T Critical Value Calculator, Two-Tailed

Each tailα / 2

df (one sample)n − 1

Reject if|t| > t*

What Is T Critical Value Two-Tailed?

A two-tailed t critical value is the point that leaves half of alpha in each tail of the t distribution. If your t statistic is further from zero than this value, the result is significant at level alpha.

Enter alpha, or switch to a confidence level, and the degrees of freedom. For a one-sample test the degrees of freedom are n − 1. The calculator also shows the matching z value so you can see how much wider the t cut-off is.

The same number is the multiplier used for a confidence interval for a mean.

How to Use the T Critical Value Two-Tailed Calculator

Enter α, or switch to a confidence level.
Enter the degrees of freedom, n − 1 for a one-sample test.
Use the ± value as your cut-off.

T Critical Value Two-Tailed Formula

Critical value

t^*=t_{1-\alpha/2,;df}

Degrees of freedom (one sample)

df=n-1

T Critical Value Two-Tailed Variables Explained

Symbol	Meaning	Notes
α	Significance level, split across both tails
df	Degrees of freedom	n − 1 for one sample
t*	Critical value	Reject H₀ if \|t\| > t*
α/2	Area in each tail

T Critical Value Two-Tailed Worked Example

With the example values loaded in the calculator above, the steps are:

Two-tailed: split α = 0.05 equally, so each tail holds 0.025.
The critical value is the t score with 0.975 of the area to its left, using 14 degrees of freedom: t* = 2.1448.
By symmetry the other critical value is −2.1448. Reject H₀ if |t| > 2.1448.

Result: Two-tailed t critical value (±) = ± 2.1448.

Worked example: α = 0.05, df = 14

Each tail holds 0.025. The t value with 0.975 of the area to its left and 14 degrees of freedom is 2.1448.

So the critical values are ±2.1448. A sample with t = 2.5 is beyond this limit and is significant at the 5 percent level.

Compared with z

For small samples the t critical value is larger than the matching z value, 1.96 at 95 percent, because the t distribution has heavier tails. As df grows, t gets closer to z.

Where T Critical Value Two-Tailed Is Used

Hypothesis tests

Get the cut-off for a two-tailed t test.

Confidence intervals

Find the t multiplier for a mean.

Replacing a t table

Get exact values for any degrees of freedom, not just table rows.

Common T Critical Value Two-Tailed Mistakes to Avoid

Use the right df for your test.
For a one-tailed test the critical value uses the full α in one tail.

T Critical Value Two-Tailed Terms and Definitions

Critical value: The cut-off that separates the rejection region from the rest.
Degrees of freedom: The number of independent pieces of information used to estimate the spread.

T Critical Value Two-Tailed FAQs

What is the t critical value for a two-tailed test at 0.05?

It depends on the degrees of freedom. With 14 degrees of freedom it is 2.1448, and it falls toward 1.96 as df grows.

How do I use it?

If the absolute value of your t statistic is larger than the critical value, reject the null hypothesis.

How is it different from one-tailed?

A two-tailed test splits α between both tails, so its critical value is larger than the one-tailed value at the same α.

What is it for confidence intervals?

It is the multiplier on the standard error: mean ± t* × SE.