Geometric Distribution Calculator
Calculate first-success trial probabilities, cumulative probability and waiting moments for independent Bernoulli trials.
YOUR CALCULATION
Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Count the successful trial itself, so the support begins at one rather than zero failures.
P(K=k)=(1−p)^(k−1)p; P(K≤k)=1−(1−p)^k; E[K]=1/p
Worked example
For p=0.2, first success on trial 3 has probability 0.128 and success within three trials has probability 0.488.
Assumptions and input details
Independent trials with unchanged p. Not a without-replacement model. Very small tail probabilities can round to zero; this calculator does not infer p from observations.
References: NIST: probability distributions
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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