# Chi-square calculator

To view the graph of the `χ`^{2} 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 `χ`^{2} value.
In Excel: `p` = `CHIDIST(`

.
`χ`^{2},`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 `χ`^{2} that will give the specified `p`-value for the chi-square distribution.
In Excel: `χ`^{2} = `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 on SPHINCS+, a stateless hash-based signature scheme chosen as one of the first quantum-resistant signature algorithms in NIST's post-quantum cryptography standardization project.

## 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.

## Contact us

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*This page last updated 22 May 2023.*