Enter the observation counts for two raters evaluating two categories (2×2 Matrix).
Rater 2: Yes
Rater 2: No
Rater 1: Yes
Rater 1: No
Results
Total Observations (N):–
Observed Agreement (Po):–
Expected Agreement (Pe):–
Cohen's Kappa (κ):–
Agreement Level: –
function calculateKappa() {
// 1. Get input values
var a = parseFloat(document.getElementById('cell_a').value);
var b = parseFloat(document.getElementById('cell_b').value);
var c = parseFloat(document.getElementById('cell_c').value);
var d = parseFloat(document.getElementById('cell_d').value);
// 2. Validate inputs
if (isNaN(a) || isNaN(b) || isNaN(c) || isNaN(d)) {
alert("Please enter valid numbers for all four fields.");
return;
}
if (a < 0 || b < 0 || c < 0 || d = 1) {
kappa = 0; // Mathematically undefined or irrelevant in this context, treated as 0 for chance
} else {
kappa = (observedAgreement – expectedAgreement) / (1 – expectedAgreement);
}
// 7. Determine Interpretation
var interpText = "";
var k = kappa; // alias
if (k < 0) {
interpText = "No Agreement (Less than chance)";
} else if (k <= 0.20) {
interpText = "Slight Agreement";
} else if (k <= 0.40) {
interpText = "Fair Agreement";
} else if (k <= 0.60) {
interpText = "Moderate Agreement";
} else if (k <= 0.80) {
interpText = "Substantial Agreement";
} else if (k 0.6) {
interpBox.style.backgroundColor = "#d4edda";
interpBox.style.color = "#155724";
} else if (kappa > 0.2) {
interpBox.style.backgroundColor = "#fff3cd";
interpBox.style.color = "#856404";
} else {
interpBox.style.backgroundColor = "#f8d7da";
interpBox.style.color = "#721c24";
}
document.getElementById('resultArea').style.display = "block";
}
How to Calculate Kappa Inter-Rater Reliability
When conducting research that involves subjective assessment—such as medical diagnoses, coding qualitative data, or grading student essays—it is crucial to demonstrate that the data collection method is reliable. Cohen's Kappa (κ) is the standard statistical metric used to measure inter-rater reliability (agreement) for categorical items. Unlike simple percent agreement calculation, Cohen's Kappa is robust because it takes into account the agreement that could happen purely by chance.
Understanding the 2×2 Contingency Table
To calculate Kappa, data is usually arranged in a 2×2 matrix (contingency table) representing the classifications made by two independent raters. The input fields in the calculator above correspond to these four quadrants:
Both Agree Yes (a): Number of items where both Rater 1 and Rater 2 said "Yes" (or Category A).
R1 Yes / R2 No (b): Cases where Rater 1 said "Yes" but Rater 2 said "No".
R1 No / R2 Yes (c): Cases where Rater 1 said "No" but Rater 2 said "Yes".
Both Agree No (d): Number of items where both raters agreed on "No" (or Category B).
The Cohen's Kappa Formula
The statistic is calculated using the observed agreement ($P_o$) and the expected agreement by chance ($P_e$).
κ = ( P_o – P_e ) / ( 1 – P_e )
Where:
$P_o$ (Observed Agreement): The proportion of times the raters actually agreed. Formula: $(a + d) / Total$
$P_e$ (Expected Agreement): The proportion of agreement expected by random chance based on the raters' individual tendencies.
Interpreting the Kappa Score
The value of Kappa ranges from -1 to +1. While +1 implies perfect agreement and 0 implies agreement equivalent to chance, negative values indicate agreement less than chance (systematic disagreement). The table below outlines the standard interpretation guidelines proposed by Landis and Koch (1977):
Kappa Value (κ)
Strength of Agreement
< 0.00
Poor (Less than chance)
0.00 – 0.20
Slight Agreement
0.21 – 0.40
Fair Agreement
0.41 – 0.60
Moderate Agreement
0.61 – 0.80
Substantial Agreement
0.81 – 1.00
Almost Perfect Agreement
Why use Cohen's Kappa instead of Percent Agreement?
Percent agreement is calculated simply as $(a + d) / Total$. While easy to understand, it can be misleading.
Example: Imagine a rare disease that only 5% of patients have. If two doctors effectively just guess "No Disease" for every single patient, they will have a 95% agreement rate. However, they aren't actually demonstrating diagnostic skill—they are just relying on the base rate probability. Cohen's Kappa penalizes this "chance" agreement, likely resulting in a Kappa near 0 for the doctors in this example, which correctly identifies the lack of true diagnostic reliability.