Binomial distribution calculator
Calculate exactly k, at most k or at least k successes in n independent trials with a constant success probability p.
Your numbers stay in this browser. No account or upload to the server is needed.
How do I use this page?
- Enter the number of trials n from 1 to 1,000.
- Enter success probability p from 0 to 1 and the number of successes k.
- Compare the exact and cumulative probabilities, mean np and the chart.
Method and worked example
For X~Bin(n,p), the probability of exactly k successes is C(n,k)p^k(1−p)^(n−k).
The model requires constant p, independent trials and two outcomes per trial. When p changes between trials, an ordinary binomial model does not fit.
Cumulative probabilities sum the exact values over the relevant k values. The calculation uses logarithms for the binomial coefficient to reduce overflow.
Example: n=20, p=0.3 and k=6. The expected value is np=6; the tool also reports the chance of exactly, at most and at least 6 successes.