# Google Sheets CHISQ.DIST Function: Syntax, Examples & Tips - URL: https://betteranalyst.com/google-sheets/chisqdist-function - Author: Better Analyst Formula Bot is now Better Analyst—same account, more powerful analysis.Formula Bot is now Better Analyst—same account and workflows, with more powerful analysis, dashboards, and automation. [Learn what changed](https://betteranalyst.com/formula-bot-is-now-better-analyst) Returns the left-tailed chi-square probability, or the chi-square density, at a value. ``` =CHISQ.DIST(x, degrees_freedom, cumulative) ``` Generate FormulaExplain Formula One free generation or explanation per browser, shared across Excel and Google Sheets. Account usage limits apply afterward. Describe the CHISQ.DIST you need in plain EnglishGenerate Formula ## Parameters | Parameter | Required | Description | | - | - | - | | **x** | Yes | The value at which to evaluate the distribution. Must be 0 or greater. | | **degrees\_freedom** | Yes | The number of degrees of freedom. Decimals are truncated; must be at least 1. | | **cumulative** | Yes | TRUE returns the cumulative (left-tailed) probability up to **x**; FALSE returns the probability density at **x**. | ## What Is CHISQ.DIST? CHISQ.DIST evaluates the chi-square distribution from the left. With **cumulative** set to TRUE, it returns the probability that a chi-square random variable is **less than or equal to x**. With **cumulative** set to FALSE, it returns the height of the density curve at **x**. The chi-square distribution describes the sum of squares of independent standard normal variables. It only takes non-negative values, is skewed to the right, and has one parameter: **degrees of freedom**. With few degrees of freedom the curve is bunched near zero with a long right tail; as degrees of freedom grow, it shifts right and becomes more symmetric. Its mean equals the degrees of freedom. In practice you meet it most often in hypothesis tests: goodness-of-fit tests (does observed data match an expected pattern?), tests of independence in contingency tables (are two categories related?), and tests about a variance. ## How CHISQ.DIST Works - **cumulative = TRUE** gives the area under the curve from 0 up to **x**. This is a probability between 0 and 1. - **cumulative = FALSE** gives the density at **x**, which is useful for plotting the curve but is not itself a probability. For hypothesis tests you usually want the **right** tail, because large chi-square statistics are the evidence against the null hypothesis. The right-tail probability is `1 - CHISQ.DIST(x, df, TRUE)`, or more directly [CHISQ.DIST.RT](https://betteranalyst.com/google-sheets/chisqdistrt-function). ## Basic Examples ### Left-tailed probability ``` =CHISQ.DIST(3.841, 1, TRUE) ``` Returns about 0.95. With 1 degree of freedom, 95% of the distribution lies at or below 3.841. ### Density at a point ``` =CHISQ.DIST(2, 2, FALSE) ``` Returns about 0.1839. With 2 degrees of freedom the density is ½·e^(−x/2), so at x = 2 it is ½·e^(−1). ### Converting to a p-value ``` =1 - CHISQ.DIST(B5, B6, TRUE) ``` Turns a test statistic in B5 with degrees of freedom in B6 into a right-tailed p-value. ### Probability within a range ``` =CHISQ.DIST(8, 4, TRUE) - CHISQ.DIST(2, 4, TRUE) ``` The chance that a chi-square variable with 4 degrees of freedom falls between 2 and 8. ## Plotting the Distribution List x values from 0 to 20 in column A, then in column B: ``` =CHISQ.DIST(A2, 5, FALSE) ``` Insert a line chart to see the shape of the distribution for 5 degrees of freedom. Repeat with other degrees of freedom to compare curves. ## Common Use Cases - **Variance tests**: the lower tail matters when testing whether a variance is unusually small - **Teaching statistics**: plotting densities and showing how shape changes with degrees of freedom - **Building two-sided tests**: combine left and right tails for a confidence interval on a variance - **Simulation checks**: compare simulated statistics with theoretical probabilities ## Common Errors - **#NUM!**: **x** is negative, or **degrees\_freedom** is less than 1. - **#VALUE!**: An argument is text, or **cumulative** is not TRUE/FALSE. - **Using the wrong tail**: Most chi-square tests need the right tail. Using CHISQ.DIST directly as a p-value will give the opposite of what you expect. - **Treating density as probability**: With FALSE the result is a curve height, not a chance. ## Tips and Best Practices - CHISQ.DIST(x, df, TRUE) + CHISQ.DIST.RT(x, df) always equals 1. Use this to check your formulas. - The inverse of the left-tailed function is [CHISQ.INV](https://betteranalyst.com/google-sheets/chisqinv-function). - Keep degrees of freedom in a labelled cell so readers can see how it was calculated. ## Related Functions - [CHISQ.DIST.RT](https://betteranalyst.com/google-sheets/chisqdistrt-function): right-tailed probability (p-value) - [CHISQ.INV](https://betteranalyst.com/google-sheets/chisqinv-function): inverse of the left-tailed distribution - [CHISQ.INV.RT](https://betteranalyst.com/google-sheets/chisqinvrt-function): critical value from a right-tail probability - [CHISQ.TEST](https://betteranalyst.com/google-sheets/chisqtest-function): p-value of a test from observed and expected tables - [ROUND](https://betteranalyst.com/google-sheets/round-function): round results for reporting ## Example use case A quality engineer wants to know whether the variance of a machine's output is unusually small. After computing the test statistic in B5 with 24 degrees of freedom, =CHISQ.DIST(B5, 24, TRUE) gives the left-tailed probability used in the test. ## Need more help with Google Sheets formulas? Sign up for Better Analyst and get unlimited AI-powered formula generation, explanations, and advanced data analysis. 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