The Geometric Distribution Calculator determines the probability of achieving the first success on a specific trial (x) when each trial has a constant probability of success (p). It uses the formula P(X=x)=(1−p)x−1pP(X = x) = (1 – p)^{x – 1} pP(X=x)=(1−p)x−1p and also provides the mean 1/p1/p1/p and variance (1−p)/p2(1 – p)/p^2(1−p)/p2. This calculator is helpful for modeling independent trials, such as quality control testing, game outcomes, or reliability scenarios where each attempt has the same success rate.