# T Critical Value Calculator + Online Solver With Free Steps

The T Critical Value Calculator is a free online statistics tool for computing the T value for one-tailed and two-tailed probability.

Additionally, the student t distribution table’s mapped t-value is displayed by the critical values calculator as well.

## What Is a T Critical Value Calculator?

The T Critical Value Calculator is an online tool that calculates the T distribution cut-off point. It closely resembles the Z critical value.

The only significant variation is that the cutoff parameters for the t distribution and normal distribution have slightly varying values, respectively.

T value determines how much of a difference there is in comparison to the variation in the sampled data. It is simply the calculated variation stated in conventional error units.

A considerable difference is demonstrated if the t value is higher. There is a possibility of no substantial variation if the t-value is equal to 0.

A critical value calculator determines the t distribution’s critical values based on the probability of 2 alpha values as well as the DOF (Degree of Freedom). A hypothetical probability distribution that mimics a standard distribution is referred to as a “T-Distribution table.

The closer a distribution resembles a conventional normal distribution with a mean of 0 and a standard deviation of 1 depending on the total number of DOFsIt resembles the conventional normal curve which is uniform, bell-shaped, and linear.

A degree of freedom (DOF) and importance level of alpha is applied to compute the T’s Critical value by using a T critical value calculatorIn this article, we’ll go over how to determine the t critical value using both the Formula for the alpha calculation and the t distribution table.

## How To Use a T Critical Value Calculator?

You can use the T Critical Value Calculator by following the detailed instructions below. The calculator will provide you with the desired results in a few seconds. You can therefore easily use the calculator to get the T Critical Value for the given data points.

### Step 1

Fill in the provided input boxes with the Degrees of Freedom, Level of Significance, Total number of tails, and the direction.

### Step 2

To calculate the T Critical Value for the provided data and to view the complete, step-by-step solution for the T Critical Value Calculation, click the “Submit” button.

## How Does a T Critical Value Calculator Work?

The T Critical Value Calculator works by calculating the Alpha Value before computing the critical Probability.

Use this formula to determine the alpha value:

value of alpha = 1 – ( $\frac{confidence \; level}{100}$)

The degree of confidence indicates how likely it is that a statistical parameter also applies to the population being studied. Typically, a percentage is used to represent this figure.

A 95 percent degree of confidence within a sample group, for instance, denotes that there is a 95 percent likelihood that the given criteria will hold for the full population.

You would use the given calculation to ascertain the alpha value with an 85% level of confidence.

Alpha = 1 – ( $\frac{85}{100}$) = 1 – (0.85) = 0.15

It comes to 0.15. This example’s alpha value is 0.15.

### T Table

The freedom degrees (DOF) in a T distribution are different from those in a standard distribution.

A distribution that is utilized to evaluate an overall mean hypothesis when the overall standard deviation is unknown, the sampling size is small, and the sampling means are expected to have a standard distribution.

To calculate the value of T using the t table, just use the aforementioned t critical value table.

 Df/one tail α=0.25 α=0.1 α=0.05 α=0.025 α=0.005 Df/two tails α=0.5 α=0.2 α=0.1 α=0.05 α=0.01 1 1 3.078 6.314 12.71 63.66 2 0.816 1.886 2.92 4.303 9.925 3 0.765 1.638 2.353 3.182 5.841 4 0.741 1.533 2.132 2.776 4.604 5 0.727 1.476 2.015 2.571 4.032 6 0.718 1.44 1.943 2.447 3.707 7 0.711 1.415 1.895 2.365 3.499 8 0.706 1.397 1.86 2.306 3.355 9 0.703 1.383 1.833 2.262 3.25 10 0.7 1.372 1.812 2.228 3.169 11 0.697 1.363 1.796 2.201 3.106 12 0.695 1.356 1.782 2.179 3.055 13 0.694 1.35 1.771 2.16 3.012 14 0.692 1.345 1.761 2.145 2.977 15 0.691 1.341 1.753 2.131 2.947 16 0.69 1.337 1.746 2.12 2.921 17 0.689 1.333 1.74 2.11 2.898 18 0.688 1.33 1.734 2.101 2.878 19 0.688 1.328 1.729 2.093 2.861 20 0.687 1.325 1.725 2.086 2.845 21 0.686 1.323 1.721 2.08 2.831 22 0.686 1.321 1.717 2.074 2.819 23 0.685 1.319 1.714 2.069 2.807 24 0.685 1.318 1.711 2.064 2.797 25 0.684 1.316 1.708 2.06 2.787 26 0.684 1.315 1.706 2.056 2.779 27 0.684 1.314 1.703 2.052 2.771 28 0.683 1.313 1.701 2.048 2.763 29 0.683 1.311 1.699 2.045 2.756 30 0.683 1.31 1.697 2.042 2.75 100 0.677 1.29 1.66 1.984 2.626 Z 0.674 1.282 1.645 1.96 2.576 50% 80% 90% 95% 99%

## Solved Examples

Let’s solve some examples to better understand the working of the T Critical Value Calculator.

### Example 1

For a significance level of 5% and 30 degrees of freedom, determine the crucial t value (one tail and two tails).

#### Solution

First, determine the values.

Level of significance = 5% = $\frac{5}{100}$ = 0.05

30 degrees of freedom.

Secondly, Locate the degree of freedom (DOF) and significance level in the top row and left side, respectively, of the t distribution table below. Obtain the relevant value from the table.

T’s one-tailed critical value is 1.6978.

Repeat step 1 and use the two-tailed t table below for two-tailed probability in step 3.

T critical value = 2.0428

### Example 2

Locate the essentials

Without utilizing a t & z value calculator, let’s determine the value of t.

#### Solution

To compute the t value using the t value table, follow these steps:

Determine the sample size in the first step. Consider there to be 5 samples.

n = 5

Calculate the degrees of freedom (DOFs) in step two. Add 1 less to the sample size.

df = n – 5 = 5 – 1 = 4

Determine the alpha level’s value in step three. Take 0.05 as the value for the time being.

α = 0.05

In step 4 Look up the values of df and its related alpha level in the list below. As a result, we will have:

t = 2.015