Cohen's Kappa Calculator

Enter a k×k agreement table or paired category ratings (2–8 levels) for two raters: Cohen's κ, SE under H₀ for the z test, general SE for the 95% CI, and linear/quadratic weighted κ.

Paste a table of counts, one row per line, the counts separated by tabs, commas or spaces. The grid takes the size of the paste, from 2×2 up to 8×8:

What kappa corrects for

κ = (po − pe) / (1 − pe) adjusts for agreement expected by chance. Landis & Koch benchmarks (0.41–0.60 moderate, etc.) are arbitrary—report κ with CI. See McNemar for paired binary disagreement.

κ = (p_o − p_e) / (1 − p_e)

Kappa is for raters who assign items to categories. To judge the internal consistency of a questionnaire scale answered by many respondents, use the Cronbach's alpha calculator.

Worked example

2×2 table in Load example: po = 0.85, κ = 0.70, strong agreement beyond chance for H₀: κ = 0.

Related guides and calculators

Kappa measures agreement between two raters; for the accuracy of a test against a reference see sensitivity and specificity, for a change in paired ratings the McNemar test, and for the reliability of a scale with several items Cronbach's alpha (see Cronbach's alpha explained). The chi-square test of independence tests association, not agreement.

Frequently Asked Questions

Which SE is used for the z test?

SE under H₀ (Fleiss, Cohen & Everitt 1969); the 95% CI uses the general SE.

Kappa paradox?

High p_o but low κ can happen when marginal totals are skewed and p_e is large.

Ordinal categories?

Use linear or quadratic weighted κ to penalize disagreements by distance.

sklearn match?

Unweighted κ matches sklearn.metrics.cohen_kappa_score; weights match weights='linear'|'quadratic'.

Paired ratings list?

Switch to paired ratings and enter parallel lists with category codes 1…k; the calculator builds the k×k table with buildAgreementTable before computing κ.

What is maximum κ?

With fixed marginals, κ cannot exceed (P_max − p_e)/(1 − p_e), where P_max is perfect agreement subject to those margins (Sim & Wright 2005).

Is κ = 1 perfect agreement?

Only if every count lies on the diagonal; κ = 1 implies p_o = 1.

How do I interpret negative κ?

Negative κ means observed agreement is below chance; check for systematic disagreement or coding errors.

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