Binomial Distribution Calculator
Probability of k successes in n trials.
Enter your values
Results update instantly as you type — no submit needed.
Results
- P(X = k)
- 0.161351
- P(X ≤ k)
- 0.762378
- P(X ≥ k)
- 0.398973
- Mean
- 7
- Standard deviation
- 2.1331
Quick answer
The binomial distribution gives the chance of exactly k successes in n independent trials each with probability p.
P(X=k) = C(n,k) p^k (1−p)^(n−k)
How to use the Binomial Distribution Calculator
- 1Enter the number of independent trials.
- 2Enter the number of successes you are testing.
- 3Enter the success probability as a decimal.
Frequently asked questions
When is binomial appropriate?
Fixed trials, two outcomes, constant probability and independence.
What if n is huge?
Use the normal approximation when np and n(1−p) both exceed 5.