing Note

Calculations run synchronously in your local browser using logarithmic math. No password parameters or configuration values are transmitted over the network.