Student t Distribution Explorer

1 / Set up the question

Your t distribution

Degrees of freedom (df)

Use a whole number from 1 to 1,000,000. For a one-sample mean, df = n − 1. Smaller df give heavier tails.

What do you want to find? Shaded region

Cutoff (t)

Try a classroom example

Predict, then check

Your probability estimate (0 to 1)

Estimate the shaded fraction, then compare it with the answer.

2 / See the connection

Student t curve and shaded area

Drag a cutoff or the shaded region. The area, mathematics, and Excel formulas update together.

3 / Follow the math

Connect cutoffs and probability

4 / Do the same in Excel

Equivalent Excel formulas

Shown values are rounded; calculations use full precision. Excel formulas keep the original inputs.

How the five Excel functions fit together

T.DIST(t, df, TRUE): Signed t cutoff → area to its left.
T.DIST.RT(t, df): Signed t cutoff → area to its right.
T.DIST.2T(c, df): Nonnegative magnitude c → combined area below −c and above c.
T.INV(p, df): Left-tail probability → signed t cutoff. A probability below 0.5 gives a negative cutoff.
T.INV.2T(p, df): Combined two-tail probability → positive critical magnitude. For middle 95%, pass 0.05.

TRUE gives cumulative probability; FALSE gives density height, not area. Since T is continuous, P(T = t) = 0.

The standard Student t distribution is symmetric about zero. Its mean is undefined at df = 1; its variance is undefined at df ≤ 2. Larger df bring it closer to the standard normal curve. There is no separate mean or standard-deviation input.

Excel truncates noninteger df; this explorer requires whole-number df so its displayed formulas use exactly the same model. A right-tail probability above 0.5 has a negative cutoff; a two-sided critical magnitude is always nonnegative.

No sign-in, analytics, storage, external fonts, or transmitted student data. All answers are also available as text. Print or save as PDF for a worked example.