CHISQ.DIST in Excel: Calculate Chi-Square Cumulative Probability or Density

=CHISQ.DIST(x, deg_freedom, cumulative)

All three arguments are required. x is the evaluation point, deg_freedom determines the distribution, and the logical cumulative selects its form. TRUE returns probability at or below x; FALSE returns density at x.

Use nonnegative x and a justified positive degree count. Degrees of freedom are not estimated from data by this function. They depend on the statistical procedure that produced the quantity being evaluated.

A density is a height per unit of x. It is not the probability of observing exactly x in a continuous model. To calculate a probability over an interval, subtract two cumulative values rather than two density values.

Enter 0, 2, 4, 8 and 12 in A2:A6. Put =CHISQ.DIST(A2,4,TRUE) in B2 and fill down. Independent cumulative targets are 0, 0.2642411177, 0.5939941503, 0.9084218056 and 0.9826487348.

For four degrees of freedom, an elementary mathematical check is =1-EXP(-A2/2)*(1+A2/2). Put it in C2 and fill down. It should agree with the corresponding cumulative calculation at these moderate inputs.

The cumulative column increases with x. A decreasing result suggests that a right-tail function was substituted. Keep the degree count fixed while constructing the table; changing it down the rows compares different distributions.

In D2 enter =CHISQ.DIST(A2,4,FALSE) and fill down. Independent density targets are 0, 0.1839397206, 0.1353352832, 0.0366312778 and 0.0074362565.

For this particular degree count, =A2*EXP(-A2/2)/4 checks the density. It rises and then falls, unlike the cumulative function. A density of zero at the lower endpoint here does not establish the same endpoint behavior for every degree count.

Do not label D as “chance of this exact value.” A continuous variable has zero probability at any individual point, even where its density is positive. The cumulative calculation measures accumulated area instead.

The probability between two and eight is =CHISQ.DIST(8,4,TRUE)-CHISQ.DIST(2,4,TRUE), independently 0.6441806879. The remaining probability is distributed below two and above eight.

The upper tail above eight is independently 0.0915781944. At these moderate values, =1-CHISQ.DIST(8,4,TRUE) is a useful check; CHISQ.DIST.RT directly expresses the upper-tail event. For very small upper tails, subtracting a cumulative value near one can lose numerical precision.

Endpoints do not change interval probability for a continuous distribution. This differs from a count distribution, where including or excluding a threshold can change the answer.

Microsoft uses =CHISQ.DIST(0.5,1,TRUE), independently 0.5204998778, and =CHISQ.DIST(2,3,FALSE), independently 0.2075537487. These match its rounded examples and deliberately use different modes and degrees.

A further round-trip check is =CHISQ.DIST(CHISQ.INV(0.9,4),4,TRUE), with mathematical target 0.9. Pass the full inverse result rather than a manually rounded display. The check evaluates consistent inputs, not the suitability of a model for observed data.

Microsoft documents #NUM! for negative x or degrees below one or above 10^10. Noninteger degrees are truncated. For example, its documented conversion makes 4.9 use four degrees; that is not permission to choose an unjustified fractional degree count.

The reference also documents #VALUE! for nonnumeric arguments. Its syntax explicitly permits the logical cumulative argument, so use TRUE or FALSE as shown rather than treating that broad error sentence as excluding logical mode values.

Check the tail, mode and degree count before changing display precision. These worked cases do not certify native endpoint density, text coercion or extreme-tail accuracy. A probability from a justified reference distribution is not the probability that a hypothesis is true.

• 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.DIST 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 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.