Student T Distribution Calculator

Work out student t distribution instantly with clear inputs, formula shown and shareable results.

About Student T Distribution Calculator

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.

Formula

t CDF

computed from the regularised incomplete beta with x = df/(df + t²)

Worked example

With the default values below, Student T Distribution Calculator returns Probability for the chosen region of 0.0499963545. Change any input above and every figure here is recalculated in your browser.

Inputs used

t value: 2.086
Degrees of freedomaccepts 1–5,000: 20
Which regionone of Two-tailed, One-tailed (right), Left of t: Two-tailed

Results

Probability for the chosen region: 0.0499963545
P(T ≤ t): 0.9750018228
Two-tailed 5% critical value: 2.085963
Equivalent normal two-tailed p: 0.0369784952

Step by step

1Values used
2t CDF
3Probability for the chosen region= 0.0499963545
4P(T ≤ t)= 0.9750018228
5Two-tailed 5% critical value= 2.085963
6Equivalent normal two-tailed p= 0.0369784952

Assumptions and limits

The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 10 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

What is the two-tailed 5% critical value on 20 df?

About 2.086, compared with 1.96 for the normal — the difference shrinks as df rises.

When can I just use z?

Beyond about 30 degrees of freedom the difference is under 2%, though software makes using t just as easy.