Cohen’s Kappa Calculator
Cohen’s kappa measures agreement between two raters while correcting for agreement expected from their marginal category frequencies. The 2×2 counts represent two categories.
How to use this calculator
- Enter the four counts for the two raters in a consistent row/column order.
- Check that all inputs use the same units, period and population scope.
- Change one assumption at a time when comparing scenarios.
Formula used by interrater agreement kappa calculator
κ = (observed agreement − expected agreement) ÷ (1 − expected agreement).
- κ = (observed agreement − expected agreement) ÷ (1 − expected agreement).
- Kappa depends on category prevalence and marginal distributions. Review raw agreement, counts and study design together.
- The tool validates inputs and rounds displayed figures for readability; it does not validate assumptions against external records.
Worked examples
Worked example
Two raters agree on 42 positive and 40 negative items; 18 items are disagreements.
Observed agreement = (42 + 40)/100 = 82%; expected agreement is computed from row and column totals.
The result is Cohen’s kappa for the table.
Understanding the result
Cohen’s kappa measures agreement between two raters while correcting for agreement expected from their marginal category frequencies. The 2×2 counts represent two categories.
Kappa depends on category prevalence and marginal distributions. Review raw agreement, counts and study design together.
Important notes
Kappa depends on category prevalence and marginal distributions. Review raw agreement, counts and study design together.
Treat the result as an estimate from the entered assumptions. For commercial, statistical, engineering or health-related decisions, verify relevant specifications and professional guidance.
Frequently asked questions
Can kappa be negative?
Yes. Observed agreement can be lower than agreement expected from marginal frequencies.
Does kappa apply to more than two raters?
This calculator is for two raters and a 2×2 table.
How should I interpret this result?
Kappa depends on category prevalence and marginal distributions. Review raw agreement, counts and study design together.
Related calculators
- 2×2 Matrix Calculator — Add, subtract and multiply 2×2 matrices and calculate each determinant with transparent row and column inputs.
- Cohen’s d Effect Size Calculator — Estimate standardized mean difference using the pooled sample standard deviation of two independent groups.
- Circle Calculator — Calculate circle area, circumference, and diameter from radius.
- Probability Calculator — Calculate simple event probability from favorable outcomes and total outcomes.
- Pythagorean Theorem Calculator — Find the hypotenuse of a right triangle from the two perpendicular sides.
- Test Grade Calculator — Calculate the score needed on a final assessment to reach a target overall grade.
Related explanations
Learn the method behind the number or compare the terminology before using the calculator.
- How to Calculate Probability — Learn basic probability formulas, complementary probability, and how to calculate simple event chances.
- How to Calculate Salary from an Hourly Rate — Convert hourly pay into weekly, monthly, and annual estimates and understand the assumptions behind the result.
- Percent Difference — Understand percent difference, when it is appropriate, and how it differs from percentage change and percent error.
This page provides a calculation tool plus explanatory information so you can understand what the result means and when the underlying method may not fit your situation.