Independent Samples Confidence Interval Calculator

This simple confidence interval calculator uses a t statistic and two sample means (M1 and M2) to generate an interval estimate of the difference between two population means (μ1 and μ2).

The formula for estimation is:

μ1 - μ2 = (M1 - M2) ± ts(M1 - M2)


M1 & M2 = sample means
t = t statistic determined by confidence level
s(M1 - M2) = standard error = √((s2p/n1) + (s2p/n2))

To perform this calculation you need to know your two sample means, the number of items in your samples, and the standard deviations for your two samples. (If you need to calculate means and standard deviations from sets of raw scores, you can do so using our descriptive statistics tools.) The calculation works on the assumption that the two population variances are equal (i.e., it uses a pooled standard deviation in order to calculate the standard error portion of the confidence interval calculation).

The Calculation

Please enter your data into the fields below, with your sample 1 mean being the higher of your two means, select a confidence level (the calculator defaults to 95%), and then hit Calculate. Your result will appear at the bottom of the page.

Sample 1 Mean (M1):  
Sample 1 Size (n1):  
Standard Deviation 1 (s1):  
Sample 2 Mean (M2):  
Sample 2 Size (n2):  
Standard Deviation 2 (s2):  
Confidence Level:  

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

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