Student's t Table: Critical Values of the t-Distribution

Student's t Table

Rows: degrees of freedom (df) · Columns: tail area α · Cells: critical value t with area α to its right

Tip: click any value to highlight its row and column.

How to read this table

1. Work out the degrees of freedom: n − 1 for a one-sample or paired t-test, n₁ + n₂ − 2 for a pooled two-sample t-test.
2. Choose the column for your α. Use the two-tailed header for two-sided tests and confidence intervals, and the one-tailed header for one-sided tests.
3. Read the critical value where the row and column meet. Reject H₀ if |t| is larger (two-sided) or if t is beyond it in the direction of the alternative (one-sided).
4. If your df is not listed, use the next smaller df (a slightly conservative choice) or the calculator above for the exact value.

Worked example

A 95% confidence interval from a sample of n = 11 has df = 10. Row 10, two-tailed α = 0.05 gives t = 2.228, so the interval is x̄ ± 2.228 × s/√11. The z value for the same interval is 1.960: the wider t multiplier accounts for estimating the standard deviation from only 11 observations.

For a test with t = 2.50 on 15 df, row 15 shows 2.131 (two-tailed α = 0.05) and 2.602 (two-tailed α = 0.02). Because 2.50 falls between them, the two-sided p-value is between 0.02 and 0.05. The calculator above gives the exact p-value.

Click the underlined links to highlight the value in the table.

Formula and how the values were computed

Each cell is the (1 − α) quantile of Student's t-distribution with the given df, computed in double precision and rounded to three decimals. The ∞ row is the standard normal distribution.

Frequently asked questions