T.DIST Function

Excel 2010+ Statistical

The Excel T.DIST function returns the left-tailed Student's t-distribution — either the cumulative probability or the probability density — for a given t-value and degrees of freedom.

Quick answer:

=T.DIST(2,10,TRUE) left-tail cumulative probability ≈ 0.9633

Syntax

=T.DIST(x, deg_freedom, cumulative)

Argument		Description
`x`	Required	The t-value at which to evaluate the distribution.
`deg_freedom`	Required	The degrees of freedom (a positive integer).
`cumulative`	Required	`TRUE` returns the cumulative distribution (area to the left of x); `FALSE` returns the probability density at x.

How to use it

The Student's t-distribution looks like a bell curve with heavier tails; it converges on the normal distribution as the degrees of freedom rise. T.DIST gives the left tail.

=T.DIST(2, 10, TRUE) // cumulative ≈ 0.9633

=T.DIST(2, 10, FALSE) // density ≈ 0.0611

Set cumulative to TRUE for a p-value-style probability (area to the left of x) or FALSE to read the height of the curve at a single point.

Three flavors of t: use T.DIST for the left tail, T.DIST.RT for the right tail, and T.DIST.2T for both tails combined. The old single function TDIST still works but is now in the Compatibility category.

Try it: interactive demo

Live demo

Pick a T.DIST example to see the formula and its result.

example

Result:

Practice workbook

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Frequently asked questions

What does the cumulative argument do?

TRUE returns the area under the curve to the left of x (a cumulative probability), while FALSE returns the probability density — the height of the curve — at exactly x.

How is T.DIST different from the old TDIST?

Legacy TDIST was right-tailed and could only return one or two tails. The modern family splits this into T.DIST (left, with a cumulative switch), T.DIST.RT (right), and T.DIST.2T (two-tailed).

What are degrees of freedom here?

For a one-sample t-test it is the sample size minus one. They control the heaviness of the tails: fewer degrees of freedom mean fatter tails, and the curve approaches the normal distribution as they grow.

Can deg_freedom be a decimal?

Excel truncates any non-integer deg_freedom to a whole number before computing. Use a positive value; zero or negative degrees of freedom return an error.

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Related functions: T.DIST.RT · T.DIST.2T · T.INV · T.INV.2T · T.TEST · NORM.DIST