CHIINV Function (OpenOffice Calc)

• Introduced: First release not established; documented by OpenOffice.org 3.3.
• Supported in: Apache OpenOffice 4.1.16; this is not a final supported version.
• Scope: Desktop Calc with English semicolon-separated formulas. Locale and other-product contracts may differ.
• Checked: October 14, 2026. Eight reference formulas and 1 boundary case were recalculated in Apache OpenOffice 4.1.16 on Linux x86-64, Build 9816 after XLSX import; other explanatory calculations are independent references.

CHIINV returns a chi-square cutoff whose right-tail probability is the supplied Probability. For example, a 0.05 upper-tail probability identifies a cutoff exceeded 5% of the time under the chosen chi-square model. It is not the lower-tail inverse CHISQINV. Release implementation.

=CHIINV(Probability; DegreesOfFreedom)

Exactly two arguments are required. Probability must satisfy 0<Probability≤1 in the inspected 4.1.16 evaluator. DegreesOfFreedom is rounded down and must then be at least 1. Probability=1 corresponds to cutoff 0. Probability=0 is rejected because the limiting cutoff is unbounded; do not replace it with a finite maximum value.

Values below are rounded to twelve decimal places. These eight formulas were also recalculated in Apache OpenOffice 4.1.16 on Linux x86-64, Build 9816 after XLSX import. Saved results agree with the independent references to the checked precision.

=CHIINV(0.05;10) is approximately 18.307038053275. Substituting that unrounded result into =CHIDIST(A2;10) should recover 0.05. A smaller right-tail probability asks for a farther-right cutoff, so inverse values increase as Probability decreases.

For a central 90% interval of the chi-square variable with 10 degrees of freedom, use upper-tail probabilities 0.95 and 0.05. The cutoffs are approximately 3.940299136119 and 18.307038053275. Keep their order explicit: the larger tail probability belongs to the smaller cutoff.

A variance interval is a different calculation from that central interval of a chi-square variable. Under independent normal observations with sample size 11 and sample variance 4, a 90% variance interval uses 10×4 divided by the two chi-square cutoffs in reverse order. Its lower endpoint is =40/CHIINV(0.05;10) and its upper endpoint is =40/CHIINV(0.95;10).

Dividing by the larger cutoff creates the smaller variance bound. This inversion is easy to miss if a worksheet merely labels the inverse probabilities “lower” and “upper.” The formulas depend on the normal-sampling model and on using the sample variance with n−1 degrees of freedom; they are not an automatic interval for arbitrary data or for a standard deviation without a final square root.

The source rejects Probability≤0 or>1 and DegreesOfFreedom<1 after flooring. The source’s inverse solver may return a nonconvergence error if it cannot obtain the requested numerical root. Preserve the error rather than treating it as a valid zero cutoff.

Fractional degrees are floored, so =CHIINV(0.05;2.9) uses 2. Rounding a probability prematurely changes the quantile; retain full precision in worksheet cells and round only the display. Very small probabilities and extreme degrees of freedom require additional accuracy assessment beyond the ordinary examples here.

Observed boundary checks

These additional cases were saved from the same 4.1.16 import session. Error displays are errors even where the ODS numeric attribute is zero.

• Function-specific official evidence
• Pinned evaluator and domain checks

The saved import workbook retained the stated formula identities. A deliberately stale SUM cache became 3 and an uncached SUM became 7, confirming recalculation. The observed scope is the named release and method only; explanatory composite formulas are independently calculated unless specifically listed among the native cases. Other releases, locales and extreme-value limits were not established by these ordinary examples.