statistics
How to read a t-table (step by step)
Reading a t-table means matching your degrees of freedom (usually sample size minus one) to a row, your significance level and tail choice to a column, and reading off the critical t-value you compare against your calculated test statistic.
By UtilBloom · Published 2026-10-05 · Updated 2026-10-05
Anatomy of a t-table
A standard Student's t-distribution table is a grid: rows are labeled by degrees of freedom (df), usually running from 1 up through 30, then larger jumps (40, 60, 120, and finally ∞, which converges to the standard normal z-table). Columns are labeled by a significance level, sometimes shown as the one-tailed α (0.10, 0.05, 0.025, 0.01, 0.005) and sometimes as the two-tailed α (0.20, 0.10, 0.05, 0.02, 0.01), so the very first thing to check is which convention your specific table uses, the header row or a footnote should say explicitly. Each cell where a row and column intersect is the critical t-value: the threshold your calculated t-statistic must exceed (in absolute value, for a two-tailed test) to be statistically significant at that α. Unlike the normal distribution, the t-distribution has fatter tails at low df to account for the extra uncertainty of estimating the population standard deviation from a small sample, so critical values shrink toward the familiar 1.96 as df grows large.
Finding your degrees of freedom
For a one-sample t-test or a paired t-test, df = n − 1, where n is your sample size. For an independent two-sample t-test with equal variances assumed, df = n1 + n2 − 2. For Welch's t-test (unequal variances, the safer default when you are not sure), df is computed with the Welch-Satterthwaite equation and is almost never a whole number, software reports something like df = 27.4, which you then round down to the nearest table row if you are doing it by hand, or use directly if you have a calculator or the Statistics Hub's t-distribution tool. For simple linear regression, df for the slope's t-test is n − 2 (one df lost for the intercept, one for the slope). For multiple regression with k predictors, df = n − k − 1. Getting df wrong is the single most common lookup error, double-check which test design you actually ran before you pick a row.
Choosing the one-tailed or two-tailed column
Once you know df, decide whether your test is one-tailed or two-tailed, see our companion guide on that choice if you are unsure, then find the column matching your chosen significance level under the correct tail convention. If your table only lists one-tailed α values in its header and you need a two-tailed critical value at α = 0.05, look up the column for α = 0.025 (half of 0.05) instead, since a two-tailed 5% test puts 2.5% in each tail. For df = 20 and a two-tailed test at α = 0.05, you would look up the one-tailed α = 0.025 column at row df = 20, giving a critical value of approximately 2.086. That means any calculated t-statistic with absolute value greater than 2.086 is significant at the 5% level, two-tailed, for that sample size.
Worked lookup examples
Example 1: You run a one-sample t-test on n = 15 observations, two-tailed, α = 0.05. df = 15 − 1 = 14. Looking up the two-tailed α = 0.05 column (equivalently one-tailed α = 0.025) at df = 14 gives a critical value of about 2.145. If your calculated t-statistic is 2.40, it exceeds 2.145, so you reject the null hypothesis. Example 2: You run an independent two-sample t-test, n1 = 12, n2 = 10, equal variances assumed, one-tailed, α = 0.01. df = 12 + 10 − 2 = 20. Looking up the one-tailed α = 0.01 column at df = 20 gives a critical value of about 2.528. A calculated t-statistic of 2.3 would not exceed this threshold, so you fail to reject the null at this strict one-tailed 1% level.
When to use software or a calculator instead of the table
Printed t-tables only list a handful of α values and a limited set of df rows, so any non-standard significance level (say α = 0.03) or an exact fractional df from a Welch test forces you to interpolate, which introduces error. A t-distribution calculator or statistical software computes the exact critical value or exact p-value for any df and any α instantly, which is why most real analysis today reports an exact p-value rather than a table-based pass/fail at a fixed α. The table remains useful for building intuition, understanding how critical values shrink as sample size grows, and for quick manual checks when you do not have a calculator handy, but once you move past a classroom exercise, prefer an exact calculator or software output over manual table lookups.
FAQ
Why does a t-table have an "infinity" row?
As degrees of freedom increase, the t-distribution converges to the standard normal distribution. The ∞ row shows the z-table critical values (for example 1.96 at two-tailed α = 0.05), useful once your sample is large enough that the t and z results are nearly identical.
What if my df isn't listed in the table?
Round down to the nearest listed df for a more conservative (larger) critical value, or use an exact calculator. Interpolating between rows by hand is possible but rarely necessary with calculators available.
Do t-tables differ between textbooks?
The underlying distribution is identical, but table layouts differ: some list one-tailed α across columns, others two-tailed, and some include both. Always read the column headers of the specific table you are using.
Is a t-table the same as a z-table?
No. The t-distribution has heavier tails at low degrees of freedom to reflect extra uncertainty from estimating the population standard deviation. A z-table assumes a known population standard deviation and is a single row, not a grid by df.