# The Excel T.DIST Function

## Function Description

The Excel T.DIST function calculates the one-tailed Student's T Distribution, which is a continuous probability distribution that is frequently used for testing hypotheses on small sample data sets.

The T.DIST function is new to Excel 2010 and so is not available in earlier versions of Excel.

The syntax of the function is:

T.DIST( x, degrees_freedom, cumulative )

where the function arguments are:

x-The value at which you want to evaluate the distribution.
degrees_freedom-The number of degrees of freedom (must be ≥ 1).
cumulative-

A logical argument which denotes the type of distribution to be used:

 TRUE = Cumulative Distribution Function FALSE = Probability Density Function

## T.Dist Function Examples

### Example 1 Cumulative Student's T-Distribution with 10 Degrees of Freedom

The above chart on the right shows the one-tailed cumulative Student's T Distribution with 10 degrees of freedom.

If you want to calculate the value of this function at x = 1, this can be done using the Excel T.Dist function, as follows:

=T.DIST( 1, 10, TRUE )

This gives the result 0.829553434, or 82.96%.

## Example 2 Probability Density Function with 10 Degrees of Freedom

The above chart on the right shows the one-tailed probability density function for the Student's T Distribution, with 10 degrees of freedom.

If you want to calculate the value of this function at x = -1, this can be done using the Excel T.Dist function, as follows:

=T.DIST( -1, 10, FALSE )

This gives the result 0.230361989, or 23.04%.

For further information and examples of the Excel T.Dist function, see the Microsoft Office website.

## T.Dist Function Errors

If you get an error from the Excel T.Dist function this is likely to be one of the following:

Common Errors
 #NUM! - Occurs if either:The supplied cumulative is TRUE and degrees_freedom < 1orThe supplied cumulative is FALSE and degrees_freedom < 0. #DIV/0! - Occurs if the supplied cumulative is FALSE and degrees_freedom = 0. #VALUE! - Occurs if any of the supplied arguments are non-numeric.