📊 Shannon Entropy Calculator – Measure Information Randomness
The Shannon Entropy Calculator quantifies the average unpredictability, or information density, of any text, password, or data file. Developed by Claude Shannon in 1948 as part of his foundational work in information theory, entropy has become an essential metric in cryptography, data compression, and cybersecurity analysis.
What Is Shannon Entropy?
Entropy measures how much surprise is encoded in a data source. If every character in a string is the same (e.g., "aaaaaaa"), entropy is 0 — no new information per symbol. If all symbols appear equally often, entropy reaches its theoretical maximum — every next symbol is completely unpredictable.
The formula is:
H(X) = -Σ p(xᵢ) × log_b(p(xᵢ))
Where:
p(xᵢ) = count(xᵢ) / total symbols
b = 2 (bits), e (nats), or 10 (hartleys)Alphabet Modes Explained
The calculator supports three ways to define a "symbol" in your data:
🔤 Character Mode
Each Unicode character is a symbol. Ideal for analyzing text, passwords, and multilingual content. Handles emoji and special characters correctly.
🔢 Byte Mode (0–255)
Analyzes raw byte values. Best for binary files, encrypted blobs, and compressed archives where byte-level distribution reveals file type.
⚡ Bit Mode
Treats data as a stream of individual 0s and 1s. Useful for evaluating PRNG quality, hardware RNG output, and bias detection. Ideal entropy: 1.0 bit/bit.
Interpreting Your Results
| Entropy (bits/byte) | Interpretation | Typical Source |
|---|---|---|
| 0.0 – 1.0 | Very Low | Highly repetitive or constant data |
| 1.0 – 3.5 | Low | Natural language, patterned text |
| 3.5 – 5.5 | Medium | Mixed or semi-structured content |
| 5.5 – 7.5 | High | Compressed files, Base64-encoded data |
| 7.5 – 8.0 | Very High | AES/RSA ciphertext, TRNG output |
Logarithm Base and Output Units
The choice of logarithm base changes the unit of measurement, not the underlying information content:
- Base 2 → entropy in bits (most common; used in computer science)
- Base e → entropy in nats (used in physics and information theory)
- Base 10 → entropy in hartleys (used in signal processing)
To convert: 1 bit = ln(2) ≈ 0.693 nats = log₁₀(2) ≈ 0.301 hartleys
Practical Applications
Password Strength Assessment
Shannon entropy provides a lower bound on password strength. A password drawing from a 95-character ASCII printable set has a theoretical maximum of log₂(95) ≈ 6.57 bits/character. However, actual entropy depends on how randomly characters were chosen — "Password1!" reuses patterns and has far lower entropy than a truly random 10-character string.
Detecting Encrypted or Compressed Files
A text file or source code typically has entropy between 3.5 and 5.5 bits/byte. After encryption (AES, ChaCha20) or compression (gzip, zstd), byte-level entropy jumps to ≥ 7.5 bits/byte, approaching the theoretical maximum of 8 bits/byte. This property is used in malware analysis to detect obfuscated payloads embedded in executables.
Data Compression Efficiency
Shannon entropy defines the theoretical compression limit. If your data has H = 4.2 bits/character but you're storing it in 8 bits, there's room for roughly 47.5% compression before hitting the entropy ceiling. Values already near maximum entropy (e.g., JPEG images, ZIP files) will not compress further.
File Upload & Privacy
Files are processed entirely client-side in your browser. No data is transmitted to any server. Binary files are read as raw byte arrays for accurate byte-level analysis. Maximum file size is 10 MB to prevent browser memory issues.