When to use this calculator
The result is for exactly the chosen count, not that count or more.
Explore the probability & distributions calculators for other questions in this topic. For a related calculation, use the Binomial Standard Deviation Calculator: Find the standard deviation of the success count in a binomial model.
PUTTING IT INTO PRACTICE
Binomial Probability: a worked example
The values below are an illustrative example, not a recommendation. Replace them with measurements or assumptions that match your question.
| Input | Example value |
|---|---|
| Trials (integer) | 5 |
| Successes (integer) | 2 |
| Success probability (%) | 50 |
| Result | 31.25 % |
- Check the input labels and enter the example values above.
- Apply the relationship: P(X=k) = C(n,k) × p^k × (1−p)^(n−k).
- The result is 31.25 %, rounded for display.
How to interpret your result
Requires independent trials with a fixed success probability and a fixed trial count.
A distribution model is an assumption about the process, not a guarantee about outcomes. Independence, constant probability and fixed interval definitions matter. Exactly-k probabilities differ from cumulative probabilities.
Frequently asked questions
Does exactly two successes mean two or more?
No. Exactly two counts only outcomes with two successes. Two or more is a cumulative probability covering several counts.
When is the binomial probability calculator useful?
The result is for exactly the chosen count, not that count or more.
How do I use the binomial probability calculator?
Enter trials (integer), successes (integer), success probability (%). The result updates automatically. Use the units shown beside each input; the example values illustrate the method.
Which formula does this calculator use?
P(X=k) = C(n,k) × p^k × (1−p)^(n−k).
What should I check before using the result?
Requires independent trials with a fixed success probability and a fixed trial count.
How are results rounded?
Scalar numbers display up to six decimal places, with scientific notation for very large or small values. Text, fraction, date and schedule outputs use the format described on the tool. Intermediate calculations use JavaScript floating-point arithmetic. Keep sensible precision for your measurements.
Further reading
For background on this topic, see NIST: probability distributions ↗. This is a topic reference, not an external review or endorsement of this tool.
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