Confidence Interval for a Mean Calculator

This confidence interval calculator works out a range that is likely to contain the true population mean, based on your sample data. You enter the sample mean, the standard deviation, the sample size and the confidence level you want, and the tool returns the lower and upper bounds of the interval along with the margin of error built into it. The method uses the standard normal multiplier, so a 95 percent level uses a z value of about 1.96, a 90 percent level uses 1.645 and a 99 percent level uses 2.576. The interval is the mean plus or minus that multiplier times the standard error, where the standard error is the standard deviation divided by the square root of the sample size. Researchers, students, quality analysts and survey teams use confidence intervals to express how precise an estimate is, rather than relying on a single point figure that hides the uncertainty. A wider interval means less precision, while a narrower interval means more. Three tips help you read the result well. First, larger samples shrink the interval because the square root of the sample size sits in the denominator, so collecting more data tightens your estimate. Second, a higher confidence level widens the interval, because you are asking for more certainty that the true mean is captured. Third, this normal based method suits reasonably large samples, so for very small samples a t distribution interval is more accurate. Always report the confidence level alongside the bounds so readers know exactly what the range means and can compare it fairly with other studies.

CI = mean +/- z * sd / sqrt(n). Estimate only, not financial or tax advice.