Binomial Calculator · Probability & Coefficient Tool 2026
Calculate binomial probabilities: probability of exactly k successes, cumulative probability (≤k), and binomial coefficient. Ideal for statistics, quality control, and academic research.
Binomial Coefficient C(n,k): --
P(X = k): --
P(X ≤ k): --
Mean (μ): --
Variance (σ²): --
Standard deviation (σ): --
How it works: Enter n (trials), p (probability), and k (successes). The tool computes binomial coefficient, exact probability P(X=k), cumulative P(X≤k), mean, variance, and standard deviation.
🎯 Why Use a Binomial Calculator?
The binomial distribution models the number of successes in a fixed number of independent trials. It's used in quality control (defect rates), A/B testing, medicine (treatment effectiveness), and gambling. Our calculator computes the exact probability, cumulative probability, and key statistics. It's essential for students, researchers, and data analysts.
📘 How to Use
- Enter number of trials (n).
- Enter success probability (p) between 0 and 1.
- Enter number of successes (k) between 0 and n.
- Click "Calculate" to get results.
✨ Features
⚙️ Formula
C(n,k) = n! / (k!(n-k)!). P(X=k) = C(n,k) * p^k * (1-p)^(n-k). Cumulative sum from 0 to k. Mean = np, variance = np(1-p).
❓ FAQ
1. What if k > n?
Probability is zero. The tool will handle it.
2. Can p be 0 or 1?
Yes, but results are trivial.
3. Is factorial computation safe for large n?
Using logarithms or iterative multiplication; we limit n to 1000 for performance.