CHISQ.DIST.RT in Excel: Calculate a Chi-Square Upper-Tail Probability

=CHISQ.DIST.RT(x, deg_freedom)

Both arguments are required. x is a chi-square-scale evaluation point and deg_freedom is the distribution’s degree count. RT selects the right tail. There is no cumulative/density flag in this function.

The input x is not a raw count or a probability. If it comes from a test statistic, calculate that statistic using the appropriate procedure first. CHISQ.DIST.RT does not infer expected counts, degrees of freedom or model assumptions from a data range.

For a continuous model, probability above x and at or above x are equal. A right-tail probability decreases as x increases with degrees held fixed. It is not a posterior probability that a hypothesis is true or false.

Put 0, 2, 4, 8 and 12 in A2:A6. Enter =CHISQ.DIST.RT(A2,4) in B2 and fill down. Independent targets are 1, 0.7357588823, 0.4060058497, 0.0915781944 and 0.0173512652.

For four degrees, the independent expression is =EXP(-A2/2)*(1+A2/2). Put it in C2 and fill down. Unlike a left-tail cumulative column, these values decrease down the table.

The mathematical value at zero is one. These expected values are independent calculations; they are not screenshots or a native Excel run. The simple expression should not be generalized to other degree counts unchanged.

Put category labels A through E in E2:E6 and observed counts 12, 18, 24, 16 and 30 in F2:F6. Put the hypothesized expected count 20 in each cell G2:G6. Both totals are 100.

In H2 enter =(F2-G2)^2/G2 and fill down. Independent contributions are 3.2, 0.2, 0.8, 0.8 and 5. =SUM(H2:H6) gives the statistic 10.

For this illustrative five-category model with fixed probabilities and no parameters estimated from the observations, use four degrees. =CHISQ.DIST.RT(SUM(H2:H6),4) targets 0.0404276820. The expected counts here are all twenty; this demonstration does not endorse applying a chi-square approximation to arbitrary sparse or dependent data.

=CHISQ.INV.RT(0.05,4) has independent threshold 9.4877290368. The example statistic ten exceeds that threshold and has upper-tail probability below 0.05. These are two views of the same mathematical comparison.

Select a procedure and significance level before examining results. The numerical comparison does not prove a cause, validate every assumption or give the probability that the hypothesis is false. A formal analysis needs the appropriate design and interpretation.

If degrees or expected counts are changed, recalculate both the statistic and reference distribution. Merely changing the threshold’s cell label does not update the underlying model.

The dedicated reference evaluates 18.307 with 10 degrees: =CHISQ.DIST.RT(18.307,10) independently gives 0.0500005891, which rounds to the displayed 0.0500006.

The input is already rounded. It should not be expected to give exactly 0.05. To construct an exact mathematical 5% threshold, use the inverse with 0.05 and retain its full stored output.

At moderate values, the left-tail complement =1-CHISQ.DIST(10,4,TRUE) targets the same result as the quick answer. A direct upper-tail function avoids writing a subtraction from a nearly one cumulative result when the required tail is very small.

Microsoft documents #VALUE! for nonnumeric arguments and truncation of noninteger degrees. Degrees below one or above 10^10 produce documented #NUM! errors.

The current dedicated remarks repeat the nonnumeric-argument sentence and do not specify the negative-x error there. Validate x as nonnegative, but do not treat the omission as evidence that negative inputs are valid or import another function’s native error rule.

Check that a probability was not supplied as x and that RT was not dropped from the name. Native error behavior, endpoint details and extreme-tail tolerances were not executed. A displayed zero in a tiny-tail calculation may require a precision investigation rather than an immediate substantive conclusion.

• 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.
• Introduced: Microsoft’s alphabetical catalog marks CHISQ.DIST.RT 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.DIST.RT 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.