Confidence Interval Calculator

This calculator builds a confidence interval for a population mean using the z-interval method and returns the lower and upper bounds, the margin of error and the standard error. A confidence interval gives you a range of plausible values for an unknown population mean based on a sample you have collected. Rather than reporting only the sample mean as a single estimate, the interval acknowledges that samples vary and provides the range within which the true mean is likely to fall at your chosen level of confidence. The confidence level you select (90%, 95% or 99% are the most common) determines the critical z-value used to compute the width of the interval. A 95% confidence level uses z = 1.96, meaning the interval stretches roughly two standard errors either side of the sample mean. The standard error is the population or sample standard deviation divided by the square root of the sample size, so larger samples produce narrower, more precise intervals. To use the calculator, enter your sample mean, the standard deviation, the sample size and the confidence level. You receive the lower bound, upper bound, margin of error and standard error instantly. This tool is suited to students learning inferential statistics, researchers reporting survey results, and analysts communicating uncertainty in their estimates. The z-interval is most appropriate when the sample size is large (typically above 30) or when the population standard deviation is known; for small samples with unknown SD, a t-interval is preferable.

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