Work out student t distribution instantly with clear inputs, formula shown and shareable results.
Student's t distribution has heavier tails than the normal, reflecting the extra uncertainty from estimating the standard deviation. As the degrees of freedom grow it converges to the standard normal.
t CDF
computed from the regularised incomplete beta with x = df/(df + t²)
About 2.086, compared with 1.96 for the normal — the difference shrinks as df rises.
Beyond about 30 degrees of freedom the difference is under 2%, though software makes using t just as easy.