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Degrees of Freedom Calculator


The degrees of freedom calculator assists you in calculating this particular statistical variable for one and two-sample t-tests, chi-square tests, and ANOVA.

What are Degrees of Freedom? Definition

In a data sample, 

“Degrees of freedom determine the total number of logically independent values of information which might vary”.

The Degrees of freedom are like how many independent variables we have in statistical analysis and let you know the number of items selected before we have to put any restrictions in place. 

The formula of Degree of Freedom:

Here we have three types of tests in which we can use the different formulas according to their situations which are as follows:

  1. Sample t-Test
  2. ANOVA Test
  3. Chi-Square Test

1. Degree of Freedom Sample t-Test:

Here we have two types of t-test samples

  • One Sample t-test.
  • Two Sample t-tests.

Degree of Freedom One Sample t-Test:

The general formula for the degrees of freedom is:

df  =  N  -  1

Where N represents the total number of values in a dataset and df describes the Degree of Freedom. To find the degrees of freedom calculation, you just need to subtract one from the total number of items in a data sample.

Degree of Freedom Two Sample t-Test:

So, how should you continue if you want to find the degrees of freedom when you have two samples? In this case, we have two conditions according to its variance,

  • Equal Variances:
  • Unequal Variances.

In the equal variance of the data set, the degrees of freedom equation can be interpreted as follows:

df  =  N₁  +  N₂  – 2

Where N1 represents the first sample and N2 refers to the second sample in a data set
whereas the degree of freedom formula for unequal variance is as follows:

df = (σ₁/N₁ + σ₂/N₂)2 / [σ₁2 / (N₁2 * (N₁-1)) + σ₂2 / (N₂2 * (N₂-1))],

Here, σ = Variance, and the rest are the number of samples that we already discussed above.

2. Degrees of Freedom Calculator ANOVA:

An ANOVA is a statistical test that is used to analyze if there is a statistically significant difference between two or more categorical groups.

There are various conditions in which we compute the degrees of freedom for ANOVA, the equations vary according to their situation which are as follows:

Between Groups:  DF  =  k – 1
Within Groups:  DF  =  N – k
Overall DOF: DF  =  N – 1
Here k = Independent comparison groups, and N = Total sample size.

3. Degrees of Freedom Chi-Square Test:

Chi-square testing is a way of testing in which we compare observed results with expected results. We can analyze the degree of freedom for chi-square by applying the following formula below:

df  =  (rows – 1)  ✕  (columns – 1)

For quick and better results, you can start using this best degrees of freedom calculator.

How To Calculate Degrees of Freedom?

Now, let’s take a closer look at the below example to clarify your concepts further:


Let’s assume the data values are 17 in a statistical calculation, How to find degrees of freedom for t test?

Here’s how:

N = 17

Now calculate the degrees of freedom:

DF  =  N - 1

DF  =  17 - 1

DF  =  16

You can also find the value from an online tool Degrees of Freedom calculator.

Working of Degree of Freedom Calculator:

You can easily find the values of the degrees of freedom with the help of dof calculator by putting a couple of inputs: 


  • Select the test type you want to calculate
  • Enter all required elements into their respective fields
  • Press the calculate button


  • Degrees of freedom for selected test type


Can you have a negative number of degrees of freedom statistics?

Negative degrees of freedom are valid. It means you have more numbers than you have variables that can be changed.

Are degrees of freedom always the same?

It is important to keep in mind that different degrees of freedom display different t-distributions depending on the sample size, so the answer is No.


From the source Degrees of Freedom in Statistics Explained: Formula and Example, What Are Degrees of Freedom? , Understanding Degrees of Freedom, and Degrees of Freedom Formula.