Chi-square distribution table (χ² table)

Rows are degrees of freedom ν, columns are α, the area in the right tail. Each cell is the χ² with P(χ² > x) = α. For example, ν = 10 and α = 0.05 give 18.307.

Critical values of χ² (right-tail α)

$ν$	$0.995$	$0.99$	$0.975$	$0.95$	$0.9$	$0.1$	$0.05$	$0.025$	$0.01$	$0.005$
$1$	$0.000$	$0.000$	$0.001$	$0.004$	$0.016$	$2.706$	$3.841$	$5.024$	$6.635$	$7.879$
$2$	$0.010$	$0.020$	$0.051$	$0.103$	$0.211$	$4.605$	$5.991$	$7.378$	$9.210$	$10.597$
$3$	$0.072$	$0.115$	$0.216$	$0.352$	$0.584$	$6.251$	$7.815$	$9.348$	$11.345$	$12.838$
$4$	$0.207$	$0.297$	$0.484$	$0.711$	$1.064$	$7.779$	$9.488$	$11.143$	$13.277$	$14.860$
$5$	$0.412$	$0.554$	$0.831$	$1.145$	$1.610$	$9.236$	$11.070$	$12.833$	$15.086$	$16.750$
$6$	$0.676$	$0.872$	$1.237$	$1.635$	$2.204$	$10.645$	$12.592$	$14.449$	$16.812$	$18.548$
$7$	$0.989$	$1.239$	$1.690$	$2.167$	$2.833$	$12.017$	$14.067$	$16.013$	$18.475$	$20.278$
$8$	$1.344$	$1.646$	$2.180$	$2.733$	$3.490$	$13.362$	$15.507$	$17.535$	$20.090$	$21.955$
$9$	$1.735$	$2.088$	$2.700$	$3.325$	$4.168$	$14.684$	$16.919$	$19.023$	$21.666$	$23.589$
$10$	$2.156$	$2.558$	$3.247$	$3.940$	$4.865$	$15.987$	$18.307$	$20.483$	$23.209$	$25.188$
$11$	$2.603$	$3.053$	$3.816$	$4.575$	$5.578$	$17.275$	$19.675$	$21.920$	$24.725$	$26.757$
$12$	$3.074$	$3.571$	$4.404$	$5.226$	$6.304$	$18.549$	$21.026$	$23.337$	$26.217$	$28.300$
$13$	$3.565$	$4.107$	$5.009$	$5.892$	$7.042$	$19.812$	$22.362$	$24.736$	$27.688$	$29.819$
$14$	$4.075$	$4.660$	$5.629$	$6.571$	$7.790$	$21.064$	$23.685$	$26.119$	$29.141$	$31.319$
$15$	$4.601$	$5.229$	$6.262$	$7.261$	$8.547$	$22.307$	$24.996$	$27.488$	$30.578$	$32.801$
$16$	$5.142$	$5.812$	$6.908$	$7.962$	$9.312$	$23.542$	$26.296$	$28.845$	$32.000$	$34.267$
$17$	$5.697$	$6.408$	$7.564$	$8.672$	$10.085$	$24.769$	$27.587$	$30.191$	$33.409$	$35.718$
$18$	$6.265$	$7.015$	$8.231$	$9.390$	$10.865$	$25.989$	$28.869$	$31.526$	$34.805$	$37.156$
$19$	$6.844$	$7.633$	$8.907$	$10.117$	$11.651$	$27.204$	$30.144$	$32.852$	$36.191$	$38.582$
$20$	$7.434$	$8.260$	$9.591$	$10.851$	$12.443$	$28.412$	$31.410$	$34.170$	$37.566$	$39.997$
$21$	$8.034$	$8.897$	$10.283$	$11.591$	$13.240$	$29.615$	$32.671$	$35.479$	$38.932$	$41.401$
$22$	$8.643$	$9.542$	$10.982$	$12.338$	$14.041$	$30.813$	$33.924$	$36.781$	$40.289$	$42.796$
$23$	$9.260$	$10.196$	$11.689$	$13.091$	$14.848$	$32.007$	$35.172$	$38.076$	$41.638$	$44.181$
$24$	$9.886$	$10.856$	$12.401$	$13.848$	$15.659$	$33.196$	$36.415$	$39.364$	$42.980$	$45.559$
$25$	$10.520$	$11.524$	$13.120$	$14.611$	$16.473$	$34.382$	$37.652$	$40.646$	$44.314$	$46.928$
$26$	$11.160$	$12.198$	$13.844$	$15.379$	$17.292$	$35.563$	$38.885$	$41.923$	$45.642$	$48.290$
$27$	$11.808$	$12.879$	$14.573$	$16.151$	$18.114$	$36.741$	$40.113$	$43.195$	$46.963$	$49.645$
$28$	$12.461$	$13.565$	$15.308$	$16.928$	$18.939$	$37.916$	$41.337$	$44.461$	$48.278$	$50.993$
$29$	$13.121$	$14.256$	$16.047$	$17.708$	$19.768$	$39.087$	$42.557$	$45.722$	$49.588$	$52.336$
$30$	$13.787$	$14.953$	$16.791$	$18.493$	$20.599$	$40.256$	$43.773$	$46.979$	$50.892$	$53.672$
$40$	$20.707$	$22.164$	$24.433$	$26.509$	$29.051$	$51.805$	$55.758$	$59.342$	$63.691$	$66.766$
$50$	$27.991$	$29.707$	$32.357$	$34.764$	$37.689$	$63.167$	$67.505$	$71.420$	$76.154$	$79.490$
$60$	$35.534$	$37.485$	$40.482$	$43.188$	$46.459$	$74.397$	$79.082$	$83.298$	$88.379$	$91.952$
$70$	$43.275$	$45.442$	$48.758$	$51.739$	$55.329$	$85.527$	$90.531$	$95.023$	$100.425$	$104.215$
$80$	$51.172$	$53.540$	$57.153$	$60.391$	$64.278$	$96.578$	$101.879$	$106.629$	$112.329$	$116.321$
$90$	$59.196$	$61.754$	$65.647$	$69.126$	$73.291$	$107.565$	$113.145$	$118.136$	$124.116$	$128.299$
$100$	$67.328$	$70.065$	$74.222$	$77.929$	$82.358$	$118.498$	$124.342$	$129.561$	$135.807$	$140.169$

Formulas

Expression	Equals
$χ^{2}$	$\sum \frac{( O - E ) ^{2}}{E}$
$ν (goodness of fit)$	$k - 1$
$ν (contingency table)$	$(r - 1) (c - 1)$
$P (χ^{2} > χ_{α, ν}^{2})$	$α$

Notes

A chi-square test rejects the null hypothesis when the statistic exceeds the table value, so almost every test uses the right tail, α = 0.05 or 0.01.

The 0.995 to 0.90 columns are for the left tail, used for example in a confidence interval for a variance.

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