When two individuals or systems are tasked with evaluating the same data—like marking exams or diagnosing medical cases—Cohen’s Kappa becomes essential. It measures inter-rater agreement, adjusting for agreement that may occur by chance.
Cohen’s Kappa Calculator
🎯 What Is Cohen’s Kappa?
Cohen's Kappa (κ) is a statistical coefficient that assesses the agreement between two raters beyond chance. It’s especially useful when analyzing categorical data (e.g., Yes/No, True/False).
The value of κ ranges from -1 to 1:
κ = 1: Perfect agreementκ = 0: Agreement by chanceκ < 0: Less than chance agreement
🔍 How to Use the Cohen’s Kappa Calculator
- Input the following values:
- Number of times both raters said "Yes"
- Number of times Rater 1 said "Yes", Rater 2 said "No"
- Number of times Rater 1 said "No", Rater 2 said "Yes"
- Number of times both said "No"
- Click “Calculate”
The tool displays:- Observed Agreement (Po)
- Expected Agreement (Pe)
- Cohen’s Kappa (κ)
- Level of agreement (e.g., Moderate, Substantial)
- Click “Reset” to enter new values.
📊 Example Calculation
Suppose you observe the following outcomes:
| Rater 2: Yes | Rater 2: No | |
|---|---|---|
| Rater 1: Yes | 30 | 10 |
| Rater 1: No | 5 | 55 |
Total observations = 30 + 10 + 5 + 55 = 100
Observed agreement (Po) = (30 + 55) / 100 = 0.85
Expected agreement (Pe) = [(30+10)/100 × (30+5)/100] + [(5+55)/100 × (10+55)/100]
= (0.4×0.35) + (0.6×0.65) = 0.14 + 0.39 = 0.53
Cohen’s Kappa (κ) = (0.85 - 0.53) / (1 - 0.53) = 0.68
Interpretation: Substantial agreement
💡 Benefits of Using This Tool
- 🧠 Accurate and Fast: Calculates in real-time
- 🧾 Simple Interface: Clean design for ease of use
- 🎓 Educational: Ideal for students, researchers, and data analysts
- 📱 Responsive: Works well on mobile and desktop
📘 Formula Behind the Calculator
- Observed Agreement (Po) = (a + d) / N
- Expected Agreement (Pe) = [(a + b)/N × (a + c)/N] + [(c + d)/N × (b + d)/N]
- Cohen’s Kappa (κ) = (Po - Pe) / (1 - Pe)
Where:
- a = both raters agree on “Yes”
- b = Rater 1 says “Yes”, Rater 2 says “No”
- c = Rater 1 says “No”, Rater 2 says “Yes”
- d = both raters agree on “No”
- N = total observations
📊 Kappa Interpretation Scale (Landis & Koch)
| Kappa Value | Interpretation |
|---|---|
| < 0 | Poor (Less than chance) |
| 0.01–0.20 | 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 |
❓ 20 Frequently Asked Questions (FAQs)
1. What is Cohen's Kappa used for?
To measure inter-rater agreement for categorical variables beyond chance.
2. What does a Kappa of 1 mean?
Perfect agreement between raters.
3. Is a Kappa of 0 good?
No, it means agreement is due to chance.
4. What if Kappa is negative?
It suggests less agreement than expected by chance.
5. Can this calculator handle more than two raters?
No, it is designed for exactly two raters.
6. What does Po stand for?
Po = Observed Agreement.
7. What does Pe stand for?
Pe = Expected Agreement by chance.
8. Is Cohen’s Kappa affected by prevalence?
Yes, low prevalence can distort kappa.
9. What fields use Cohen’s Kappa?
Psychology, medicine, education, content moderation, etc.
10. How accurate is Cohen’s Kappa?
It's reliable but can be influenced by marginal totals and prevalence.
11. How do I interpret 0.55 Kappa?
Moderate agreement.
12. Is there a better alternative to Cohen’s Kappa?
Other methods like Fleiss' Kappa exist for >2 raters.
13. Can I use decimals in input?
No, this calculator expects whole number counts.
14. Can I embed this calculator on my site?
Yes, if you have access to the code.
15. Can I use this for medical diagnosis agreement?
Absolutely—it’s widely used in diagnostic reliability studies.
16. What if I enter zero for all values?
You’ll get an error prompt—there must be at least one non-zero.
17. Is this tool free?
Yes, it is completely free to use.
18. Can this calculate weighted Kappa?
No, it calculates only unweighted Cohen’s Kappa.
19. How many total observations should I enter?
The sum of all four categories (Yes-Yes, Yes-No, No-Yes, No-No).
20. Is Cohen’s Kappa better than percentage agreement?
Yes, because it accounts for agreement by chance.
📌 Conclusion
Cohen’s Kappa Calculator is a quick, easy, and effective tool for anyone analyzing the consistency between two raters. Whether you’re a researcher or a student, this calculator helps you measure agreement with statistical confidence and interpretability.