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Cohen’s Kappa Calculator

Inter-rater agreement for two raters and two categories from a 2×2 table — observed agreement, expected agreement, κ and its interpretation.

Both said Yes

Rater 1 Yes, Rater 2 No

Rater 1 No, Rater 2 Yes

Both said No

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How it works

κ = (pₒ − pₑ) ÷ (1 − pₑ)

Raw percent agreement is inflated by chance — two raters flipping coins agree half the time. Kappa subtracts the agreement expected from each rater’s marginal frequencies and rescales so that 1 is perfect agreement and 0 is chance level.

Worked example

a=20, b=5, c=10, d=15 (n=50): pₒ = 0.70, pₑ = (25×30 + 25×20)/2500 = 0.50, κ = 0.40 — fair-to-moderate.

Frequently asked questions

More than two categories or raters?

Use weighted kappa for ordered categories and Fleiss’ kappa for three or more raters. This tool handles the common 2×2 case.

Why can kappa be low when agreement is high?

When one category dominates, chance agreement is already high, so kappa has little room to grow — the “kappa paradox”.

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