Hartley Entropy Calculator (Max-Entropy / H₀)

Online String Entropy Calculator - Shannon, Rényi, Min-Entropy & More

What is string entropy and why measure it?

String entropy quantifies the information content or unpredictability of text, measured in bits per character. A string of all identical characters has zero entropy; a uniformly random string has maximum entropy. Measuring entropy helps developers evaluate password strength, detect compressed or encrypted blobs, fingerprint suspicious binaries, audit randomness sources, and study language statistics. The giga.tools entropy calculator runs entirely in your browser, so no input ever leaves your machine - making it safe for sensitive secrets, API keys, or proprietary data.

How is Shannon entropy calculated for a string?

Shannon entropy uses the formula H = -Σ pᵢ · log₂(pᵢ) over the probability pᵢ of each distinct character. Practically, you count how often each character appears, divide by total length to get probabilities, multiply each by its log₂, sum, and negate. The result is bits per character: for example, English text averages roughly 4.0-4.5 bits/char, while a Base64-encoded random blob approaches ~6 bits/char. Our calculator computes this in real time as you type and also shows the total information (entropy × length).

What is Rényi entropy and when should I use a custom alpha?

Rényi entropy H_α = (1 / (1−α)) · log₂(Σ pᵢ^α) is a generalization of Shannon entropy with a tunable order parameter α. Different α values emphasize different aspects of the distribution: small α weights all symbols evenly, large α focuses on the most frequent symbols. Researchers use Rényi entropy in ecology (species diversity indices), information theory, quantum information, and cryptography. Use this variant when you need a family of related measures rather than a single fixed metric - for instance, comparing two distributions across multiple α values.

What are min-entropy, collision entropy, and Hartley entropy?

These three are special cases of Rényi entropy with fixed α: Hartley entropy (α=0) is simply log₂ of the alphabet size and represents the theoretical maximum; Shannon entropy (α=1) is the standard average information; collision entropy (α=2) equals −log₂(Σ pᵢ²) and relates to the probability of two random draws colliding; min-entropy (α→∞) is −log₂(max pᵢ) and bounds the worst-case guessing probability. Cryptographic standards (NIST SP 800-90) prefer min-entropy when estimating the security of randomness sources.

Which entropy measure is best for password strength?

For password and key strength analysis, min-entropy is the most conservative and security-relevant choice because it captures the worst-case predictability. Shannon entropy can overestimate strength when one character dominates (e.g., aaaaaaaab has high Shannon entropy per character but is trivially guessable). For practical password meters, combine min-entropy with the Password Generator and avoid relying on a single metric. Always remember that character-level entropy ignores higher-order structure like dictionary words and common substitutions.

Does this tool support Unicode and emoji correctly?

Yes - the calculator iterates input by Unicode code point, so multi-byte characters such as 日本語, 🚀, and combined surrogate pairs are each counted as a single symbol rather than separate UTF-16 units. This matches how most people intuitively perceive "characters" in a string. If you need byte-level entropy instead (useful for analyzing binary blobs or compressed data), encode your input to a hex or Base64 string first using the Base64 Encoder/Decoder.

How do I interpret the entropy value in bits per character?

The result is the average number of bits needed to encode one character under an optimal prefix code. A value of 0 means the string is perfectly predictable (one repeated symbol); the Max Entropy card shows the theoretical ceiling log₂(unique characters). A real-world English sentence typically scores 4.0-4.7 bits/char, source code 4.5-5.5, hexadecimal output ~4.0, Base64 ~5.8, and uniformly random bytes 8.0. Comparing your input against these benchmarks tells you immediately whether you're looking at natural language, structured data, or high-entropy random material.

Can I analyze a selected substring inside the input?

Yes. Select any portion of text inside the input box with your mouse or keyboard, and a tooltip appears showing the entropy of just that selection. This is extremely useful when scanning a large document for high-entropy regions that often indicate API keys, JWTs, hashes, or compressed payloads embedded in otherwise low-entropy text. Many security tools use exactly this technique to scan source code for accidentally committed secrets.

How does string entropy help detect secrets in code?

Tools like GitHub secret scanning, TruffleHog, and gitleaks flag suspicious strings partly by computing their Shannon entropy. A typical API key or token has Shannon entropy above ~3.5 bits/char and length over 20 characters - values rarely seen in natural source code. By selecting suspicious substrings in this calculator you can quickly verify whether something looks like a random secret versus regular identifier text. Combine it with the Regex Tester to build custom detection patterns.

What's the difference between character-level and byte-level entropy?

Character-level entropy treats each Unicode code point as one symbol, which makes intuitive sense for text. Byte-level entropy operates on the raw UTF-8 (or other) bytes and is the standard for analyzing binary data, compressed archives, and encrypted blobs - these typically approach the maximum 8.0 bits/byte. This tool focuses on character-level entropy because that's what most string analysis tasks call for; for binary entropy, you'll need to first encode the input.

Are there limits on input size for this entropy tool?

The calculator runs fully client-side using efficient O(n) algorithms with a single-pass frequency count, so it comfortably handles inputs of several megabytes. Very large pastes may briefly stutter the UI on slower devices since computation runs synchronously in the main thread, but typical text files, log snippets, and password lists complete in microseconds. Nothing is uploaded or logged - your input stays in your browser tab.

How does Rényi entropy generalize Shannon, Hartley, and min-entropy?

All three are points on the Rényi entropy curve H_α: at α=0 you get Hartley (log of alphabet size, distribution-blind), at α=1 (via L'Hôpital's limit) you get Shannon (the classical average), at α=2 you get collision entropy, and as α→∞ you get min-entropy (worst-case). The curve is monotonically non-increasing in α, so H_0 ≥ H_1 ≥ H_2 ≥ H_∞. Use the Rényi variant of this tool to explore the curve interactively - slide α to see how each measure transitions into the next on your own data.

Built with ❤️ for cryptographers, security engineers, and information theorists at giga.tools.