Statistics Calculators

Geometric Distribution Calculator

Calculate the probability that the first success occurs on a specific trial, given a constant probability of success per trial.

P(first success on trial k) —

P(first success on or before trial k) —

Mean (expected trials to first success) —

Standard deviation —

About the Geometric Distribution Calculator

The geometric distribution models the number of independent trials needed to get the first success, when each trial has the same probability of success — like the number of coin flips until the first heads.

Formula: P(X = k) = (1 − p)ᵈ⁻¹ × p · Mean = 1 ÷ p · Variance = (1 − p) ÷ p²

Unlike the binomial distribution, which counts successes in a fixed number of trials, the geometric distribution counts the trials themselves, stopping at the first success. It's widely used to model waiting times in discrete, repeated attempts.