Google Sheets CHIINV Function: Syntax, Examples & Tips

What Is CHIINV?

CHIINV returns the value of a chi-square variable whose right-tail probability equals the probability you supply. For a significance level of 0.05, it returns the critical value a test statistic must exceed to be significant.

CHIINV is a legacy function. Google Sheets supports it for compatibility with older spreadsheets. The modern equivalent is CHISQ.INV.RT, which takes identical arguments and returns the same number. Use the modern name in new work.

Chi-Square Background

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 CHIINV Works

CHIINV is the inverse of CHIDIST. If CHIDIST(x, df) returns p, then CHIINV(p, df) returns x.

Despite the general-sounding name, CHIINV works from the right tail. It is not the inverse of the left-tailed cumulative distribution; that job belongs to CHISQ.INV. Mixing the two up turns a 5% critical value into a 95% one.

Basic Examples

5% critical value, 1 degree of freedom

=CHIINV(0.05, 1)

Returns about 3.841.

1% critical value, 5 degrees of freedom

=CHIINV(0.01, 5)

Returns about 15.086.

Modern equivalent

=CHISQ.INV.RT(0.05, 1)

Returns the same 3.841.

Check the inverse

=CHIDIST(CHIINV(0.1, 8), 8)

Returns 0.1.

Legacy Function Map

Common Use Cases

• Updating older workbooks: recognising and replacing legacy formulas
• Significance thresholds: the minimum statistic needed to reject a null hypothesis
• Textbook exercises: matching examples written with the older name

Common Errors

• #NUM!: probability is outside 0 to 1, or degrees_freedom is less than 1.
• #VALUE!: Non-numeric arguments.
• Passing 0.95 instead of 0.05: CHIINV expects the right-tail area, so the significance level goes in, not the confidence level.
• Assuming a left-tail inverse: For left-tail percentiles, use CHISQ.INV.

Tips and Best Practices

• Replacing CHIINV with CHISQ.INV.RT is safe; results are identical.
• Compare a statistic against the critical value with IF to label results automatically.
• Round critical values with ROUND to three decimals for reports.

Related Functions

• CHISQ.INV.RT: critical value from a right-tail probability
• CHIDIST: legacy right-tailed probability
• CHITEST: legacy chi-square test
• CHISQ.INV: inverse of the left-tailed distribution
• ROUND: round results for reporting