When to use this calculator
Counts concentrate more tightly in relative terms as trial counts increase, although the absolute standard deviation can increase.
Explore the probability & distributions calculators for other questions in this topic. For a related calculation, use the Expected Monetary Value Calculator: Combine two mutually exclusive outcomes using a chosen probability.
PUTTING IT INTO PRACTICE
Binomial Standard Deviation: 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) | 100 |
| Success probability (%) | 50 |
| Result | 5 successes |
- Check the input labels and enter the example values above.
- Apply the relationship: Standard deviation = √(n × p × (1−p)).
- The result is 5 successes, rounded for display.
How to interpret your result
Applies to independent identical Bernoulli trials and measures variation in the 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 standard deviation calculator useful?
Counts concentrate more tightly in relative terms as trial counts increase, although the absolute standard deviation can increase.
How do I use the binomial standard deviation calculator?
Enter trials (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?
Standard deviation = √(n × p × (1−p)).
What should I check before using the result?
Applies to independent identical Bernoulli trials and measures variation in the 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.
Calculators Map editorial process · Updated · Methods and limitations