Fleiss' Kappa Calculator
Measure inter-rater reliability when more than two raters assign items to categorical labels.
Enter counts for each item by category. Every row must sum to n (raters per item).
What is Fleiss' kappa?
Fleiss' kappa is a statistical measure of agreement for categorical ratings when you have multiple raters. It answers a practical question: how much agreement are we seeing beyond what we would expect by chance?
If three, five, or ten people are labeling data (for example: spam vs. not spam, disease class A/B/C, positive/neutral/negative sentiment), raw agreement can be misleading. Some agreement always occurs randomly. Fleiss' kappa adjusts for this and gives you a normalized score.
When to use this calculator
- You have a fixed number of raters per item.
- Ratings are categorical (nominal categories, not continuous scores).
- You want one reliability summary for the full annotation set.
- You have more than two raters (for two raters, Cohen's kappa is commonly used).
How to use the Fleiss kappa calculator
Step 1: Set your design
Enter:
- N = number of items/subjects rated
- n = number of ratings per item
- k = number of categories
Step 2: Enter your count matrix
After generating the table, each row represents one item. In that row, enter how many raters selected each category. Example with n = 5 could be 2, 3, 0 for a 3-category system.
Important: every row must sum to n. The calculator highlights any row where this is violated.
Step 3: Compute and interpret
Click Calculate Fleiss' Kappa. The tool returns:
- Observed agreement (P̄)
- Expected chance agreement (Pe)
- Fleiss' kappa (κ)
- A quick interpretation label
Formula used
The calculator applies the standard Fleiss' kappa equations:
- For each item i: Pi = ( Σ nij2 − n ) / ( n(n − 1) )
- Category proportion: pj = (1 / (Nn)) Σ nij
- Mean observed agreement: P̄ = (1/N) Σ Pi
- Expected agreement: Pe = Σ pj2
- Kappa: κ = (P̄ − Pe) / (1 − Pe)
Interpretation guide (common heuristic)
- < 0.00: Poor agreement
- 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
Use these labels cautiously. Context matters: category imbalance, task difficulty, rater training, and prevalence effects can all influence kappa.
Practical tips for better inter-rater reliability
1) Improve label definitions
Ambiguous categories are one of the biggest causes of disagreement. Build a concise rubric with clear boundary cases and examples.
2) Run pilot rounds
Before full-scale annotation, test a small batch, review disagreements, and refine your instructions.
3) Monitor category prevalence
If one category dominates, kappa may appear lower than expected despite high raw agreement. Review both kappa and confusion patterns.
4) Pair metrics
For a complete reliability report, consider including raw percent agreement and per-category performance summaries along with Fleiss' kappa.
FAQ
Can Fleiss' kappa be negative?
Yes. Negative values suggest agreement is worse than chance expectation.
Do all items need the same number of raters?
Classical Fleiss' kappa assumes a fixed number of ratings per item. This calculator enforces that condition.
Is Fleiss' kappa for ordinal categories?
Fleiss' kappa treats categories as nominal (no ordering). For ordered ratings, weighted approaches are often more appropriate.