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# 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 **DOFs**. It 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 calculator**. In 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**** **