Calculators
Min-Entropy Calculator
Calculate discrete min-entropy in bits and nats and best single-guess success from outcome counts, weights or probabilities in your browser.
Enter one non-negative weight per outcome, separated by spaces, commas or semicolons. Weights are normalized automatically. Use 1–10000 values and at most 200000 characters. Nonzero weights must be between 1e-100 and 1e100; at least one must be positive. Calculation runs locally in your browser.
How discrete min-entropy works
Min-entropy is H∞ = −log₂(max pᵢ). It measures uncertainty using only the most likely outcome. Enter one non-negative count, weight or probability per distinct outcome; weights are normalized automatically. For weights 1, 1, 2 the maximum probability is 0.5 and min-entropy is 1 bit. Equal weights across n outcomes give log₂(n) bits; a certain outcome gives zero. Nats use natural logarithms. Zero weights contribute no probability. Unlike Shannon entropy, min-entropy focuses on the best single guess rather than average information. This describes the distribution you supply; it does not estimate password strength or certify a random source. Enter 1–10000 weights separated by spaces, commas or semicolons, up to 200000 characters. Commas separate values, not thousands. Nonzero values must be between 1e-100 and 1e100; at least one must be positive. Scaling by the maximum and compensated summation reduce overflow and rounding error. Results display up to 12 significant digits. All processing stays in your browser.
Frequently Asked Questions
Everything you need to know about this tool, how it works, and privacy.
What is min-entropy?
It is −log₂ of the largest normalized outcome probability. It measures uncertainty against the best single guess.
Do weights need to sum to one?
No. Counts and non-negative weights are normalized automatically. At least one weight must be positive; zero weights are allowed.
What is an example?
For weights 1, 1, 2, the largest probability is 0.5, min-entropy is 1 bit and the best single guess succeeds 50% of the time.
How does it differ from Shannon entropy?
Shannon entropy averages information across outcomes. Min-entropy uses only the largest probability and is no greater than Shannon entropy for the same distribution.
Can this certify a password or random generator?
No. The result describes only the supplied discrete distribution. It does not infer unknown probabilities, dependence or source quality.