Binary Rater Agreement Cohen Kappa Calculator
Calculate observed agreement, marginal chance agreement and unweighted Cohen’s kappa from a paired binary rating table.
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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
Sum the diagonal for observed agreement and use matching row/column marginal proportions for expected agreement. Normalize excess agreement by one minus expected agreement.
κ=(po−pe)/(1−pe); po=(a+d)/n; pe=[(a+b)(a+c)+(c+d)(b+d)]/n²
Worked example
Counts 40,10,5,45 have observed agreement 0.85 and expected agreement 0.5, giving kappa 0.7.
Assumptions and input details
Two raters, the same items and the same two category meanings. Counts are nonnegative whole paired observations, each at most 1e9. This is unweighted binary kappa; no multi-rater extension, confidence interval or significance test. Kappa is undefined when chance agreement equals one and can be negative. There is no universal qualitative grading scale here, and agreement does not establish correctness.
References: scikit-learn: Cohen kappa definition
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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