Cohen’s Kappa (κ) Inter-Rater Reliability & Chance Agreement Calculator

Measure inter-annotator labeling reliability corrected for chance agreement.

Cohen’s Kappa Coefficient (κ)
0.82 κ
Observed Percent Agreement (P_o) 91 %
Chance Expected Agreement (P_e) 50.18 %
Total Annotated Items (N) 200 items
Inputs
items
Items rated Positive by both Rater 1 and Rater 2 (a).
items
Items rated Positive by Rater 1 and Negative by Rater 2 (b).
items
Items rated Negative by Rater 1 and Positive by Rater 2 (c).
items
Items rated Negative by both Rater 1 and Rater 2 (d).
Results & Graph
Cohen’s Kappa Coefficient (κ)
0.82 κ
Observed Percent Agreement (P_o)
91 %
Chance Expected Agreement (P_e)
50.18 %
Total Annotated Items (N)
200 items

Cohen’s Kappa Coefficient (κ)

Graph 1 • Both Positive A Sensitivity Recalculates the domain equation across 50% to 150% of the primary input while holding other parameters constant.
0 κ 0.5 κ 1.1 κ 50%: 0.74 κ 0.7 50% 75%: 0.79 κ 0.8 75% 100%: 0.82 κ 0.8 100% 125%: 0.84 κ 0.8 125% 150%: 0.85 κ 0.8 150%
Graph 2 • Primary & Supporting Metric Comparison Compares the primary output alongside supporting domain benchmarks.
Cohen’s Kappa Coefficient (κ) 0.82 κ Observed Percent Agreement (P_o) 91 % Chance Expected Agreement (P_e) 50.18 % Total Annotated Items (N) 200 items
Graph 3 • Exact Output Table & Units Displays each calculated output in its exact domain unit.
Cohen’s Kappa Coefficient (κ)0.82 κObserved Percent Agreement (P_o)91 %Chance Expected Agreement (P_e)50.18 %Total Annotated Items (N)200 items
Summary: Observed agreement is 91% vs. 50.18% expected by chance, yielding Cohen’s κ = 0.819 (Almost Perfect).
Summary: Observed agreement is 91% vs. 50.18% expected by chance, yielding Cohen’s κ = 0.819 (Almost Perfect).
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Formula & Mathematical Methodology: Cohen’s Kappa (κ) Systems Engineering Formula

Po = (a + d) / N
Pe = [(a+b)(a+c) + (c+d)(b+d)] / N²
κ = Po − Pe1 − Pe
P_o = (a + d) / N; P_e = [(a+b)(a+c) + (c+d)(b+d)] / N²; κ = (P_o − P_e) / (1 − P_e)
  • bothPositiveA: Both Positive A (items)
  • rater1PosRater2NegB: Rater1 Pos Rater2 Neg B (items)
  • rater1NegRater2PosC: Rater1 Neg Rater2 Pos C (items)
  • bothNegativeD: Both Negative D (items)

Rounding: Binary/decimal capacities and engineering metrics retain full floating-point precision and round to 2 decimal places.

Worked Example: Architecture Sizing Example: Cohen’s Kappa (κ)

Measure inter-annotator labeling reliability corrected for chance agreement.

  1. Enter the workload parameters, model dimensions, or network link specifications.
  2. Compute the sizing equation: P_o = (a + d) / N; P_e = [(a+b)(a+c) + (c+d)(b+d)] / N²; κ = (P_o − P_e) / (1 − P_e).
  3. Inspect the primary capacity metric, headroom buffers, and 3 SVG visualizations.
Result: Calculates Cohen’s Kappa (κ) via P_o = (a + d) / N; P_e = [(a+b)(a+c) + (c+d)(b+d)] / N²; κ = (P_o − P_e) / (1 − P_e).

Frequently Asked Questions

How does the Cohen’s Kappa (κ) Inter-Rater Reliability & Chance Agreement Calculator compute capacity?

It evaluates P_o = (a + d) / N; P_e = [(a+b)(a+c) + (c+d)(b+d)] / N²; κ = (P_o − P_e) / (1 − P_e) directly in your browser and plots three custom SVG diagrams.

Can I compare different cluster or model configurations side by side?

Yes. Use the "Compare (0/3)" button in the results panel to pin up to three configurations.

Does this tool upload any of my architecture parameters?

No. All calculations run 100% client-side in your browser.

Mathematics & Statistics · Machine Learning & Evaluation

Cohen’s Kappa (κ) Inter-Rater Reliability & Chance Agreement Calculator: inputs, method, and how to read the result

Measure inter-annotator labeling reliability corrected for chance agreement.

Choose inputs for the case you are checking

The defaults are illustrative. Replace them with values for your case and keep the units shown beside each field.

  • Both Positive A: Items rated Positive by both Rater 1 and Rater 2 (a).
  • Rater1 Pos Rater2 Neg B: Items rated Positive by Rater 1 and Negative by Rater 2 (b).
  • Rater1 Neg Rater2 Pos C: Items rated Negative by Rater 1 and Positive by Rater 2 (c).
  • Both Negative D: Items rated Negative by both Rater 1 and Rater 2 (d).

What the calculation includes

With the default values shown, Cohen’s Kappa Coefficient (κ) is 0.82 κ. The calculation follows Cohen’s Kappa (κ) Systems Engineering Formula; the formula and variable definitions above show how the inputs combine.

One-input check: With the other defaults held constant, changing Both Positive A from 85 items to 93.5 items changes Cohen’s Kappa Coefficient (κ) from 0.82 κ to 0.83 κ. This is a comparison inside the calculator's stated model, not a prediction.

Where to use caution

  • Uses industry-standard IEEE, IETF RFC, and GPU/cloud hardware sizing conventions.
  • Capacity planning estimate; benchmark under production traffic patterns before finalizing cluster or hardware procurement.

Scope: IEEE / IETF / Cloud Systems Engineering Standard Check the assumptions and limitations against your situation before relying on the estimate.

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