T-Distribution Critical Values Calculator
A t critical value is the line in the sand. Once you know your degrees of freedom and how confident you need to be, it tells you exactly where the rejection region begins — both for significance tests and for the margin of error in a confidence interval. Enter your numbers below for an exact value, or scroll to the full t-table if you just need to look one up.
Find a Critical Value
The Full t-Table (Two-Tailed Critical Values)
Each column is the two-tailed significance level. Read down the df row, across the column for your α. These are the exact published values the calculator interpolates between for non-integer df.
| df | α=.20 | α=.10 | α=.05 | α=.02 | α=.01 |
|---|---|---|---|---|---|
| 1 | 3.078 | 6.314 | 12.706 | 31.821 | 63.657 |
| 2 | 1.886 | 2.920 | 4.303 | 6.965 | 9.925 |
| 3 | 1.638 | 2.353 | 3.182 | 4.541 | 5.841 |
| 4 | 1.533 | 2.132 | 2.776 | 3.747 | 4.604 |
| 5 | 1.476 | 2.015 | 2.571 | 3.365 | 4.032 |
| 6 | 1.440 | 1.943 | 2.447 | 3.143 | 3.707 |
| 7 | 1.415 | 1.895 | 2.365 | 2.998 | 3.499 |
| 8 | 1.397 | 1.860 | 2.306 | 2.896 | 3.355 |
| 9 | 1.383 | 1.833 | 2.262 | 2.821 | 3.250 |
| 10 | 1.372 | 1.812 | 2.228 | 2.764 | 3.169 |
| 11 | 1.363 | 1.796 | 2.201 | 2.718 | 3.106 |
| 12 | 1.356 | 1.782 | 2.179 | 2.681 | 3.055 |
| 13 | 1.350 | 1.771 | 2.160 | 2.650 | 3.012 |
| 14 | 1.345 | 1.761 | 2.145 | 2.624 | 2.977 |
| 15 | 1.341 | 1.753 | 2.131 | 2.602 | 2.947 |
| 16 | 1.337 | 1.746 | 2.120 | 2.583 | 2.921 |
| 17 | 1.333 | 1.740 | 2.110 | 2.567 | 2.898 |
| 18 | 1.330 | 1.734 | 2.101 | 2.552 | 2.878 |
| 19 | 1.328 | 1.729 | 2.093 | 2.539 | 2.861 |
| 20 | 1.325 | 1.725 | 2.086 | 2.528 | 2.845 |
| 21 | 1.323 | 1.721 | 2.080 | 2.518 | 2.831 |
| 22 | 1.321 | 1.717 | 2.074 | 2.508 | 2.819 |
| 23 | 1.319 | 1.714 | 2.069 | 2.500 | 2.807 |
| 24 | 1.318 | 1.711 | 2.064 | 2.492 | 2.797 |
| 25 | 1.316 | 1.708 | 2.060 | 2.485 | 2.787 |
| 26 | 1.315 | 1.706 | 2.056 | 2.479 | 2.779 |
| 27 | 1.314 | 1.703 | 2.052 | 2.473 | 2.771 |
| 28 | 1.313 | 1.701 | 2.048 | 2.467 | 2.763 |
| 29 | 1.311 | 1.699 | 2.045 | 2.462 | 2.756 |
| 30 | 1.310 | 1.697 | 2.042 | 2.457 | 2.750 |
| 40 | 1.303 | 1.684 | 2.021 | 2.423 | 2.704 |
| 60 | 1.296 | 1.671 | 2.000 | 2.390 | 2.660 |
| 120 | 1.289 | 1.658 | 1.980 | 2.358 | 2.617 |
| ∞ | 1.282 | 1.645 | 1.960 | 2.326 | 2.576 |
Which Distribution for Which Job?
The t-distribution is one member of a small toolkit. Picking the wrong one is the most common stats mistake in student reports.
t vs z vs χ² vs F
| Student tBest | Normal (z) | Chi-square (χ²) | F |
|---|
Use the t-distribution whenever you estimate the standard deviation from your sample — which is almost always.
Worked Example: A Researcher's Rejection Region
A psychologist tests whether a training program changes reaction time, with 22 participants (df = 21). She wants a 95% two-tailed test, so α = 0.05 split across two tails. The table gives t* = 2.074 at df = 22 (and 2.080 at df = 21 — the calculator interpolates to 2.080). Her rule: if the observed t-statistic is outside ±2.080, the program's effect is significant. That single number is what turns "the mean dropped 40 ms" into "this is real, not noise."
How to Read a t-Table (Step by Step)
- Find your df down the first column (usually n − 1; if yours isn't listed, use the next smaller row or let the calculator interpolate).
- Pick your α column by the two-tailed significance you need (.05 for 95% confidence, .01 for 99%).
- The intersection is t*. For a one-tailed test at 95% confidence, use the .10 column instead of .05.
- Apply it: reject H₀ if |t| > t*, or build CI = estimate ± t*·SE.
Frequently Asked Questions
What is a t critical value?
It's the cutoff on Student's t-distribution that bounds the rejection region (for tests) or the margin-of-error multiplier (for intervals). At df = 22 and 95% two-tailed, t* ≈ 2.074.
Why does t* depend on degrees of freedom?
Small samples estimate the standard deviation noisily, so the distribution has heavier tails and demands a larger cutoff. As df → ∞ the t-distribution becomes the normal, and t* → z*.
How is a t critical value different from a z critical value?
z* assumes σ is known (or n is huge). t* corrects for estimating σ from the sample. They converge near df = 30 but differ sharply for small samples.
One-tailed vs two-tailed — which should I use?
Two-tailed for "different from" (either direction). One-tailed only for a pre-registered directional claim; its cutoff is smaller because the rejection area sits in one tail.