Cohen's Kappa Calculator
Enter the agreement table for two raters (same categories on rows and columns). The tool will compute observed agreement, expected agreement, Cohen’s kappa, approximate standard error, 95% confidence interval, and an interpretation based on Landis & Koch.
2–6 categories
Cohen's κ
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Observed agreement (Po)
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Expected agreement (Pe)
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Interpretation
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Formula
\( P_o = \frac{\sum_i n_{ii}}{N} \)
\( P_e = \frac{\sum_i (n_{i+} \cdot n_{+i})}{N^2} \)
\( \kappa = \frac{P_o - P_e}{1 - P_e} \)
where \(n_{ii}\) are diagonal (agreements), \(n_{i+}\) are row totals, \(n_{+i}\) are column totals, \(N\) is total.
Landis & Koch (1977) scale (rule of thumb)
- < 0: poor
- 0.00–0.20: slight
- 0.21–0.40: fair
- 0.41–0.60: moderate
- 0.61–0.80: substantial
- 0.81–1.00: almost perfect
This is just guidance; report kappa, Po, Pe and sample size.
Formula (LaTeX) + variables + units
This section shows the formulas used by the calculator engine, plus variable definitions and units.
Formula (extracted LaTeX)
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Formula (extracted text)
\( P_o = \frac{\sum_i n_{ii}}{N} \) \( P_e = \frac{\sum_i (n_{i+} \cdot n_{+i})}{N^2} \) \( \kappa = \frac{P_o - P_e}{1 - P_e} \) where \(n_{ii}\) are diagonal (agreements), \(n_{i+}\) are row totals, \(n_{+i}\) are column totals, \(N\) is total.
Variables and units
- No variables provided in audit spec.
Sources (authoritative):
- NIST — Weights and measures — nist.gov · Accessed 2026-01-19
https://www.nist.gov/pml/weights-and-measures - FTC — Consumer advice — consumer.ftc.gov · Accessed 2026-01-19
https://consumer.ftc.gov/
Changelog
Version: 0.1.0-draft
Last code update: 2026-01-19
Last code update: 2026-01-19
0.1.0-draft · 2026-01-19
- Initial audit spec draft generated from HTML extraction (review required).
- Verify formulas match the calculator engine and convert any text-only formulas to LaTeX.
- Confirm sources are authoritative and relevant to the calculator methodology.