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Degrees of Freedom Calculator

Degrees of Freedom Calculator


Test type

Sample Size (N)

Sample Size (N₁)

Sample Size (N₂)

Variance (σ₁)

Variance (σ₂)

Number of columns in the table

Number of rows in the table

Number of groups (k)

Degrees of freedom within groups

Degrees of freedom between groups

Hypothesized mean (h):

Sample mean (x):

Sample Standard Deviation


Table of Content

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Let this free degrees of freedom calculator perform degrees of freedom calculation for various types of statistical tests.

Be with us and get to know how this dof calculator assists in determining this particular parameter for various types of analytical operations.

Let’s move on to the topic of discussion!

What Are Degrees of Freedom?

The possible values in a dataset that can be altered to get the proper estimation of the data are called degrees of freedom.

How To Find Degrees of Freedom?

No doubt the best way to calculate this statistical variable is by using this free degrees of freedom calculator. But you must also comprehend the manual calculations that are possible only if you take into consideration the following expressions:

Degrees of Freedom Formula:

Let’s have a look at the following statistical tests and their related formulas for degrees of freedom calculation:

1-Sample t-Test:

For this test, you can calculate dof by following the equation below:

df = N – 1


N = Total values present in a dataset

df = Degrees of Freedom

2-Sample t-Test:

Here we have a suitable partition for equal and unequal variances:

Equal Variances:

In case of equal dispersion of the data set, the degree of freedom is calculated by this formula:

df = N₁ + N₂ – 2

N₁ = First sample entities

N₂ = Second sample entities

Unequal Variances:

In case of unequal data expansion, the degree of freedom formula is given as:

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


σ = Variance (for calculations, tap variance calculator)


For this statistical procedure, we have the following degrees of freedom equations:

Between Groups:

df = k – 1,

Within Groups:

df = N – k,

Overall DOF:

df = N – 1

Chi-Square Test:

The degrees of freedom statistics for Chi Squared test can be analysed by subjecting to the formula as given below:

df = (rows – 1) * (columns – 1)

For quick and better approximations, start using this best degrees of freedom calculator.

How To Calculate Degrees of Freedom?

Let’s move ahead and resolve a couple of examples to clarify the concept in more depth!

Example # 01:

How to find degrees of freedom for t Test with data values as 23?


Here we have:

N = 23

Calculating degrees of freedom:

df = N-1

df = 23 -1

df = 22

Example # 02:

How to determine degrees of freedom for a Chi Square table representing the marital status by education below:

Status  Middle or Lower School (%) High School (%) Bachelor’s (%)    Master’s (%)  PhD (%)  Total (%) 
Single  46 40 25 17 18 30
Married  31 40 54 67 64 50
Divorced  15 10 11 6 9 10
Widowed  8 10 11 11 9 10
Total  100 100 100 100 100 100


Here we have:

Number of column = 5

Number of rows = 4

Performing degree of freedom calculation:

df = (rows – 1) * (columns – 1)

df = (4 – 1) * (5 – 1)

df = 3 * 4

df = 12

How Degrees of Freedom Calculator Works?

Let’s learn together how you can swiftly find degree of freedom in a couple of clicks with this free dof calculator. Stay with it!


  • From first drop-down list, select for which test you wish to find this particular variable
  • After you make a selection, do enter all required elements in their designated fields
  • At last, tap the calculate button

The free degree of freedom calculator determines:

  • Degree of freedom for selected test type
  • T-Statistics
  • Standard Deviations


Is higher degrees of freedom better?

A higher df value indicates that the possibility of fitting data values in a set are more. Moreover, it allows the data to be structured properly and smoothly.

What is degree of freedom in structural analysis?

In structural analysis, the degrees of freedom corresponds to 6 possible variations that could occur at a particular point.

What is degree of freedom in earthquake engineering?

In the light of earthquake engineering, the degrees of the freedom are actually the lateral displacement of heavy storey masses or buildings.

What is degree of freedom of a dynamic system?

In a dynamic system:
The degrees of freedom are defined as the quantities in number that are required to explain the position and structure of a system.

What do you mean by the degree of freedom of a joint?

The degree of freedom of any joint varies according to the type of it. But you can easily relate this analysis with the help of this best degrees of freedom calculator.

What is degrees of freedom of a sample data with 67 data elements?

The dof for the given values of the data set is 66.

Can degrees of the freedom be zero?

Yes, of course! A zero dof means we are having only one one data value in a dataset and it can not be moved anywhere. Also, it means the unknown variables are also nil.


For various statistical tests, degree of freedom allows you to find critical cutoff values. Statisticians make a vast use of the degrees of freedom calculator to comprehend the data set analysis and dispersion.


From the source of Wikipedia: Degrees of freedom, Applications, Mechanics

From the source of Degrees of Freedom, critical values

From the source of Lumen Learning: F Distribution, Concept Review