Google Sheets CHISQ.INV.RT Function: Syntax, Examples & Tips

What Is CHISQ.INV.RT?

CHISQ.INV.RT returns the chi-square critical value for a right-tail probability. If you plan to reject a null hypothesis at the 5% level, CHISQ.INV.RT(0.05, df) tells you how large the test statistic must be. Any statistic above that number is significant.

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.

CHISQ.INV.RT replaces the legacy CHIINV; the two take the same arguments and return the same value.

How CHISQ.INV.RT Works

It is the inverse of CHISQ.DIST.RT. If CHISQ.DIST.RT(x, df) returns p, then CHISQ.INV.RT(p, df) returns x. Smaller probabilities give larger critical values, because you are cutting off a thinner slice of the right tail.

It is also linked to the left-tailed inverse: CHISQ.INV.RT(p, df) = CHISQ.INV(1 - p, df).

Basic Examples

Critical value at 5% with 1 degree of freedom

=CHISQ.INV.RT(0.05, 1)

Returns about 3.841.

Critical value for a 3 × 3 table

=CHISQ.INV.RT(0.05, 4)

Returns about 9.488. A 3 × 3 table has (3 − 1) × (3 − 1) = 4 degrees of freedom.

Exact check with 2 degrees of freedom

=CHISQ.INV.RT(0.05, 2)

Returns about 5.991, which is 2 × ln 20.

Compare a statistic with the critical value

=IF(F10 > CHISQ.INV.RT(0.05, F11), "Reject H0", "Fail to reject H0")

Reference Values

All of these can be reproduced with CHISQ.INV.RT, so you never need a printed table.

Common Use Cases

• Hypothesis testing: decide significance by comparing a statistic with a critical value
• Dashboards: show the threshold a metric must pass, alongside the current statistic
• Teaching: build your own chi-square table for any significance levels
• Process control: alarm limits for variance-based control charts

Common Errors

• #NUM!: probability is outside 0 to 1, or degrees_freedom is below 1.
• #VALUE!: An argument is text.
• Passing the confidence level: Use the significance level (0.05), not the confidence level (0.95). CHISQ.INV.RT(0.95, 1) returns a tiny number near 0.004.
• Wrong degrees of freedom: Goodness-of-fit uses categories − 1; independence tests use (rows − 1) × (columns − 1).

Tips and Best Practices

• Store α in a named cell so all tests in the sheet use the same level.
• Report both the statistic and the critical value; readers can see how close the result was.
• If you just need a p-value, use CHISQ.DIST.RT or CHISQ.TEST instead.

Related Functions

• CHISQ.DIST.RT: right-tailed probability (p-value)
• CHISQ.INV: inverse of the left-tailed distribution
• CHIINV: legacy inverse right-tailed function
• CHISQ.TEST: p-value of a test from observed and expected tables
• IF: turn a p-value into a decision