Geometric distribution calculator
The model counts independent trials until the first success, so X starts at 1.
Probabilities around the selected k
| k | P(X = k) | P(X ≤ k) | P(X ≥ k) |
|---|---|---|---|
| Fill in the fields above — the result is computed on this page. | |||
How do I use this page?
- Choose a probability calculation or quantile.
- Enter p and k or quantile level q.
- Compare the result with the mean and nearby k values.
What this page does not do: The model requires constant p and independent trials. Do not use it when probability changes over time or when sampling without replacement from a small population.
Further reading
Theory — what is the geometric distribution?
The geometric distribution describes the trial number on which the first success occurs, assuming each trial has the same probability p and trials are independent. In this convention X takes values 1, 2, 3, and so on, counting all trials including the one that succeeds. This distribution has the memoryless property: no success in earlier trials does not change the probability of success later on. Here X is the total number of trials until the first success, so the smallest possible value is 1.
Frequently asked questions
Does X count failures or all trials?
Does success become more likely after many failures?
See also
A/B test calculator
Compare two proportions in an A/B test. Calculate conversion rates, difference, uplift, z score, p value and c
A/B test planning — sample size, MDE and duration
Plan a two-proportion experiment, estimate detectable effect and traffic duration.
ACF and PACF autocorrelation calculator
Calculate ACF and PACF across time-series lags. Review the chart, reference bounds and coefficient table.