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Calculators / Math / Confidence interval for a mean
Confidence interval for a mean calculator
Calculate a z-based confidence interval from a mean, standard deviation and sample size.
On this page
Margin of error1.96
Lower bound48.04
Upper bound51.96
Calculator controls
How to calculate
Calculate a z-based confidence interval from a mean, standard deviation and sample size.
Margin of error = z*sd/sqrt(size); Lower bound = mean-z*sd/sqrt(size); Upper bound = mean+z*sd/sqrt(size)
Worked example
Sample mean: 50; Standard deviation: 10; Sample size: 100; Z critical value: 1.96.
Margin of error: 1.96 ; Lower bound: 48.04 ; Upper bound: 51.96 .
Assumptions and limits
This z interval assumes independent observations and an appropriate normal/large-sample model. Unknown population variation may require a t interval.
Results are rounded for display; calculations use unrounded values. Read our calculation methodology.
Understanding the result
Calculate a z-based confidence interval from a mean, standard deviation and sample size. The displayed figures use the inputs and formula shown on this page.
When this tool is useful
Use the confidence interval for a mean to compare a scenario, check an estimate, or verify a manual calculation.
Understanding your inputs
| Input | What to enter |
|---|---|
| Sample mean | Enter a number of at least -1000000000000 and no more than 1000000000000. |
| Standard deviation | Enter a number of at least 0.000001 and no more than 1000000000000. |
| Sample size | Enter a number of at least 1 and no more than 1000000000. |
| Z critical value | Enter a number of at least 0.000001 and no more than 1000000000000. |
Frequently asked questions
What should I check before using the confidence interval for a mean result?
This z interval assumes independent observations and an appropriate normal/large-sample model. Unknown population variation may require a t interval.
Is this confidence interval for a mean result exact?
It is exact for the stated mathematical model and entered values. Real-world results can differ when rates, timing, fees, definitions or measurement conditions differ.