Symbol Count Shannon Entropy Calculator
Calculate empirical entropy, observed support and ideal coding bounds from labelled symbol counts.
YOUR CALCULATION
Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Normalize the counts to empirical probabilities and sum −p log2 p over positive counts. Compare this mean information with uniform entropy and fixed-width coding for the observed support.
H=−Σp log2 p; uniform maximum=log2(K); fixed width=ceil(log2(K))
Worked example
Counts 50,25,25 give probabilities 0.5,0.25,0.25 and entropy 1.5 bits/symbol. A fixed-width code for three observed symbols needs two bits per symbol before overhead.
Assumptions and input details
Zero-order empirical symbol model; labels are unique and counts are nonnegative whole numbers. Zero-count labels are excluded from observed support. One observed symbol has zero entropy and a zero-bit mathematical fixed-width bound when support is already known. These figures are not a guaranteed compressed file size or randomness/security test. Up to 200 labels.
References: Tufts University: Shannon entropy of a discrete distribution
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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