When to use this calculator
This returns the margin only. Subtract and add it to the sample mean for the corresponding symmetric interval.
Explore the sampling uncertainty calculators for other questions in this topic. For a related calculation, use the Normal Mean Confidence Interval Calculator: Find a symmetric normal-model interval from a mean, known population deviation and chosen critical value.
PUTTING IT INTO PRACTICE
Normal Confidence Interval Margin: 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 |
|---|---|
| Chosen z critical value | 1.96 |
| Known population standard deviation | 10 |
| Sample size (integer) | 100 |
| Result | 1.96 input measurement units |
- Check the input labels and enter the example values above.
- Apply the relationship: Margin = z × standard deviation/√n.
- The result is 1.96 input measurement units, rounded for display.
How to interpret your result
Requires an appropriate normal-model interval with known population deviation; not a t interval.
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.
When is the normal confidence interval margin calculator useful?
This returns the margin only. Subtract and add it to the sample mean for the corresponding symmetric interval.
How do I use the normal confidence interval margin calculator?
Enter chosen z critical value, known population 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?
Margin = z × standard deviation/√n.
What should I check before using the result?
Requires an appropriate normal-model interval with known population deviation; not a t interval.
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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