# Documentation/Calc Functions/TDIST

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## Function name:

TDIST

## Category:

Statistical Analysis

## Summary:

Calculates area to the tail(s) of the probability density function of the Student's t-distribution(often known more simply as just the t-distribution). The Student's t-distribution is often used to test a hypothesis about a population’s mean when the population’s standard deviation is not known. The Student’s t-distribution can be used with any statistic whose distribution is approximately normal.

## Syntax:

TDIST(**Number**; **DegreesFreedom**; **Mode**)

## Returns:

Returns a positive real number in the range 0 to 1 (exclusive) representing the total area under the tail(s) of the probability distribution function of the specified Student’s t-distribution.

## Arguments:

**Number** is a non-negative real number or a reference to a cell containing that number which is the value for the Student's t-distribution is to be calculated.

**DegreesFreedom** is a positive integer value or a reference to the cell containing that number which is the number of degrees of freedom for the Student's t-distribution.

**Mode** = 1 returns the one-tailed test, **Mode** = 2 returns the two-tailed test.

- If
**Number**is less than 0 then the function returns an error value. - If
**DegreesFreedom**is less than 1 then the function returns an error value. - If
**DegreesFreedom**and**Mode**is a non-integer value then the function uses its floor value, i.e. it is truncated to an integer. - If
**Mode**is less than 1 or greater than or equal to 3 then the function returns an error value.

## Additional details:

- The formula for TDIST is:

where

Here, x is the **Number**, df is **DegreesFreedom** and tails is **Mode**.

- It is such that T.DIST.RT(x ,y) = 0.5*T.DIST.2T(x, y), T.DIST.RT(x, y) = TDIST(x, y, 1), T.DIST.RT(x, y) = 1 – T.DIST(x, y, 1) and T.DIST.2T(x, y) = TDIST(x, y, 2).
- For more details about the Student's t-distribution, visit Wikipedia.

## Examples:

Formula | Description | Returns |
---|---|---|

=TDIST(5.8;1.5;1) | The function calculates the area to the single-tailed probability density function of the Student’s t-distribution. Here DegreesFreedom is non-integer value 1.5 so the function truncates it to integer 1. |
0.054346705732263 |

=TDIST(5.8;1.5;2) | The function calculates the area to the two-tailed probability density function of the Student’s t-distribution. Here DegreesFreedom is non-integer value 1.5 so the function truncates it to integer 1. |
0.108693411464525 |

=TDIST(5.8;1.5;3) | The function returns an error value since Mode can only be 1 or 2. |
Err:502 |

## Related LibreOffice functions:

## ODF standard:

## Equivalent Excel functions:

TDIST