To view the graph of the χ2 distribution for your calculated values, click on the show graph button after doing the calculation.
Compute the p-value for a chi-square distribution
- Handbook of Mathematical Functions by Milton Abramowitz and Irene Stegun
- Numerical Recipes in C by William H. Press, Flannery,Teukolsky and Vetterling
- Schaum's Easy Outline of Probability and Statistics by John Schiller, A. Srinivasan and Murray Spiegel
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The p-value is the area under the chi-square probability density function (pdf) curve
to the right of the specified χ2 value.
In Excel: p =
See Chi-square formulae for more details of the mathematics.
Compute the inverse of the p-value for a chi-square distribution
This is the value of χ2 that will give the specified p-value for the chi-square distribution.
In Excel: χ2 =
Table of selected percentiles
Other statistical calculators
See our Binomial distribution calculator which calculates a table of the binomial distribution for given parameters and displays graphs of the distribution function, f(x), and cumulative distribution function, F(x).
An aside on Post-Quantum Cryptography
-  Abramowitz, M. and IA Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, National Bureau of Standards, Applied Mathematics Series 55, Tenth Printing, 1972.
-  Menezes, AJ, PC van Oorschot and SA Vanstone, Handbook of Applied Cryptography, CRC Press LLC, 1997.
-  NIST/SEMATECH. e-Handbook of Statistical Methods, http://www.itl.nist.gov/div898/handbook/ (accessed January 2013).
-  Press, WH, SA Teukolsky, WT Vetterling and BP Flannery, Numerical Recipes in C: The Art of Scientific Computing, Second Edition, Cambridge University Press, 1992.
-  Spiegel, MR, J Schiller, RA Srinivasan, Schaum's Easy Outline of Probability and Statistics, McGraw-Hill, 2001.
Many thanks to Phil O'Sullivan, statistician extraordinaire, for his help and advice on this subject.
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This page last updated 22 May 2023.