Confidence Interval Calculator
Build a normal (z) confidence interval for a mean from sample mean, SD, sample size, and a common confidence level. Educational large-n form, not a Student-t table product.
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How to build a mean confidence interval
- Enter the sample mean you already computed from your data.
- Enter standard deviation s (0 or greater) and sample size n as an integer of at least 2.
- Choose a confidence percent: 80, 90, 95, 98, or 99. The page maps that choice to a fixed normal z.
- Read lower and upper bounds, margin of error, standard error, and the z that was used. Nothing is uploaded.
Normal mean confidence interval
x̄ ± z × (s / √n) for common levels
| Formula | x̄ ± z × (s / √n) |
|---|---|
| Levels | 80, 90, 95, 98, 99 with fixed normal z |
| Outputs | Lower bound, upper bound, margin of error, SE, z |
| Defaults | mean = 100, s = 15, n = 25, level = 95 |
| Approximation | Large-n normal / z interval |
| Not included | Student-t critical values or proportion Wilson intervals |
What this confidence interval page computes
A confidence interval for a mean states a range around the sample mean using a critical z and the standard error s / √n. This page supports five common percents and returns both endpoints plus the margin of error. It is a classroom normal approximation. It is not a bootstrap interval, not a Bayesian credible interval, and not a t-table product for small n.
How bounds and margin are formed
SE = s / √n. Margin of error = z × SE. Bounds are mean minus margin and mean plus margin. Built-in z values include about 1.282 for 80%, 1.645 for 90%, 1.960 for 95%, 2.326 for 98%, and 2.576 for 99%. With defaults mean = 100, s = 15, n = 25, and 95%, SE = 3 and the margin is about 5.88, so the interval runs near 94.12 to 105.88.
Margin of error, SE, and related calculators
Entities: sample mean, standard error, critical z, margin of error, and confidence level. The one-sample t statistic without an interval is on t-score. Standardizing a single observation is z-score. Planning how large n should be for a proportion Wald sketch is sample size. Averaging a typed list first is the mean calculator.
Use cases
Homework that already gives x-bar, s, and n and asks for a 95% z interval. Comparing how 90% versus 99% widens the margin for the same SE. Not a survey vendor deliverable and not a replacement for software that uses exact t quantiles when n is small.
How to read the percent
A 95% interval is a procedure that covers the true mean in 95% of repeated samples under the model assumptions. It is not the probability that this one realized interval contains the mean in a Bayesian sense. Raising the confidence percent raises |z| and widens the margin; raising n shrinks SE and tightens the interval.
Limits
Only the listed percents unless you somehow feed a custom z through the engine API. No proportion Wilson/Agresti form on this page. No finite population correction. Educational only. CZNull does not receive the numbers.