About this calculator
What the t-distribution is for
When you estimate a mean and have to use the sample standard deviation s instead of σ, the standardized sample mean follows a t-distribution rather than the standard normal. It is bell-shaped and centered at 0 but has thicker tails, so cutoffs are a little farther out than z cutoffs.
The shape depends on the degrees of freedom; for one sample, df = n − 1. As df grows, the t-distribution gets closer and closer to the standard normal.
Common use
For a 95% confidence interval, the critical value t* is the cutoff with a middle area of 0.95. Choose "A value (cutoff)" and "Middle area" above.