Enter your degrees of freedom and significance level to find a critical t-value for a one-tailed test, two-tailed test, or confidence interval. Explore the matching t-distribution, compare table values, or download a printable reference. Critical values are rounded to three decimal places.
For a one-sample or paired t-test, df = n − 1. Fractional df is supported.
Enter 0.05 for 5%. For two tails, α is the total across both tails.
±2.093
df = 19 · Two-tailed test
Reject H₀ if t < −2.093 or t > 2.093.
Total α = 0.05; each tail = 0.025.
Critical values are rounded to three decimals.
Find df in the first column and use the header for your test type. Values are positive magnitudes; use a negative cutoff for a left-tailed test.
| One tail α | 0.25 | 0.1 | 0.05 | 0.025 | 0.02 | 0.01 | 0.005 | 0.002 | 0.001 |
|---|---|---|---|---|---|---|---|---|---|
| Two tails α | 0.5 | 0.2 | 0.1 | 0.05 | 0.04 | 0.02 | 0.01 | 0.004 | 0.002 |
| Confidence | 50% | 80% | 90% | 95% | 96% | 98% | 99% | 99.6% | 99.8% |
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Hover to preview; click or tap to pin. Use arrow keys to move and Enter to select. Scroll within the table for more rows and columns. ∞ denotes the normal limit.
The lookup accepts fractional df and values up to 1,000,000; it does not round your df to a printed row. The ∞ row is the normal-distribution limit, not a replacement for every df above 100.
Suppose you are conducting a right-tailed one-sample t-test with 12 observations (df = 11) and a significance level of α = 0.05.
qt(1 - 0.05, 11)
# [1] 1.795885For a two-tailed one-sample t-test with 20 observations (df = 19) and a significance level of α = 0.05 (0.025 in each tail):
qt(1 - 0.025, 19)
# [1] 2.093024For a one-sample t-test, df = n − 1. For a paired t-test, n is the number of pairs. A pooled two-sample t-test uses df = n₁ + n₂ − 2. Welch's t-test uses an estimated df that may be fractional.
The t-distribution is used when estimating a mean with an unknown population standard deviation. It is relevant for large samples too. The usual one-sample t procedure assumes independent observations and a normally distributed population for exact small-sample inference.
For a two-sided confidence interval for a mean, use x̄ ± t* × s / √n. The lookup gives t*; the mean confidence interval calculator computes the interval.
For more on tail probabilities and critical values, see NIST's Student's t distribution reference.