Shannon Entropy Calculator
Calculate the Shannon entropy and information content of any text string.
How to Use the Shannon Entropy Calculator
- Type or paste any text into the input field.
- Click Calculate — the entropy in bits per symbol, total information in bits, maximum entropy, and redundancy are displayed.
- Review the character frequency table to see the probability and individual information content of each symbol.
- Compare entropy values across different texts to understand their relative randomness and compressibility.
Schnellreferenz
| Von | Nach |
|---|---|
| aaaaaaa (7 identical chars) | 0.000 bits/symbol |
| abababab (2 chars) | 1.000 bit/symbol |
| abcdefgh (8 unique chars) | 3.000 bits/symbol |
| English text (typical) | ~4.0–4.5 bits/symbol |
| Random ASCII (95 chars) | ~6.57 bits/symbol |
| Random bytes (256 vals) | 8.000 bits/symbol |
Anwendungsfälle
- •Estimating the compressibility of a text before applying a lossless compression algorithm.
- •Analyzing randomness of passwords, keys, or cryptographic data.
- •Studying information theory concepts in computer science and communications courses.
- •Comparing the information density of different languages or writing styles.
Formel
Shannon entropy H is calculated as H = −Σ p(x) · log₂(p(x)), where p(x) is the probability of each unique symbol x in the string. The result is expressed in bits per symbol. Maximum entropy for an alphabet of size n is log₂(n) bits. Redundancy = 1 − H / H_max. Total information = H × string length (bits).
Häufig gestellte Fragen
What is Shannon entropy?
Shannon entropy, introduced by Claude Shannon in 1948, measures the average amount of information (or uncertainty) in a source of data. A string with high entropy is more random and less compressible; a string with low entropy is more predictable and contains more redundancy. It is the theoretical lower bound for lossless compression.
What does entropy in bits per symbol mean?
Entropy in bits per symbol tells you how many bits are needed on average to represent each character if the string were encoded optimally. For example, a perfectly random string of 256 equally probable characters has entropy of 8 bits/symbol. A string of all identical characters has entropy of 0 bits/symbol.
What is redundancy in the context of entropy?
Redundancy measures how much more space the original encoding uses compared to the theoretical minimum. It is calculated as 1 − H / H_max, where H_max = log₂(unique characters). A redundancy of 0 means the text is perfectly random (no compression possible); a redundancy of 1 means all characters are the same.