How to use the T.INV function in Excel

In this article, we will learn How to use the T.INV function in Excel.

What is hypothesis testing, Inverse of T distribution and degree of freedom?

In statistics, Hypothesis testing is used to find the estimation of mean for the population dataset using the different distribution function based on the part of population dataset named sample dataset. A statistical hypothesis, sometimes called confirmatory data analysis, is a hypothesis that is testable on the basis of observing a process that is modeled via a set of random variables. A statistical hypothesis test is a method of statistical inference. There are two types of hypothesis. One is a null hypothesis which is the claimed statement and other is the alternate hypothesis which is just opposite of the null hypothesis. For example if we say maximum limit to lead in a maggi packet must not exceed 225 ppm (parts per million) and someone claims that there is more than fixed limit than null hypothesis (denoted by U0) and the alternate hypothesis (denoted by Ua)

U0 = lead content in maggi packet is more than or equal to 225ppm. 

Ua = lead content in maggi packet is less than 225 ppm.

So the above hypothesis is an example of a right-tailed test as the underlying situation lies in the right side of the  distribution curve. If the underlying situation lies on the left side then it would be called a left-tailed test. Let's take one more example which illustrates a one-tailed test. For example if selina said she can do 60 push ups on an average. Now you might doubt that statement and try to hypothesize the situation in statistics term then, the null and the alternate hypothesis is stated below

U0 = selina can do 60 pushups

Ua = selina cannot do 60 pushups

This is a two-tailed test where the underlying situation lies on both sides of the claimed statement. These tailed tests affect the outcome of the statistics. So choose the null and alternative hypothesis carefully. T distribution is a family of continuous probability distribution when estimating the mean of a normally distributed population in situations where the sample size is small (generally < 30) and the population standard deviation is unknown.

T distribution inverse function :

Inverse of t distribution function returns the random sample value corresponding to the t distribution probability value for the given sample. The inverse function only considers the left-tailed student t distribution while evaluating. For this function we need Degree of freedom for the output.

Degree of Freedom variable :

Now you must be wondering what is the degree of freedom (also known as df). Mathematically, the degree of freedom(df) of a distribution is equal to the number of standard normal deviations being summed. But how can we understand the concept of degree of freedom? Degree of freedom is the number of independent possibilities in an event. For example if we toss a coin 100 times and say heads occur 48 times and then we can conclude the tails occured 52 times so the degree of freedom is 1. But if we say on a route of traffic lights (generally has 3 color lights) we want to know the probability of red light in any given sample of time. For this the degree of freedom will be 2 as we will require information for at least 2 color lights. So the degree of freedom is the 1 - sample size of distribution. We can evaluate the probability value for the distribution using the T.DIST or TDIST or T.DIST.2T or T.DIST.RT function for the variable x

But to get the x value corresponding to the probability value and given degrees of freedom for the distribution we use the T.INV function in Excel. Let's understand the use of T.INV function as inverse t distribution calculator

T.INV Function in Excel

The T.INV function in Excel returns the inverse of t distribution i.e it returns the student t distribution x value corresponding to the probability value. The function takes probability and degrees of freedom for the distribution.a

T.INV Function syntax:

=T.INV(prob , deg_freedom)

prob : value at which x is evaluated

deg_freedom : degrees of freedom


Example :

All of these might be confusing to understand. Let's understand how to use the function using an example. Here we have a probability value and degree of freedom. We need to calculate the probability percentage for the t distribution one tailed test using the TDIST function in Excel

Use the formula:

=T.INV(B3 , B4)

The x value for t distribution for probability 0.7 or 70% comes out to be 0.57 for the student t distribution left-tailed test.

Here are all the observational notes using the T.INV function in Excel
Notes :

  1. The function only works with numbers. If any argument other than cumulative is non numeric, the function returns #VALUE! error.
  2. The function returns #NUM! Error.
    1. If argument prob < 0 or > 1
    2. If the degree of freedom is < 1 or >10^10.
  3. Value in decimal and value in percentage id the same value in Excel. Convert the value to percentage, if required.
  4. You can feed the arguments to the function directly or using the cell reference as explained in the example.

Hope this article about How to use the T.INV function in Excel is explanatory. Find more articles on statistical formulas and related Excel functions here. If you liked our blogs, share it with your friends on Facebook. And also you can follow us on Twitter and Facebook. We would love to hear from you, do let us know how we can improve, complement or innovate our work and make it better for you. Write to us at


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