Confidence Interval Calculator
Enter a sample mean, standard deviation, and sample size to calculate a confidence interval.
Last updated: September 5, 2026
Frequently asked questions
What does a 95% confidence interval mean?
If you repeated the sampling process many times and built a confidence interval each time, about 95% of those intervals would contain the true population mean - it's a statement about the reliability of the method, not a 95% probability that this specific interval contains the true value.
How do I calculate a confidence interval?
Margin of error = z-score × (standard deviation ÷ √sample size). Then add and subtract that margin from your sample mean to get the interval's lower and upper bounds. The z-score depends on your chosen confidence level (1.96 for 95%, for example).
Why does a larger sample size produce a narrower confidence interval?
The margin of error divides by the square root of the sample size, so larger samples shrink the margin - more data means less uncertainty about where the true population mean lies, narrowing the interval around your estimate.
Should I use a z-score or t-score for my confidence interval?
Use a t-score (from the t-distribution) for smaller samples, typically under 30, since it accounts for extra uncertainty in a small-sample standard deviation estimate. This calculator uses the z-distribution, which is a reasonable approximation once your sample size is 30 or more.
How do I calculate a 99% confidence interval instead of 95%?
Select 99% as the confidence level, which uses a larger z-score (about 2.576 instead of 1.96) - the resulting interval will be wider than a 95% interval for the same data, since higher confidence requires a larger margin of error.
What's the confidence interval for a sample mean of 50, standard deviation of 10, and n=100 at 95% confidence?
Margin of error = 1.96 × (10/√100) = 1.96 × 1 = 1.96. The interval is 50 ± 1.96, or about 48.04 to 51.96.
Does a wider confidence interval mean the estimate is less accurate?
It means there's more uncertainty about the true population mean's exact location, often because of a smaller sample size, higher variability in the data, or a higher chosen confidence level - it's not that the sample mean itself is wrong, just that the range of plausible true values is broader.