Online Tool Store
Binomial Distribution Calculator
Calculate the probability of an exact number of successes and cumulative results for n trials with success probability p.
🔒 This tool runs entirely in your browser. Your files are never uploaded to a server.
P(X = k)
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P(X ≤ k)
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P(X ≥ k)
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Distribution (P(X = i) for each i)
Mean (n·p): — · Std. dev.: —
How the Binomial Distribution Calculator works
- Enter the number of trials (n), the probability of success on each trial (p), and the number of successes you care about (k).
- The tool computes P(X=k) using the binomial probability mass function: C(n,k) × p^k × (1-p)^(n-k).
- It also sums the distribution to give cumulative probabilities P(X≤k) and P(X≥k), and charts the full distribution across every possible outcome.
FAQ
What does the binomial distribution model?
It models the number of successes in a fixed number of independent trials, each with the same success probability — like counting heads in 10 coin flips, or defective parts in a batch of 50.
What's the difference between P(X=k) and P(X≤k)?
P(X=k) is the probability of exactly k successes (the probability mass function). P(X≤k) is the cumulative probability of k or fewer successes, and P(X≥k) is the cumulative probability of k or more — useful for questions like "what's the chance of at least 3 defects."
Why does the tool use logarithms internally?
For large n, computing n! directly overflows standard floating-point numbers. Working in log-space (summing log-factorials, then exponentiating once at the end) keeps the calculation numerically stable up to n=200.
How we compare
| Feature | Online Tool Store | Statistics software (R, Python) | Textbook binomial table |
|---|---|---|---|
| Instant, no install | ✓ | ✗ | ✓ |
| Any n and p, not just fixed table entries | ✓ | ✓ | ✗ |
For very large n or specialized statistical work, a full statistics package still offers more precision and additional distribution tools.