Enter your degrees of freedom and significance level (alpha), then choose one-tailed or two-tailed test to look up the Student's t critical value. The t-Table Calculator returns the exact t critical value you need for hypothesis testing — no printed table required.
t Critical Value
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Effective α per Tail
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Confidence Level
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Degrees of Freedom Used
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A t critical value is the threshold value from Student's t-distribution that your test statistic must exceed to reject the null hypothesis. It is determined by your chosen significance level (α) and degrees of freedom. If your calculated t-statistic is greater than the critical value (in absolute terms), your result is statistically significant.
The t distribution table (also called the Student's t-table) lists critical values of the t-distribution for various combinations of degrees of freedom and significance levels. It was historically used to look up critical values by hand; this calculator automates that lookup using the mathematical inverse of the t-distribution's cumulative distribution function.
Degrees of freedom (df) represent the number of independent values that can vary in a statistical calculation. For a one-sample t-test, df = n − 1, where n is your sample size. For a two-sample t-test, df is typically calculated using the Welch–Satterthwaite equation. More degrees of freedom make the t-distribution closer to the standard normal distribution.
A one-tailed test checks for an effect in a specific direction (e.g., greater than or less than), placing all of α in one tail of the distribution. A two-tailed test checks for an effect in either direction, splitting α equally between both tails. Two-tailed tests are more conservative and are the default in most research contexts unless a directional hypothesis is specified in advance.
To find the t critical value, you need three pieces of information: your degrees of freedom (usually sample size minus 1), your significance level (α, commonly 0.05), and whether your test is one-tailed or two-tailed. Enter these into the calculator above and the critical value is returned directly. For a two-tailed test at α = 0.05 with 10 df, the critical value is approximately ±2.228.
The most common significance level is α = 0.05, meaning you accept a 5% probability of rejecting a true null hypothesis (Type I error). In fields requiring stricter standards — such as medicine or physics — α = 0.01 or α = 0.001 may be used. The choice should be made before data collection based on the consequences of a Type I error in your specific context.
As degrees of freedom increase, the t-distribution approaches the standard normal distribution (z-distribution). This means the t critical value decreases and converges toward the corresponding z critical value. For example, at α = 0.05 two-tailed, the critical value is 12.706 at df = 1, 2.228 at df = 10, and approaches 1.960 as df → ∞.
The t critical value is a fixed threshold determined by your significance level and degrees of freedom before you run your test. The p-value is calculated from your actual data and test statistic after running the test. If your test statistic exceeds the critical value, equivalently your p-value will be less than α — both lead to the same conclusion about rejecting the null hypothesis.