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Fleiss' Kappa Calculator

Calculate Fleiss' Kappa to measure agreement among three or more raters classifying items into two categories.

Result

Fleiss' Kappa
0.5139
Interpretation
Moderate

About the Fleiss' Kappa

The Fleiss' Kappa Calculator measures how much agreement exists among three or more raters classifying the same set of subjects into one of two categories, correcting for the agreement expected from chance alone. It extends the same logic as Cohen's Kappa to panels larger than two raters, which is common in content moderation, diagnostic panels, and survey coding.

How It Works

You enter how many raters chose category A for each subject, one count per subject, along with the fixed number of raters who scored every subject. The calculator derives the overall proportion of ratings falling into each category, measures how much agreement actually occurred subject by subject, compares that to the agreement expected from random guessing, and combines the two into a single kappa statistic.

With N subjects and m raters per subject, let pA be the overall proportion of all ratings in category A (pB = 1 - pA). Chance-expected agreement is Pe = pA^2 + pB^2. For each subject with cA raters choosing A and cB = m - cA choosing B, observed agreement is Pi = [cA(cA-1) + cB(cB-1)] / [m(m-1)]. Fleiss' Kappa = (mean of all Pi - Pe) / (1 - Pe).

Examples

Six subjects, five raters each

With category A counts of 5, 4, 0, 3, 5, 1 across six subjects rated by five raters each, the overall category A rate is 60 percent, expected chance agreement is 0.52, and the average observed agreement per subject works out to about 0.767, producing a kappa of roughly 0.514 - labeled Moderate agreement.

Unanimous raters

With four subjects rated by three raters each, and category A counts of 3, 3, 0, 0 (every rater agrees on every subject), observed agreement is 1 for each subject and expected chance agreement is 0.5, giving a kappa of exactly 1.0 - labeled Almost perfect agreement.

Advantages

  • Extends chance-corrected agreement measurement beyond two raters, so panels of three, five, or more judges can be assessed with a single statistic instead of averaging pairwise Cohen's Kappa values.
  • Needs only category tallies per subject rather than each individual rater's full response sheet, keeping data entry manageable for large rating panels.
  • Produces both a numeric kappa value and a plain-language interpretation band, useful when reporting reliability results to non-statisticians.

Common Mistakes

  • Entering an inconsistent number of raters per subject, when the formula as implemented assumes a fixed number of raters scores every subject.
  • Confusing Fleiss' Kappa with Cohen's Kappa, which is built specifically for exactly two raters rather than a multi-rater panel.
  • Reading a low kappa as proof the raters are careless, when it may instead reflect an ambiguous category definition or genuinely borderline subjects.

Edge Cases to Watch For

  • Requires more than one rater per subject; a single rater leaves nothing to measure agreement against.
  • Each subject's category A count cannot exceed the number of raters per subject; larger values are rejected.
  • If expected agreement Pe works out to exactly 1 (a degenerate, all-one-category dataset), kappa is undefined and the calculator returns an error instead of dividing by zero.
  • This version handles exactly two categories per subject; classification into three or more categories requires a different form of the statistic.

Common Use Cases

  • Research teams validating that multiple independent coders classify open-ended survey responses or moderation decisions consistently.
  • Clinical or diagnostic panels checking whether several reviewers agree on a binary classification, such as normal versus abnormal on a set of scans.
  • Survey and data-labeling projects that need a single reliability number before trusting a large-scale labeling effort.
Written & fact-checked by the Calculateus TeamLast updated August 5, 2026How we verify our formulas

Frequently asked questions

How is Fleiss' Kappa different from Cohen's Kappa?

Cohen's Kappa measures agreement between exactly two raters. Fleiss' Kappa extends the same chance-corrected agreement concept to three or more raters classifying the same set of items, which is common in settings like content moderation, medical diagnosis panels, or survey coding where multiple independent judges review each item.

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Conclusion

Fleiss' Kappa Calculator turns a table of per-subject category tallies into one chance-corrected agreement score, showing whether a multi-rater panel is classifying consistently or effectively guessing. The interpretation band offers a quick read, but the underlying kappa value is what should be reported alongside the data.