T Distribution Table
Use this Student's t distribution table to find critical t values for a chosen number of degrees of freedom and significance level. Switch between one-tailed and two-tailed conventions, or choose a central confidence level.
df = 9; upper-tail α = 0.05
Reference critical values are rounded to four decimal places. Custom lookups use the full precision of the entered degrees of freedom and significance level.
Student's t Critical Values Table
The Student's t distribution depends on degrees of freedom. For a selected df and upper-tail probability α, a positive critical t value is the threshold leaving α probability to its right. The distribution is symmetric, so the corresponding lower-tail threshold is its negative.
| df ↓ / α → | 0.1 | 0.05 | 0.025 | 0.01 | 0.005 | 0.001 |
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One-tailed α = 0.025 corresponds to two-tailed total α = 0.05 and central confidence 95%. A 68% confidence interval still depends on df; it has no universal t critical value.
How to Read a T Distribution Table
Identify degrees of freedom, decide whether the problem is one-tailed or two-tailed, and then choose the α column. For df = 9, a one-tailed test at α = 0.05 uses t ≈ 1.8331. A two-tailed test with total α = 0.05 uses ±2.2622 because 0.025 is placed in each tail.
One-Tailed vs. Two-Tailed T Tables
A one-tailed t test places the full significance level in one tail. A two-tailed test splits the total significance level equally between both tails, so the positive cutoff uses α/2. Do not read the same column for both without checking the table heading.
T Table for Confidence Intervals
A conventional two-sided 95% t confidence interval uses the critical value t_(1−0.025, df). For df = 10, this is approximately 2.2281. The appropriate degrees of freedom and standard error depend on the underlying statistical procedure.
How to Estimate a P-Value from a T Table
Locate the row for your df and compare the absolute test statistic with nearby positive critical values. The surrounding columns can bound a one- or two-tailed p-value. A coarse printed table does not necessarily contain an exact p-value for an arbitrary t statistic.
Worked Example: Two-Tailed t Test at 5%
For df = 9 and two-tailed α = 0.05, each tail contains 0.025. Read the upper-tail 0.025 column in row df = 9: t ≈ 2.2622. The symmetric cutoffs are −2.2622 and +2.2622.
Frequently Asked Questions
What is a t distribution table?
It is a reference table of Student's t critical values for specified degrees of freedom and tail probabilities.
How do I read a t table?
Find the df row and the column for the required one-tailed or two-tailed α. Read the positive critical value, using the negative sign for the symmetric lower-tail cutoff when relevant.
What is the difference between one-tailed and two-tailed t values?
One-tailed α is placed in one tail. Two-tailed α is split between the lower and upper tails, making the positive cutoff larger for the same total α.
What degrees of freedom should I use?
Use the df formula for the specific statistical test. A simple one-sample t procedure uses df = n − 1, but other tests can use different formulas or approximations.
How do I find the critical t for a 95% confidence interval?
Choose the two-sided 95% confidence level (total α = 0.05) and read the t critical value for your df. For df = 10 it is approximately 2.2281.
Does a t table give an exact p-value?
A conventional printed t table normally provides selected critical values and can only bracket many p-values. A validated t distribution calculator can evaluate the probability more precisely.
What happens as degrees of freedom increase?
The Student's t distribution approaches the standard normal distribution, so its critical values approach the corresponding Z critical values.
Sources
Reviewed: October 2026. Reference grids and lookups are calculated locally; no observations are sent to a server.