Binomial Distribution Calculator
Probability of k successes in n trials.
Enter your values
ⓘ Live results
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.
Worked example
Using the values the calculator loads with:
Inputs
- Number of trials20
- Successes8
- Probability of success0.35
Results
- P(X = k)0.161351
- P(X ≤ k)0.762378
- P(X ≥ k)0.398973
- Mean7
- Standard deviation2.1331
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.
About this calculator
- Built and reviewed by James Whitfield · How we build and test calculators
- Report an error
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.