Statistics Utility
Confidence Interval Calculator
Calculate a two-sided confidence interval for a population mean using a t critical value or z critical value.
Method
When the standard deviation is estimated from the same sample, the tool uses the Student t interval: sample mean ± t critical × sample standard deviation ÷ square root of n, with n−1 degrees of freedom. When a population standard deviation is treated as known, the tool uses the corresponding standard-normal z critical value.
Worked example
Using the NIST example with mean 53.7, sample standard deviation 6.567, n = 10, and 95% confidence gives t critical ≈ 2.262157 and an interval of approximately 49.00 to 58.40.
When this is useful
Useful for estimating uncertainty around a sample mean when the assumptions behind the selected t or z method are reasonable.
Privacy
The values you enter into this calculator are processed in your browser by Practical Tools Hub application assets. The calculator does not need to send your calculation inputs to a third-party calculation service.
Limitations
The interval method assumes the observations and sampling model justify the selected procedure. A 95% confidence interval does not mean there is a 95% probability that a fixed parameter lies inside the one interval you computed. The confidence level describes the long-run coverage of the method under its assumptions.