Geometric Distribution Calculator
This calculator gives the probability that the first success occurs on a selected trial of independent repeated attempts with a fixed success chance.
How to use this calculator
- Enter a success probability between 0 and 1 and the positive trial number.
- Confirm that all inputs use the stated units and the same population, period or scope.
- Change one assumption at a time when comparing scenarios.
Formula used by the geometric distribution calculator
P(X=k)=(1−p)^(k−1)p
- P(X=k)=(1−p)^(k−1)p
- The success probability must remain constant and trials must be independent.
- Inputs are validated against required ranges and outputs are rounded for readability.
Worked examples
Worked example
A 25% chance of success on each independent trial and first success on trial 3.
The probability is 0.75²×0.25 = 14.0625%.
The probability is 0.75²×0.25 = 14.0625%.
Understanding the result
This calculator gives the probability that the first success occurs on a selected trial of independent repeated attempts with a fixed success chance.
The success probability must remain constant and trials must be independent.
Important notes
The success probability must remain constant and trials must be independent.
Use the result as a calculation aid for the inputs supplied; confirm critical specifications independently.
Frequently asked questions
Does k count failures?
No. Here k is the trial number on which the first success occurs.
What is the expected trial number?
For constant success probability p, the mean waiting trial is 1/p.
How do I use this calculator?
Enter a success probability between 0 and 1 and the positive trial number.
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Related explanations
Learn the method behind the number or compare the terminology before using the calculator.
- How to Calculate Probability — Learn basic probability formulas, complementary probability, and how to calculate simple event chances.
- Probability — Understand probability as a measure of how likely an event is and review simple probability formulas.
This page provides a calculation tool plus explanatory information so you can understand what the result means and when the underlying method may not fit your situation.