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T.DIST Function

Excel 2010+

Summary

The T.DIST function calculates the Student's left-tailed t-distribution, essential for statistical hypothesis testing with small sample datasets. This function replaces traditional t-distribution tables by providing precise probability values directly within Excel.

Syntax

T.DIST(x, deg_freedom, cumulative)

Parameters

Parameter	Type	Required	Description
x	`Number`	Yes	The numeric value at which to evaluate the distribution
deg_freedom	`Integer`	Yes	An integer ≥ 1 indicating the number of degrees of freedom
cumulative	`Boolean`	Yes	TRUE returns cumulative distribution; FALSE returns probability density

Using the T.DIST Function

T.DIST is primarily used in statistical analysis for hypothesis testing when dealing with small sample sizes where the normal distribution assumption doesn't hold. Set cumulative to TRUE for left-tail probabilities (most common in one-tailed tests) or FALSE to get the exact probability density at a specific point.

Common T.DIST Examples

Cumulative Left-Tail Probability

=T.DIST(60,1,TRUE)

Calculates the left-tailed cumulative t-distribution for x=60 with 1 degree of freedom. Result: 0.99469533 (99.47% of distribution below 60)

Probability Density Function

=T.DIST(8,3,FALSE)

Returns the probability density at x=8 with 3 degrees of freedom. Result: 0.00073691 (height of t-distribution curve at this point)

One-Tailed Hypothesis Test

=T.DIST(2.5,20,TRUE)

Left-tail probability for t-statistic of 2.5 with 20 degrees of freedom, commonly used in hypothesis testing

Frequently Asked Questions

T.DIST calculates left-tailed probabilities (one-tailed), while T.DIST.2T calculates two-tailed probabilities symmetric around zero.

Use TRUE (default for most tests) for cumulative probabilities below x. Use FALSE for the probability density at exactly x.

T.DIST returns an error. Degrees of freedom must be at least 1.

Common Errors and Solutions

#VALUE!

Cause: Any argument is non-numeric

Solution: Ensure x is numeric and deg_freedom is an integer ≥ 1

#NUM!

Cause: deg_freedom < 1

Solution: Use degrees of freedom value of 1 or greater

#DIV/0!

Cause: Invalid cumulative value

Solution: Use TRUE or FALSE for the cumulative argument

Notes

If deg_freedom increases, t-distribution approaches normal distribution
For large samples (deg_freedom > 30), consider using NORM.DIST instead
Always verify results against statistical tables for critical values
T.DIST only provides left-tail probabilities; use T.DIST.RT for right-tail

Compatibility

Available in: Excel 2010, Excel 2013, Excel 2016, Excel 2019, Excel 2021, Microsoft 365

Not available in: Excel 2007, Excel 2003, Earlier versions

Content last reviewed: December 9, 2025
Update frequency: As needed
Excel versions tested: Excel 2010+