Confidence Interval Calculator
Build a confidence interval around your sample mean. Enter the mean, standard deviation, sample size and confidence level to get the range.
About the Confidence Interval Calculator
A confidence interval gives a plausible range for a population mean based on a sample. This calculator takes your sample mean, standard deviation, sample size and confidence level, then returns the margin of error and the lower and upper bounds. A 95 percent interval, for instance, means that if you repeated the sampling many times, about 95 percent of such intervals would contain the true mean.
How to use it
- Enter the sample mean, the average of your data.
- Enter the standard deviation of the sample.
- Enter the sample size, the number of observations.
- Enter the confidence level, such as
95percent. - Read the margin of error and the interval bounds.
The width of the interval shrinks as your sample grows and widens as the standard deviation or confidence level rises. This calculator uses a z-based normal approximation, which is reliable for larger samples; with very small samples a t-distribution is more accurate. A confidence interval is not a 95 percent probability that the mean sits inside this one range, a common misreading. All computation happens in your browser and nothing is uploaded.
Frequently asked questions
How is a confidence interval calculated?
The interval is the sample mean plus and minus the margin of error, where the margin is the z-score for your confidence level times the standard deviation divided by the square root of the sample size. For 95 percent the z-score is about 1.96.
What does a 95 percent confidence level mean?
It means that if you drew many samples and built an interval from each the same way, roughly 95 percent of those intervals would contain the true population mean. It is not a 95 percent chance that the mean is in this particular interval.
Does this use the z-distribution or the t-distribution?
It uses a z-based normal approximation, which is accurate for larger samples. For small samples, typically under about 30, a t-distribution gives a slightly wider, more accurate interval.
How can I make the interval narrower?
Increase the sample size, which reduces the standard error, or lower the confidence level. A larger sample tightens the interval, while demanding higher confidence widens it.