Confidence Interval Calculator

A confidence interval is a range of plausible values for an unknown population value, such as a mean or a proportion, built from a sample. A 95% confidence level means that if you repeated the sampling many times, about 95% of the intervals you built this way would contain the true value.

The margin of error is the critical value times the standard error. For a mean the standard error is the standard deviation divided by the square root of the sample size. For a proportion it is the square root of p-hat times one minus p-hat, divided by the sample size. The interval is the estimate plus and minus that margin.

Use Student's t for a mean when the population standard deviation is unknown and you estimate it from a small sample. The t critical value is larger than the matching z value, which widens the interval to account for the extra uncertainty. As the sample grows, t converges to z, so the choice matters most for small samples.

For z intervals it uses the standard values: 1.645 for 90%, 1.96 for 95%, and 2.576 for 99%, with an inverse-normal approximation for other levels. For t intervals it uses a table of common degrees of freedom and falls back to z for very large samples.

Higher confidence requires a larger critical value, so the margin of error grows and the interval gets wider. There is a trade-off: a wider interval is more likely to contain the true value but is less precise.

No. The calculation runs entirely in your browser, so your numbers never leave your device.