Chi-square calculator
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
Recommended reading
- 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
Affiliate disclosure: we get a small commission for purchases made through the above links
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 = CHIDIST(χ2,ν).
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 = CHIINV(p,ν).
Table of selected percentiles
See a table of selected percentiles of the chi-square distribution computed using the Javascript calculation engine behind this page. This is the usual table we see in textbooks. You can see a comparison of our results with those given by Excel.
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
Are you interested in Post-Quantum Cryptography (PQC)? Then see our pages
- SLA-DSA A Stateless Hash-Based Digital Signature Standard now standardised as FIPS.205. We take an in-depth look at the calculations required to compute a specific SLH-DSA signature.
- A simple lattice-based encryption scheme, the foundation of the post-quantum cryptosystem ML-KEM Module-Lattice-based Key-Encapsulation Mechanism Standard (formerly CRYSTALS-Kyber), with Python code.
- CryptoSys PQC is a programmers library that provides support for all three NIST-approved Post Quantum Cryptography (PQC) algorithms: ML-KEM, ML-DSA and SLH-DSA. It has interfaces for C#, VB.NET, C++ (STL), Python, golang and ANSI C, and is free. Download a copy here...
References
- [1] 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.
- [2] Menezes, AJ, PC van Oorschot and SA Vanstone, Handbook of Applied Cryptography, CRC Press LLC, 1997.
- [3] NIST/SEMATECH. e-Handbook of Statistical Methods, http://www.itl.nist.gov/div898/handbook/ (accessed January 2013).
- [4] Press, WH, SA Teukolsky, WT Vetterling and BP Flannery, Numerical Recipes in C: The Art of Scientific Computing, Second Edition, Cambridge University Press, 1992.
- [5] Spiegel, MR, J Schiller, RA Srinivasan, Schaum's Easy Outline of Probability and Statistics, McGraw-Hill, 2001.
Acknowledgements
Many thanks to Phil O'Sullivan, statistician extraordinaire, for his help and advice on this subject.
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This page last updated 10 March 2026.
