Fleiss' Kappa Calculator

Measure agreement between three or more raters, corrected for chance. Paste one row per subject with the count of raters who chose each category.

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One row per subject. Each column is a category; the cell is how many raters chose it. Every row must total the same number of raters.

Fleiss' kappa

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Calculate it yourself

Three raters classify each of three subjects into two categories. The category-count rows are 3,0; 2,1; and 0,3.

Follow this worked example, then repeat the steps with your own numbers.

  1. Calculate agreement for each subject

    Pᵢ = [sum of squared category counts − 3] ÷ [3 × (3 − 1)]. The three results are 1, 1/3 and 1.
  2. Average the subject agreements

    P̄ = (1 + 1/3 + 1) ÷ 3 = 7/9.
  3. Find expected agreement from all category assignments

    Category proportions = 5/9 and 4/9. Pₑ = (5/9)² + (4/9)² = 41/81.
  4. Adjust for chance agreement

    κ = (7/9 − 41/81) ÷ (1 − 41/81) = 22/40 = 0.55.

Each row contains category counts, not individual rater scores. Every row must add to the same number of raters.

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Use your PaperSurvey.io results

Export the collected ratings, count each subject’s category assignments and calculate Fleiss’ kappa here.

PaperSurvey Export Data dialog with Excel, CSV, SPSS and R options for collected responses.
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Example from PaperSurvey.ioThe export workflow supplies recorded ratings for a separate multiple-rater agreement calculation.

When to use Fleiss' kappa

Cohen's kappa handles exactly two raters. Fleiss' kappa extends the idea to any fixed number of raters, and the raters do not have to be the same people for every subject. You supply how many raters assigned each category to each subject rather than individual rating pairs.

Interpreting the result

Kappa ranges up to 1, where 1 is perfect agreement and 0 is agreement no better than chance. Following Landis and Koch, values below 0.20 are slight, 0.21 to 0.40 fair, 0.41 to 0.60 moderate, 0.61 to 0.80 substantial and above 0.80 almost perfect. Negative values mean less agreement than chance alone would produce.

Frequently asked questions

How should I lay out my data?

One row per subject, one column per rating category. Each cell is the number of raters who picked that category for that subject, and every row must add up to the same total number of raters.

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