t Distribution Table — Critical Values by Degrees of Freedom

How to read the table

Rows are degrees of freedom (df); columns are significance levels. The first header row is the one-tailed level (right-tail area α); the second is the matching two-tailed level (2α). Each value is the critical t with P(T > t) = α.

1. One-sample t-test with 11 observations (df = 10), two-sided α = 0.05: column two-tailed 0.05 (one-tailed 0.025), row 10 → 2.228. Reject the null hypothesis if |t| exceeds it.
2. Same df, one-tailed α = 0.05 → 1.812.
3. For df = 30 the value is 2.042; df = ∞ equals the normal value 1.960. As df grows, the t distribution approaches the normal.

df not in the table

For df not listed (e.g. a Welch test with df = 13.26), using the next smaller df gives a conservative decision. For an exact p-value use the t-test calculator — it handles fractional df directly.

Using it for confidence intervals

A 95% confidence interval for a mean is x̄ ± t(0.025, n−1) × s/√n. With 11 observations, multiply by t = 2.228.

→ Calculate it now: t-test

t critical values t(α, df)

Values computed with this site's numerical engine and cross-checked against SciPy · updated 2026-09-23