Confidence Interval Calculator
Mean ± margin of error from sample mean, s, n, and z. Click any i for detail.
Sample
Sample mean
i
Mean
x̄ — the sample average. |
|
|---|---|
Sample std. deviation s
i
s
Sample standard deviation (use σ if your course says so). |
|
Sample size n
i
n
Number of observations. |
|
z critical value
i
z
Common: 1.645 (90%), 1.96 (95%), 2.576 (99%). |
How to use this calculator
- Enter mean, s, and n.
- Pick z for your confidence level.
- Read the interval and margin of error.
- Use t critical values instead when your course requires a t-interval.
Results explained
For large samples or known σ, a z-interval for the mean is x̄ ± z·(s/√n). The term s/√n is the standard error. Smaller samples often replace z with a t critical value from n−1 degrees of freedom — this page leaves z in your hands so you can paste either.
Quick reference: z intervals
x̄ ± z · s / √n.
| Item | Detail |
|---|---|
| 90% | z ≈ 1.645 |
| 95% | z ≈ 1.96 |
| 99% | z ≈ 2.576 |
| SE | s / √n |
Not a substitute for checking normality / sampling design assumptions.
How the estimate is built
CI = mean ± z × (s / √n).
Example scenario
mean 100, s 15, n 36, z 1.96 → SE 2.5 → interval about 95.1 to 104.9.
FAQ
Should I use t instead of z?
Many intro stats courses switch to t when σ is unknown and n is small. Enter the t critical value in the z box if you want.
Is this for a proportion?
No. Proportions use √(p̂(1−p̂)/n). This page is for a mean.
What does 95% confidence mean?
In repeated sampling, about 95% of such intervals would cover the true mean — not a 95% probability for one fixed interval in Bayesian language.
Can s be zero?
Then the interval collapses to a point at the mean (unusual in real data).