Confidence Interval for Mean Calculator
Estimate a normal-approximation confidence interval around a sample mean using a supplied standard deviation, sample size and critical z value.
How to use this calculator
- Enter the mean, spread, sample size and critical z value. A 1.96 value is commonly used for an approximate 95% two-sided normal interval.
- Check the labels and units before using a result outside this page.
- Change one input at a time if you want to compare scenarios.
Formula and method
SE = s ÷ √n; interval = mean ± z × SE
- SE = s ÷ √n; interval = mean ± z × SE
- Small samples with unknown population standard deviation usually require a t critical value, not z; the interval also depends on sample design.
Worked examples
Worked example
Mean 52, standard deviation 8, n = 64, z = 1.96.
SE = 8/8 = 1; interval = 52 ± 1.96, or 50.04 to 53.96.
SE = 8/8 = 1; interval = 52 ± 1.96, or 50.04 to 53.96.
Understanding the result
Estimate a normal-approximation confidence interval around a sample mean using a supplied standard deviation, sample size and critical z value.
Small samples with unknown population standard deviation usually require a t critical value, not z; the interval also depends on sample design.
Important notes
Small samples with unknown population standard deviation usually require a t critical value, not z; the interval also depends on sample design.
Displayed outputs are rounded for readability; preserve full precision when continuing a calculation.
Frequently asked questions
What does this confidence interval mean calculator show?
Estimate a normal-approximation confidence interval around a sample mean using a supplied standard deviation, sample size and critical z value.
Which inputs should I check first?
Enter the mean, spread, sample size and critical z value. A 1.96 value is commonly used for an approximate 95% two-sided normal interval.
Can the result be used as a final professional specification?
Small samples with unknown population standard deviation usually require a t critical value, not z; the interval also depends on sample design.
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Related explanations
Learn the method behind the number or compare the terminology before using the calculator.
- How to Calculate a Z-Score — Learn how a z-score shows how far a value is from the mean in standard-deviation units.
- How to Calculate Days Between Dates — Learn how date intervals work, including leap years and inclusive vs exclusive day counting.
- Basal Metabolic Rate (BMR) — Learn what basal metabolic rate means and how BMR estimates are used in calorie planning.
This page provides a calculation tool plus explanatory information so you can understand what the result means and when the underlying method may not fit your situation.