Confidence Interval Calculator
Find the confidence interval for a mean from your sample statistics.
How to use the Confidence Interval Calculator
- Enter your sample mean and standard deviation.
- Enter the sample size and pick a confidence level.
- Read the interval and the margin of error.
CI = mean ± z × (SD ÷ √n)
About the Confidence Interval Calculator
This calculator builds a confidence interval for a mean from your sample statistics using CI = mean +/- z x (SD / sqrt(n)). You supply the sample mean, standard deviation, and sample size, then pick a confidence level, and it returns the interval along with the margin of error. The z-values are 1.645, 1.96, and 2.576 for the 90%, 95%, and 99% levels respectively.
A confidence interval expresses the uncertainty around an estimate. A 95% interval means that if you repeated the sampling many times, about 95% of the intervals produced would contain the true population mean. It does not mean there is a 95% chance the true mean sits inside this one particular interval, which is a common misreading worth avoiding.
This is a z-interval, which is best suited to large samples of about 30 or more, or cases where the population standard deviation is genuinely known. For small samples a t-interval is more appropriate because it accounts for the extra uncertainty of estimating the spread. Enter your numbers to read the interval instantly. To find the standard deviation first, use the Standard Deviation Calculator, or average a dataset with the Average Calculator.
Frequently asked questions
How is the confidence interval calculated?
The tool takes your mean and adds or subtracts the margin of error, which is the z-value times the standard deviation divided by the square root of the sample size. The z-value depends on the confidence level you choose.
What z-values does each level use?
The calculator uses 1.645 for a 90% level, 1.96 for 95%, and 2.576 for 99%. A higher confidence level uses a larger z-value, which widens the interval to be more certain of capturing the true mean.
What does a 95% confidence interval actually mean?
It means that if you repeated the sampling many times, roughly 95% of the intervals you built would contain the true population mean. It is not a 95% probability that the true mean lies within this single interval.
When should I use a t-interval instead?
Use a t-interval for small samples, generally under about 30, when the population standard deviation is unknown. The t-distribution allows for the extra uncertainty of estimating the spread from a small sample, giving a slightly wider, more honest interval.
What is the margin of error?
It is the plus-or-minus part of the interval, equal to the z-value times the standard error. A larger sample shrinks it, while a higher confidence level widens it. The calculator reports it separately from the interval bounds.