T table — critical values of the t distribution

Upper critical values of t

The last row is the normal distribution, which is what t becomes once the sample is large enough that the estimated standard deviation stops mattering. Compare any column against it to see how much a small sample costs: at df 5 the two-tailed 5% value is 2.571 against 1.960.

Questions people actually ask

How do you read a t table?

Find the row for your degrees of freedom and the column for your significance level, then check which header applies. With 10 degrees of freedom and a two-tailed test at 0.05, the value is 2.228. The same column is 0.025 one-tailed, which is why both labels sit above it here.

What are degrees of freedom in a t test?

For a one-sample test, the sample size minus one: 20 observations give df 19. For a two-sample test with equal variances, the two sample sizes added and 2 subtracted. The subtraction is there because the sample mean was estimated from the same data, which uses up one piece of information.

Why does the table stop and say infinity?

Because past about 120 degrees of freedom the t distribution is indistinguishable from the normal at the printed precision. The infinity row is the normal distribution: 1.960 two-tailed at 5%, the number every confidence interval uses.

One tailed or two tailed?

Two-tailed unless the hypothesis names a direction before the data is collected. "Does the treatment change the outcome" is two-tailed; "does it increase the outcome, and a decrease would be reported as no effect" is one-tailed. Choosing one-tailed after seeing which way the data went halves the p-value for free and is the most common way a result is talked into significance.

Why is t larger than z?

Because the standard deviation was estimated rather than known, and that estimate carries its own error. The t distribution has fatter tails to pay for it, so the interval is wider. At df 5 the two-tailed 5% value is 2.571 against 1.960 — 31% wider — and the gap closes as the sample grows.

What is the critical value for a 95% confidence interval?

The two-tailed 0.05 column. With 24 degrees of freedom that is 2.064, so the interval is the mean plus or minus 2.064 standard errors. Using 1.96 there instead makes the interval 5% too narrow, which is small on one estimate and systematic across a paper.

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Rule Calculator. "T Table." Rule Calculator. Last reviewed August 16, 2026. https://rulecalculators.com/t-table.

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Sources

• NIST/SEMATECH e-Handbook of Statistical Methods — critical values of the t distribution
• NIST/SEMATECH e-Handbook — cumulative distribution function of the standard normal

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