Information Rate Calculator
Enter source probabilities or channel parameters. The Information Rate Calculator computes Shannon entropy, mutual information, and maximum information rate.
About the Information Rate Calculator
The Information Rate Calculator is a precise, scientifically accurate tool that computes the information rate — the average information content per symbol according to Shannon's information theory. This Information Rate Calculator implements the exact entropy formula H = -Σ p log₂ p and related quantities like mutual information and channel capacity bounds. Proudly supported by Agri Care Hub.
Scientific Formulas
General Entropy: H = log₂ M (for M equally likely symbols)
Maximum Information Rate: H_max = log₂ M bits/symbol
Why This Calculator Is Essential
Information rate is the foundation of: • Data compression (Huffman, ZIP) • Error-correcting codes • Cryptography and security • Communication efficiency • Machine learning (cross-entropy loss) • Biology (DNA information content) It quantifies uncertainty and compressibility — the lower the entropy, the more predictable and compressible the source.
How to Use
- Enter probability p for binary source (e.g., 0.5 for fair coin).
- Or enter number of equally likely symbols M (e.g., 256 for bytes).
- Click “Calculate Information Rate”.
- Get entropy in bits/symbol.
When Should You Use This Tool?
- Data compression algorithm design
- Source coding theorem analysis
- Cryptography entropy estimation
- Machine learning loss functions
- Biological sequence analysis
- Teaching information theory
Scientific Foundation
Information rate (entropy rate) was defined by Claude Shannon in 1948 as the average information per symbol. Binary entropy H(p) is maximum at p=0.5 (1 bit) and zero at p=0 or 1. For discrete uniform sources, H = log₂ M. Full theory at Information Rate on Wikipedia and Shannon’s *A Mathematical Theory of Communication*.
Conclusion
The Information Rate Calculator brings Shannon's entropy — the measure of information — to your browser with perfect accuracy and beautiful design. Whether you’re a student learning information theory, a researcher analyzing data compressibility, or an engineer designing coding schemes, this tool delivers precise results every time. For more information theory tools, visit Agri Care Hub.