Google Sheets CHISQ.DIST Function: Syntax, Examples & Tips

What Is CHISQ.DIST?

CHISQ.DIST evaluates the chi-square distribution from the left. With cumulative set to TRUE, it returns the probability that a chi-square random variable is less than or equal to x. With cumulative set to FALSE, it returns the height of the density curve at x.

The chi-square distribution describes the sum of squares of independent standard normal variables. It only takes non-negative values, is skewed to the right, and has one parameter: degrees of freedom. With few degrees of freedom the curve is bunched near zero with a long right tail; as degrees of freedom grow, it shifts right and becomes more symmetric. Its mean equals the degrees of freedom.

In practice you meet it most often in hypothesis tests: goodness-of-fit tests (does observed data match an expected pattern?), tests of independence in contingency tables (are two categories related?), and tests about a variance.

How CHISQ.DIST Works

• cumulative = TRUE gives the area under the curve from 0 up to x. This is a probability between 0 and 1.
• cumulative = FALSE gives the density at x, which is useful for plotting the curve but is not itself a probability.

For hypothesis tests you usually want the right tail, because large chi-square statistics are the evidence against the null hypothesis. The right-tail probability is 1 - CHISQ.DIST(x, df, TRUE), or more directly CHISQ.DIST.RT.

Basic Examples

Left-tailed probability

=CHISQ.DIST(3.841, 1, TRUE)

Returns about 0.95. With 1 degree of freedom, 95% of the distribution lies at or below 3.841.

Density at a point

=CHISQ.DIST(2, 2, FALSE)

Returns about 0.1839. With 2 degrees of freedom the density is ½·e^(−x/2), so at x = 2 it is ½·e^(−1).

Converting to a p-value

=1 - CHISQ.DIST(B5, B6, TRUE)

Turns a test statistic in B5 with degrees of freedom in B6 into a right-tailed p-value.

Probability within a range

=CHISQ.DIST(8, 4, TRUE) - CHISQ.DIST(2, 4, TRUE)

The chance that a chi-square variable with 4 degrees of freedom falls between 2 and 8.

Plotting the Distribution

List x values from 0 to 20 in column A, then in column B:

=CHISQ.DIST(A2, 5, FALSE)

Insert a line chart to see the shape of the distribution for 5 degrees of freedom. Repeat with other degrees of freedom to compare curves.

Common Use Cases

• Variance tests: the lower tail matters when testing whether a variance is unusually small
• Teaching statistics: plotting densities and showing how shape changes with degrees of freedom
• Building two-sided tests: combine left and right tails for a confidence interval on a variance
• Simulation checks: compare simulated statistics with theoretical probabilities

Common Errors

• #NUM!: x is negative, or degrees_freedom is less than 1.
• #VALUE!: An argument is text, or cumulative is not TRUE/FALSE.
• Using the wrong tail: Most chi-square tests need the right tail. Using CHISQ.DIST directly as a p-value will give the opposite of what you expect.
• Treating density as probability: With FALSE the result is a curve height, not a chance.

Tips and Best Practices

• CHISQ.DIST(x, df, TRUE) + CHISQ.DIST.RT(x, df) always equals 1. Use this to check your formulas.
• The inverse of the left-tailed function is CHISQ.INV.
• Keep degrees of freedom in a labelled cell so readers can see how it was calculated.

Related Functions

• CHISQ.DIST.RT: right-tailed probability (p-value)
• CHISQ.INV: inverse of the left-tailed distribution
• CHISQ.INV.RT: critical value from a right-tail probability
• CHISQ.TEST: p-value of a test from observed and expected tables
• ROUND: round results for reporting