Statistics & probability
Binomial probability calculator
Find exact and cumulative success probabilities for independent trials.
A clear answer. Here’s how.
Models independent trials with a constant success probability. Shows P(X=k), P(X≤k), P(X>k) and P(X≥k), plus the model mean and standard deviation. Supports 0–10,000 trials, including p=0 or p=1. Uses numerical beta functions and log probabilities; extremely small values can underflow to zero.
See a worked example
Worked example
A fixed demonstration, separate from the values you enter above.
- Number of trials
- 10
- Success probability per trial (0–1)
- 0.5
- Success count k
- 5
Example result
- P(X = k)
- 0.24609375
- P(X ≤ k)
- 0.623046875
- P(X > k)
- 0.376953125
- P(X ≥ k)
- 0.623046875
- Model mean
- 5
- Model standard deviation
- 1.58113883008