Mutual Information Calculator
Calculate plug-in mutual information, marginal entropies and conditional entropies from a categorical count table.
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 table to a joint empirical distribution and sum only positive-probability cells.
I(X;Y)=Σ pij log2(pij/(pi pj)); H(X|Y)=H(X)−I(X;Y)
Worked example
Counts 40,10;10,40 have equal margins and mutual information 1−H₂(0.2)≈0.278071905 bits.
Assumptions and input details
Whole nonnegative counts, positive total and 2–20 rows/columns. Plug-in empirical information is biased in finite samples; no bias correction, significance test, causal interpretation or category-label ordering is supplied.
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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