Krippendorff's Alpha Calculator

Krippendorff's alpha (α) is a reliability coefficient for content analysis and annotation. Unlike percent agreement or Cohen's kappa, it works for any number of coders, tolerates missing data, and adapts to the measurement level of your categories. This tool implements the algorithm exactly as set out in Krippendorff (2011), Computing Krippendorff's Alpha-Reliability.

1. Coincidence matrix. For each unit with m ≥ 2 present values, every ordered pair of values (c, k) from that unit adds 1 / (m − 1) to the coincidence count o_ck. Units with fewer than two ratings contribute nothing, which is how missing data is handled cleanly.
2. Marginals. The value totals are n_c = Σ_k o_ck and the grand total of pairable values is n = Σ_c n_c.
3. Difference function δ²(c, k). This is what makes alpha flexible. For nominal data δ² = 0 when c = k and 1 otherwise. For interval data δ² = (c − k)². For ratio data δ² = ((c − k)/(c + k))². For ordinal data δ² = (Σ n_g from c to k − (n_c + n_k)/2)², summing the marginals of the ranks between c and k. Ordered levels give partial credit to near-miss disagreements, so the same data scores higher on interval than on nominal.
4. Observed and expected disagreement. D_o = (1/n) Σ o_ck δ² and D_e = (1/(n(n−1))) Σ n_c n_k δ². D_o is the disagreement the coders actually produced; D_e is what random coincidences of the same marginals would produce.
5. Alpha. α = 1 − D_o / D_e. Perfect agreement gives α = 1; agreement equal to chance gives α = 0; worse-than-chance (systematic) disagreement gives a negative α. When every value is identical, D_e = 0 and there is no variability to judge, so α is defined as 1 with a note. When fewer than two pairable values exist, α is undefined and the tool says so rather than showing a misleading figure.

To keep the result trustworthy, the calculator computes α two independent ways — the full coincidence-matrix form above and Krippendorff's equivalent upper-triangle single expression α = 1 − (n−1) Σ_(c<k) o_ck δ² / Σ_(c<k) n_c n_k δ² — and only displays a number when the two agree. Interpretation uses Krippendorff's thresholds: α ≥ 0.800 is reliable, α ≥ 0.667 supports tentative conclusions only, and anything lower should be discarded.

• Krippendorff, K. (2011) — Computing Krippendorff's Alpha-Reliability (canonical algorithm)
• Hayes, A. F., & Krippendorff, K. (2007) — Answering the call for a standard reliability measure for coding data
• Krippendorff, K. (2018) — Content Analysis: An Introduction to Its Methodology (4th ed.), Sage (reliability thresholds)

The δ² difference functions and the α formula on this page were last cross-checked against Krippendorff (2011) on 2026-07-09. If a result disagrees with R's krippendorffsalpha or the KALPHA macro for your data, email me the grid and I'll investigate.