Confidence Interval Calculator — How to Calculate a CI
Mean confidence interval from mean, SD, n, and 90/95/99% levels using z critical values. Example: mean 50, SD 10, n 100, 95% → about 48.04 to 51.96. One page for levels. Runs in your browser for learning.
How it works
Enter the sample mean, standard deviation, and sample size. Choose 90%, 95%, or 99% on this same page. The tool uses a z critical value, SE = SD/√n, and reports the interval with margin of error. Runs in your browser for coursework.
Formula and assumptions
SE = SD / √n; margin = z* × SE; CI = mean ± margin. Critical z used here:
- 90% → z* = 1.645; 95% → 1.96; 99% → 2.576 (common textbook values).
- Assumes a normal sampling model for the mean (known σ or large-n approximation), not a small-sample t interval.
- 90/95/99 stay as options on one URL — not separate calculator pages.
- A confidence level is a long-run coverage property of the method, not a probability that this one interval contains the true mean.
Example
Example: mean 50, SD 10, n 100, 95% → SE = 10/√100 = 1; margin = 1.96 × 1 = 1.96; CI ≈ 48.04 to 51.96.
When to use it
- Homework: build a mean CI with an explicit z critical value.
- Compare how 90%, 95%, and 99% widen the same data on one page.
- Pair with a standard-deviation or p-value page when reviewing sampling uncertainty.
Frequently asked questions
Which z values are used?
90% uses 1.645, 95% uses 1.96, and 99% uses 2.576 — common textbook z critical values.
Is this a t-interval?
No. This page uses a z-based interval for a normal/large-n mean sketch. Small-sample t intervals are not computed here.
Why keep 90/95/99 on one page?
They are confidence-level options for the same mean CI task. Separate URLs for each level are not needed.
Does 95% mean there is a 95% chance the true mean is inside this interval?
Not in that simple sense. The confidence level describes long-run coverage of the procedure under the stated model.
Related tools
Questions or feedback
Something unclear, broken, or missing? Draft a message below — we read every note about these tools.