When to use this calculator
Estimate the standard error of a sample mean. Assumes independent observations from an appropriate sampling process.
Explore the sampling uncertainty calculators for other questions in this topic. For a related calculation, use the Z Test P Value Calculator: Find an approximate normal-model p-value from a supplied z statistic and a chosen tail.
PUTTING IT INTO PRACTICE
Standard Error: 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 |
|---|---|
| Sample standard deviation | 12 |
| Sample size (integer) | 36 |
| Result | 2 |
- Check the input labels and enter the example values above.
- Apply the relationship: Standard error = sample standard deviation ÷ √n.
- The result is 2 , rounded for display.
How to interpret your result
Assumes independent observations from an appropriate sampling process.
Use a critical value and model appropriate to the study. Simple random-sampling approximations do not correct for selection bias or clustered observations. Normal approximations can be poor for small samples or extreme proportions.
Frequently asked questions
Does a larger sample remove selection bias?
No. More observations can reduce sampling variability without repairing a systematically biased selection process.
How do I use the standard error calculator?
Enter sample standard deviation, sample size (integer). The result updates automatically. Use the units shown beside each input; the example values illustrate the method.
Which formula does this calculator use?
Standard error = sample standard deviation ÷ √n.
What should I check before using the result?
Assumes independent observations from an appropriate sampling process.
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/SEMATECH statistical methods handbook ↗. This is a topic reference, not an external review or endorsement of this tool.
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