CHISQ.INV.RT in Google Sheets: Upper-Tail Critical Values
Find a chi-square upper-tail cutoff in Google Sheets, compare significance levels, check CHIINV compatibility and verify the probability direction.
Verification status: See the evidence and test scope described in this guide. How formula examples are checked
Quick answer: =CHISQ.INV.RT(0.05,2) has expected result 5.9914645471. With two degrees of freedom, the chi-square distribution has 5% of its area above that cutoff. The result is a critical value, not the p-value itself.
Syntax and documented aliases
=CHISQ.INV.RT(probability, degrees_freedom)
Google’s CHISQ.INV.RT documentation identifies probability as the right-tail area and requires it strictly between 0 and 1. degrees_freedom is numeric and at least 1; a fractional value is truncated to an integer. Both arguments are required and numeric.
Google explicitly identifies CHIINV as synonymous. It does not identify CHISQ.INV as the same function: that name uses left-tail probability. No optional arguments or defaults are documented for CHISQ.INV.RT.
The inverse page does not establish an upper bound on degrees of freedom. Do not import a maximum from another chi-square function or a different spreadsheet program without checking that function’s own contract.
Reproducible example: a 5% upper-tail cutoff
Enter this table in A1:B3:
| Row | A: Parameter | B: Value |
|---|---|---|
| 1 | Parameter | Value |
| 2 | Upper-tail area | 0.05 |
| 3 | Degrees of freedom | 2 |
In D2 enter:
=CHISQ.INV.RT(B2,B3)
Expected result: 5.991464547107982. In D3, test the legacy spelling:
=CHIINV(B2,B3)
The documented mathematical expectation is the same cutoff. This alias relationship is verified from Google’s page; it is not inferred from punctuation or Excel naming.
If the input is entered as 5%, Sheets’ numeric probability is 0.05. Entering the number 5 instead would be outside the stated probability domain.
Verify the returned cutoff
Evaluate the right-tail distribution at the result:
=CHISQ.DIST.RT(D2,B3)
Expected result: approximately 0.05, subject to finite numerical precision. This round trip uses the same degree count and the same tail direction.
For precisely two degrees of freedom, the right-tail probability is exp(−x/2). Solving p = exp(−x/2) gives:
=-2*LN(B2)
Expected result: 5.991464547107982. This provides an independent check of the example. Do not use this simplified formula for other degree counts.
The chi-square distribution’s general mathematical definition is given by NIST; the simple logarithm is the two-degree specialization, not an assertion about Sheets’ internal numerical algorithm.
Advanced application: compare several decision thresholds
Put upper-tail probabilities 0.10, 0.05, 0.01 in F2:F4. In G2 enter and fill down:
=CHISQ.INV.RT(F2,$B$3)
| Upper-tail area | Expected cutoff with 2 degrees |
|---|---|
| 0.10 | 4.6051701860 |
| 0.05 | 5.9914645471 |
| 0.01 | 9.2103403720 |
Smaller upper-tail areas require larger cutoffs. This direction check often catches a tail mistake before it reaches a report.
Suppose a suitable test produced statistic 6. It exceeds the 10% and 5% cutoffs above but does not exceed the 1% cutoff. This is a comparison under the chosen reference distribution. A significance level should be selected for the analysis before seeing which choice yields a desired conclusion.
The cutoff does not prove that observations are independent or expected counts are adequate. It also does not supply the degrees of freedom; that must come from the particular test model.
Right-tail and left-tail probabilities are complements
For the same two-degree distribution:
=CHISQ.INV(0.95,2)
has the same expected cutoff 5.9914645471, because 95% below leaves 5% above. By contrast:
=CHISQ.INV.RT(0.95,2)
has expected result 0.1025865888. Here almost all the distribution lies to the right, so the cutoff is small.
Use the left-tail inverse documentation when translating a cumulative percentile. For extremely small right-tail probabilities, calculate the right-tail inverse directly instead of first forming 1−p and risking numerical rounding to 1.
Errors, precision and troubleshooting
- Probability at 0 or 1: These endpoints are outside Google’s stated inverse contract. Do not substitute them for a very small or very large interior probability.
- Wrong probability direction: Label the input “area above cutoff” to avoid mistaking a percentile for an upper tail.
- Fractional degrees: A value such as 2.9 is truncated to 2, so the 5% example still has expected cutoff 5.9914645471. That does not validate a fractional degree model.
- Output formatted as percent: Change it to a number. A cutoff and an area have different meanings.
- Round-trip mismatch: Check the degree reference, cumulative/tail function and whether the cutoff was prematurely rounded.
The cited Google page does not enumerate exact native error codes or every text/coercion case. Its example prose and its displayed numeric solution disagree on one cutoff; these worked examples instead use independently verified original inputs. No conclusion about a native computation is drawn from that prose mismatch.
For a formula-parse failure, confirm English function names, the two dots in CHISQ.INV.RT and your spreadsheet’s argument separator. Numeric validation and statistical validity are separate checks.
Availability and verification
CHISQ.INV.RT and CHIINV are documented in the rolling Google Sheets service. Original introduction date, introduction release and last functioning numbered version were not established. A workbook migration should preserve both the numerical probability and its tail meaning.
NOT_TESTED_IN_GOOGLE_SHEETS. Google function-specific references and the supporting mathematical source were inspected on October 17, 2026. All sample values were independently calculated. No Google Sheets session, native result or screenshot is claimed.
Related published guides: LN, EXP and IF for displaying an explicitly chosen comparison rule.