Student's $t$ Distribution

(pdf )

The percentage at the top of the table is equal to the AREA to the LEFT of the critical value, $t_{cv}$, found in the table body.

Placeholder image $$ \begin{array} {r|@{\quad}r@{\,}r@{\,}r@{\,}r@{\,}r@{\,}r@{\,}r@{\,}r@{\,}r@{\,}r@{\,}r} \ \\ df&60.0\%&66.7\%&75.0\%&80.0\%&87.5\%&90.0\%&95.0\%&97.5\%&99.0\%&99.5\% &99.9\% \\ \hline \ \\ 1&0.325&0.577&1.000&1.376&2.414&3.078&6.314&12.706&31.821&63.657&318.31 \\ 2&0.289&0.500&0.816&1.061&1.604&1.886&2.920&4.303&6.965&9.925&22.327 \\ 3&0.277&0.476&0.765&0.978&1.423&1.638&2.353&3.182&4.541&5.841&10.215 \\ 4&0.271&0.464&0.741&0.941&1.344&1.533&2.132&2.776&3.747&4.604&7.173 \\ 5&0.267&0.457&0.727&0.920&1.301&1.476&2.015&2.571&3.365&4.032&5.893 \\ 6&0.265&0.453&0.718&0.906&1.273&1.440&1.943&2.447&3.143&3.707&5.208 \\ 7&0.263&0.449&0.711&0.896&1.254&1.415&1.895&2.365&2.998&3.499&4.785 \\ 8&0.262&0.447&0.706&0.889&1.240&1.397&1.860&2.306&2.896&3.355&4.501 \\ 9&0.261&0.445&0.703&0.883&1.230&1.383&1.833&2.262&2.821&3.250&4.297 \\ 10&0.260&0.444&0.700&0.879&1.221&1.372&1.812&2.228&2.764&3.169&4.144 \\ 11&0.260&0.443&0.697&0.876&1.214&1.363&1.796&2.201&2.718&3.106&4.025 \\ 12&0.259&0.442&0.695&0.873&1.209&1.356&1.782&2.179&2.681&3.055&3.930 \\ 13&0.259&0.441&0.694&0.870&1.204&1.350&1.771&2.160&2.650&3.012&3.852 \\ 14&0.258&0.440&0.692&0.868&1.200&1.345&1.761&2.145&2.624&2.977&3.787 \\ 15&0.258&0.439&0.691&0.866&1.197&1.341&1.753&2.131&2.602&2.947&3.733 \\ 16&0.258&0.439&0.690&0.865&1.194&1.337&1.746&2.120&2.583&2.921&3.686 \\ 17&0.257&0.438&0.689&0.863&1.191&1.333&1.740&2.110&2.567&2.898&3.646 \\ 18&0.257&0.438&0.688&0.862&1.189&1.330&1.734&2.101&2.552&2.878&3.610 \\ 19&0.257&0.438&0.688&0.861&1.187&1.328&1.729&2.093&2.539&2.861&3.579 \\ 20&0.257&0.437&0.687&0.860&1.185&1.325&1.725&2.086&2.528&2.845&3.552 \\ 21&0.257&0.437&0.686&0.859&1.183&1.323&1.721&2.080&2.518&2.831&3.527 \\ 22&0.256&0.437&0.686&0.858&1.182&1.321&1.717&2.074&2.508&2.819&3.505 \\ 23&0.256&0.436&0.685&0.858&1.180&1.319&1.714&2.069&2.500&2.807&3.485 \\ 24&0.256&0.436&0.685&0.857&1.179&1.318&1.711&2.064&2.492&2.797&3.467 \\ 25&0.256&0.436&0.684&0.856&1.178&1.316&1.708&2.060&2.485&2.787&3.450 \\ 26&0.256&0.436&0.684&0.856&1.177&1.315&1.706&2.056&2.479&2.779&3.435 \\ 27&0.256&0.435&0.684&0.855&1.176&1.314&1.703&2.052&2.473&2.771&3.421 \\ 28&0.256&0.435&0.683&0.855&1.175&1.313&1.701&2.048&2.467&2.763&3.408 \\ 29&0.256&0.435&0.683&0.854&1.174&1.311&1.699&2.045&2.462&2.756&3.396 \\ 30&0.256&0.435&0.683&0.854&1.173&1.310&1.697&2.042&2.457&2.750&3.385 \\ 35&0.255&0.434&0.682&0.852&1.170&1.306&1.690&2.030&2.438&2.724&3.340 \\ 40&0.255&0.434&0.681&0.851&1.167&1.303&1.684&2.021&2.423&2.704&3.307 \\ 45&0.255&0.434&0.680&0.850&1.165&1.301&1.679&2.014&2.412&2.690&3.281 \\ 50&0.255&0.433&0.679&0.849&1.164&1.299&1.676&2.009&2.403&2.678&3.261 \\ 55&0.255&0.433&0.679&0.848&1.163&1.297&1.673&2.004&2.396&2.668&3.245 \\ 60&0.254&0.433&0.679&0.848&1.162&1.296&1.671&2.000&2.390&2.660&3.232 \\ \infty &0.253&0.431&0.674&0.842&1.150&1.282&1.645&1.960&2.326&2.576&3.090 \end{array} $$