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Cohen's Kappa Calculator (Inter-Rater Agreement)

How well do two coders agree beyond chance?

Single calculationv1.0.0Verified 2026-11-01Runs in your browser

Spec sheet

cohen_1960 · v1.0.0
Method

Cohen's kappa (1960)

  1. 01p_o = share of items both raters coded the same
  2. 02p_e = Σ_c p_A(c) · p_B(c)
  3. 03κ = (p_o − p_e) / (1 − p_e)
  4. 04SE ≈ √(p_o(1 − p_o) / (n(1 − p_e)²))
Limits — read before relying on it
  • Two raters only — use Krippendorff's alpha for more coders or missing data.
  • Kappa depends on category prevalence; very unbalanced codes can give low κ despite high agreement (the kappa paradox).
  • The standard error is the large-sample approximation.
Sources
  • Cohen, J. (1960). A coefficient of agreement for nominal scales. Educational and Psychological Measurement, 20(1), 37–46standard
  • Landis & Koch (1977). The measurement of observer agreement for categorical data. Biometrics, 33, 159–174standard

Worked example

computed by the same formula

10 items, two coders

Inputs
Rater A codes (one per item, in order)
yes, yes, no, no, yes, no, yes, yes, no, yes
Rater B codes (same items, same order)
yes, no, no, no, yes, no, yes, yes, yes, yes
Result
Cohen's κ
0.583
Landis & Koch
Moderate
Observed agreement
80 %
Chance agreement
52 %
Approx. 95 % CI
0.067 to 1.1
Items
10
  1. 1. Categories(no, yes) = 2

Questions

How is the cohen's kappa calculator calculated?

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Cohen's kappa (1960). p_o = share of items both raters coded the same · p_e = Σ_c p_A(c) · p_B(c) · κ = (p_o − p_e) / (1 − p_e) · SE ≈ √(p_o(1 − p_o) / (n(1 − p_e)²))

Example: 10 items, two coders?

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Cohen's κ: 0.583; landis & koch: Moderate.

What does this calculator not cover?

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Two raters only — use Krippendorff's alpha for more coders or missing data. Kappa depends on category prevalence; very unbalanced codes can give low κ despite high agreement (the kappa paradox). The standard error is the large-sample approximation.

Where do the numbers come from?

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Sources: Cohen, J. (1960). A coefficient of agreement for nominal scales. Educational and Psychological Measurement, 20(1), 37–46; Landis & Koch (1977). The measurement of observer agreement for categorical data. Biometrics, 33, 159–174. The formula is versioned (cohen_1960 v1.0.0) and covered by automated tests.

Is my data stored?

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No. The calculation runs in your browser and nothing is sent unless you choose to save a shareable link.

Also searched ascohen's kappa calculator · inter rater reliability · intercoder agreement · kappa statistic · inter-coder reliability qualitative coding

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