Single-Sample Confidence Interval Calculator Using the Z Statistic

This simple confidence interval calculator uses a Z statistic and sample mean (M) to generate an interval estimate of a population mean (μ).

Note: You should only use this calculator if (a) your sample size is 30 or greater; and/or (b) you know the population standard deviation (σ), and use this instead of your sample's standard deviation (an unusual situation). If your data does not meet these requirements, consider using the t statistic to generate a confidence interval.

The formula for estimation is:

μ = M ± Z(sM)


M = sample mean
Z = Z statistic determined by confidence level
sM = standard error = √(s2/n)

As you can see, to perform this calculation you need to know your sample mean, the number of items in your sample, and your sample's standard deviation (or population's standard deviation if your sample size is smaller than 30). (If you need to calculate mean and standard deviation from a set of raw scores, you can do so using our descriptive statistics tools.)

The Calculation

Please enter your data into the fields below, select a confidence level (the calculator defaults to 95%), and then hit Calculate. Your result will appear at the bottom of the page.

Sample Mean (M):  
Sample Size (n):  
Standard Deviation (s):  
Confidence Level:  

Please enter your values above, and then hit the calculate button.

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