Confidence Interval Calculator

This confidence interval calculator builds a range that is likely to contain the true population mean, based on a sample. Whenever you measure an average from a sample rather than the whole population, the figure you get is an estimate, and a confidence interval is the honest way to express how precise that estimate is. A 95 percent confidence interval, the most common choice, means that if you repeated the sampling process many times, about 95 percent of the intervals built this way would contain the real mean. You enter the sample mean, the standard deviation and the sample size, and choose a confidence level of 90, 95 or 99 percent, and the calculator returns the interval along with the margin of error and the standard error. The interval is the sample mean plus and minus the margin of error, where the margin is the critical z-value for your chosen confidence level multiplied by the standard error, which is the standard deviation divided by the square root of the sample size. A higher confidence level or a smaller sample widens the interval, while a larger sample narrows it. This calculator uses the z-value, which is accurate for larger samples of around 30 or more; for small samples a t-interval is better. Enter your sample details to see the interval straight away.