How to use the Geometric Distribution Calculator
The geometric distribution describes how many tries it takes to get the first success when every try carries the same probability. Enter the per-try success probability p and the try number k you are curious about, and the tool shows the chance that the first success lands exactly on try k, P(X=k)=(1-p)^(k-1)·p, the chance of at least one success within k tries, P(X≤k)=1-(1-p)^k, and the chance that all k tries fail, (1-p)^k.
The expected number of tries is 1/p, and the median is the ceiling of ln0.5 / ln(1-p). The median answers "half of all attempts succeed within this many tries", so it is normally smaller than the expected number. Probabilities are shown as percentages with up to six decimal places. Every figure assumes independent tries with a probability that never shifts, so rate-up mechanics, pity counters and guaranteed-after-N rules are not modelled here.
This page covers the first success only. It does not cover how many tries it takes to reach r successes (the negative binomial distribution), and it does not report variance or standard deviation. If the probability you typed is not a published figure, the output is only as trustworthy as that input, so treat it as a reference. Current as of October 2026.
Frequently asked questions
No. 1/p is the long-run average over very many repeats of the same setup, not a promise about one run. The chance of still having no success after that many tries is not zero.
Yes. The geometric distribution has a long right tail, so its median sits below its mean. At a 25% success probability the expected number of tries is 4 and the median is 3.
With a success probability of 0 the first success never arrives, so the expected number of tries is infinite. The tool therefore accepts only values above 0%.