t-table (Student's t distribution table)

Rows are degrees of freedom ν, columns are α, the area in the right tail. Each cell is the t with P(T > t) = α. For example, ν = 10 and α = 0.025 give 2.228.

Critical values of t (right-tail α)

$ν$	$0.1$	$0.05$	$0.025$	$0.01$	$0.005$	$0.001$
$1$	$3.078$	$6.314$	$12.706$	$31.821$	$63.657$	$318.309$
$2$	$1.886$	$2.920$	$4.303$	$6.965$	$9.925$	$22.327$
$3$	$1.638$	$2.353$	$3.182$	$4.541$	$5.841$	$10.215$
$4$	$1.533$	$2.132$	$2.776$	$3.747$	$4.604$	$7.173$
$5$	$1.476$	$2.015$	$2.571$	$3.365$	$4.032$	$5.893$
$6$	$1.440$	$1.943$	$2.447$	$3.143$	$3.707$	$5.208$
$7$	$1.415$	$1.895$	$2.365$	$2.998$	$3.499$	$4.785$
$8$	$1.397$	$1.860$	$2.306$	$2.896$	$3.355$	$4.501$
$9$	$1.383$	$1.833$	$2.262$	$2.821$	$3.250$	$4.297$
$10$	$1.372$	$1.812$	$2.228$	$2.764$	$3.169$	$4.144$
$11$	$1.363$	$1.796$	$2.201$	$2.718$	$3.106$	$4.025$
$12$	$1.356$	$1.782$	$2.179$	$2.681$	$3.055$	$3.930$
$13$	$1.350$	$1.771$	$2.160$	$2.650$	$3.012$	$3.852$
$14$	$1.345$	$1.761$	$2.145$	$2.624$	$2.977$	$3.787$
$15$	$1.341$	$1.753$	$2.131$	$2.602$	$2.947$	$3.733$
$16$	$1.337$	$1.746$	$2.120$	$2.583$	$2.921$	$3.686$
$17$	$1.333$	$1.740$	$2.110$	$2.567$	$2.898$	$3.646$
$18$	$1.330$	$1.734$	$2.101$	$2.552$	$2.878$	$3.610$
$19$	$1.328$	$1.729$	$2.093$	$2.539$	$2.861$	$3.579$
$20$	$1.325$	$1.725$	$2.086$	$2.528$	$2.845$	$3.552$
$21$	$1.323$	$1.721$	$2.080$	$2.518$	$2.831$	$3.527$
$22$	$1.321$	$1.717$	$2.074$	$2.508$	$2.819$	$3.505$
$23$	$1.319$	$1.714$	$2.069$	$2.500$	$2.807$	$3.485$
$24$	$1.318$	$1.711$	$2.064$	$2.492$	$2.797$	$3.467$
$25$	$1.316$	$1.708$	$2.060$	$2.485$	$2.787$	$3.450$
$26$	$1.315$	$1.706$	$2.056$	$2.479$	$2.779$	$3.435$
$27$	$1.314$	$1.703$	$2.052$	$2.473$	$2.771$	$3.421$
$28$	$1.313$	$1.701$	$2.048$	$2.467$	$2.763$	$3.408$
$29$	$1.311$	$1.699$	$2.045$	$2.462$	$2.756$	$3.396$
$30$	$1.310$	$1.697$	$2.042$	$2.457$	$2.750$	$3.385$
$40$	$1.303$	$1.684$	$2.021$	$2.423$	$2.704$	$3.307$
$50$	$1.299$	$1.676$	$2.009$	$2.403$	$2.678$	$3.261$
$60$	$1.296$	$1.671$	$2.000$	$2.390$	$2.660$	$3.232$
$80$	$1.292$	$1.664$	$1.990$	$2.374$	$2.639$	$3.195$
$100$	$1.290$	$1.660$	$1.984$	$2.364$	$2.626$	$3.174$
$120$	$1.289$	$1.658$	$1.980$	$2.358$	$2.617$	$3.160$
$\infty$	$1.282$	$1.645$	$1.960$	$2.326$	$2.576$	$3.090$

Formulas

Expression	Equals
$t$	$\frac{x ˉ - μ}{s / n}$
$ν$	$n - 1$
$\overset{x}{ˉ} \pm t_{α /2, ν} \frac{s}{n}$	$CI$
$P (T > t_{α, ν})$	$α$
$t_{1 - α, ν}$	$- t_{α, ν}$

Notes

For a two-tailed test at significance α, read the α/2 column. A 95% confidence interval uses the 0.025 column.

A one-sample mean has n − 1 degrees of freedom. As they grow, the values approach the Z-table: the ∞ row shows 1.960.

Every value is computed and checked against published tables, rounded to three decimals.