Confidence Interval Calculator
Compute confidence intervals for a sample mean.
95% confidence interval
48.432 to 51.568
Margin of error
± 1.568
Standard error
0.8
Uses the z-interval; for very small samples (n < 30) the t-distribution widens the interval slightly.
What the interval means
A 95% CI is built so that if you repeated the sampling many times, 95% of the intervals would contain the true mean. The margin of error shrinks with the square root of n — quadrupling the sample halves the interval, which is why precision gets expensive.
Reading polls and studies
'52% ± 3' is a confidence interval: the true value plausibly sits anywhere from 49 to 55, so a 52–48 lead may be no lead at all. Overlapping intervals between groups usually mean the difference isn't statistically established.
Frequently asked questions
- How does the Confidence Interval Calculator work?
- Compute confidence intervals for a sample mean.
- Is the Confidence Interval Calculator free to use?
- Yes. The Confidence Interval Calculator is completely free, runs entirely in your browser, and requires no account or sign-up. Your inputs never leave your device.
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