CHISQ.INV in Excel: Find a Left-Tail Chi-Square Percentile

=CHISQ.INV(probability, deg_freedom)

Both arguments are required. probability is the left-tail cumulative fraction, and deg_freedom selects the distribution. The output is on the chi-square scale, not itself a probability.

Use 0.9 or 90% for a ninetieth percentile. The number 90 is outside the documented probability range. The examples use strictly interior probabilities so that finite quantiles can be checked without relying on untested endpoint handling.

CHISQ.INV reverses CHISQ.DIST with cumulative=TRUE. It does not reverse density mode. A density curve can have the same height at multiple evaluation points and therefore does not define a percentile inverse.

Enter 0.1, 0.5 and 0.9 in A2:A4. In B2 enter =CHISQ.INV(A2,4) and fill down. Independent targets are 1.0636232168, 3.3566939800 and 7.7794403397.

The middle row is the median of this four-degree distribution. It is not four, even though four is its mathematical mean. The distribution is asymmetric, so substituting its mean for a requested median changes the question.

Label A “left-tail probability” and B “chi-square quantile.” Applying percentage formatting to B would obscure its meaning. A quantile can exceed one without being an invalid probability because it is not a probability.

Enter =CHISQ.DIST(B2,4,TRUE) in C2 and fill down. Independent mathematical targets are 0.1, 0.5 and 0.9.

A second check, specific to four degrees, is =1-EXP(-B2/2)*(1+B2/2). It calculates the corresponding cumulative function without using an inverse function. Keep B’s full stored result; a displayed ten-decimal number is already rounded.

If the round trip does not recover A, check the degree count and cumulative flag before changing tolerances. Small floating-point residuals are different from using the wrong tail or distribution.

The interval between =CHISQ.INV(0.1,4) and =CHISQ.INV(0.9,4) contains 0.8, or 80%, of the specified distribution. Verify this by subtracting the cumulative values at the two endpoints.

Its bounds are approximately 1.0636232168 and 7.7794403397. They are not symmetric around the median. An equal-tail interval allocates equal probability outside its endpoints, not equal distances from a center.

This is a probability interval for the supplied distribution. It is not automatically a confidence interval for an unknown variance or other parameter. Such an interval needs its own derivation and transformation of the statistic.

A 5% upper-tail cutoff is the 95th percentile. =CHISQ.INV(0.95,4) independently targets 9.4877290368, matching =CHISQ.INV.RT(0.05,4).

Using 0.05 in both inverse functions does not give the same threshold. The identical result requires complementary probabilities. Record the intended tail in the worksheet rather than relying on an unlabeled “alpha” cell.

For very small upper-tail probabilities, a direct right-tail inverse avoids first forming a cumulative probability that may round to one. This is a numerical consideration, not a measured native accuracy guarantee.

The reference uses =CHISQ.INV(0.93,1), independently 3.2830202868, and =CHISQ.INV(0.6,2), independently 1.8325814637. Their displayed results are rounded, and they use different degree counts from the main dataset.

Microsoft documents #VALUE! for nonnumeric input and #NUM! for probabilities below zero or above one, or degrees below one or above 10^10. Noninteger degrees are truncated.

The stated probability condition does not exclude zero or one. Mathematically the lower-end quantile is zero and the upper-end limit is unbounded; the dedicated error wording does not establish every actual endpoint result. This guide does not claim a captured native value or error at either endpoint.

Validate positive integer degrees deliberately instead of relying on silent truncation. These independent examples check ordinary inputs, not all native coercion, convergence behavior or numerical limits.

• Current documentation: the dedicated Microsoft reference lists Excel for Microsoft 365, Excel for Microsoft 365 for Mac, Excel 2024, Excel 2024 for Mac, Excel 2021, Excel 2021 for Mac, Excel 2019, Excel 2016, Excel Web App.
• Introduced: Microsoft’s alphabetical catalog marks CHISQ.INV as introduced in Excel 2010. Exact first build and platform-specific introduction dates remain unverified.
• Last functioning version: unknown; a current help listing is not a last-working-build test.
• Evidence checked: October 15, 2026. Official documentation was freshly retrieved; examples were independently calculated. No native Excel, Mac or web-client execution was performed.

• Microsoft CHISQ.INV reference.
• Microsoft function catalog and introduction-marker explanation.
• Editorial testing standards.

Examples use English function names and comma separators. Expected numbers are rounded independent mathematical calculations; documented error expectations are labeled as such. They are not captured Excel output. All illustrative data and policies are fictional.