Critical values for the Student’s t-distribution. Find the t-value you need for any degrees of freedom and significance level.

Critical Values of the t-Distribution

Each cell shows the t-critical value for the given degrees of freedom (df) and significance level (α). The α = 0.05 two-tailed column is highlighted as the most commonly used threshold.

Reading the Values
All values are positive. For a two-tailed test, the critical region is |t| > t-critical (both tails). For a one-tailed test, use the one-tailed α row and compare your t-statistic directly. Values are computed live using the inverse t-distribution—no lookup tables stored.

How to Use This Table

  1. Find your degrees of freedom (df) in the leftmost column. For a two-sample t-test: df = n1 + n2 − 2. For a one-sample test: df = n − 1. For regression coefficients: df = n − k − 1 (where k is the number of predictors).
  2. Choose your significance level (α) across the top. The standard in most fields is α = 0.05 (two-tailed), which corresponds to a 95% confidence level.
  3. Read the intersection. The value at (df, α) is the critical t-value. If your calculated |t-statistic| exceeds this value, you reject the null hypothesis at that significance level.

Two-Tailed vs. One-Tailed

The table shows two rows of alpha values in the header:

Two-tailed α: Used when your alternative hypothesis is “μ ≠ μ0” (the effect could go either direction). The critical region is split across both tails. This is the default in most research.

One-tailed α/2: Used when your alternative hypothesis specifies a direction (“μ > μ0” or “μ < μ0”). The entire rejection region is in one tail. A two-tailed α = 0.05 corresponds to a one-tailed α = 0.025.

If you are running a one-tailed test at α = 0.05, look at the column where the one-tailed row says 0.05—which is the two-tailed α = 0.10 column.

What Happens as df Grows?

As degrees of freedom increase, the t-distribution converges toward the standard normal (Z) distribution. The last row of the table (∞) shows the Z-critical values. For df ≥ 120, the difference between t and Z is negligible.

Connecting the Dots
See how t-critical values connect to sample size calculation → Sample Size & Power

See how t-statistics and p-values work in regression output → Reading Regressions

Find a Critical Value

Enter your degrees of freedom and significance level to get the exact t-critical value.

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t-Critical Value
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Degrees of Freedom
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Alpha (α)
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Test Type

Find a P-Value from a T-Statistic

Enter a t-statistic and degrees of freedom to compute the corresponding p-value.

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Two-Tailed P-Value
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One-Tailed P-Value
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|t| Statistic
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Degrees of Freedom
Interpreting the P-Value
The two-tailed p-value is the probability of observing a t-statistic at least as extreme as yours (in either direction) under the null hypothesis. If p < α, you reject H0. The one-tailed p-value is exactly half the two-tailed value.