# Google Sheets CHISQ.INV Function: Syntax, Examples & Tips - URL: https://betteranalyst.com/google-sheets/chisqinv-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 value at which the left-tailed chi-square distribution reaches a given probability. ``` =CHISQ.INV(probability, degrees_freedom) ``` Generate FormulaExplain Formula One free generation or explanation per browser, shared across Excel and Google Sheets. Account usage limits apply afterward. Describe the CHISQ.INV you need in plain EnglishGenerate Formula ## Parameters | Parameter | Required | Description | | - | - | - | | **probability** | Yes | The left-tailed (cumulative) probability, between 0 and 1. | | **degrees\_freedom** | Yes | The number of degrees of freedom. Decimals are truncated; must be at least 1. | ## What Is CHISQ.INV? CHISQ.INV is the inverse of the left-tailed chi-square distribution. You give it a probability *p* and the degrees of freedom, and it returns the value *x* such that a chi-square variable falls at or below *x* with probability *p*. Put simply, it returns a **percentile** of the chi-square distribution. 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.INV Works CHISQ.INV undoes [CHISQ.DIST](https://betteranalyst.com/google-sheets/chisqdist-function) with `cumulative` set to TRUE. If `CHISQ.DIST(x, df, TRUE)` returns *p*, then `CHISQ.INV(p, df)` returns *x*. Because it counts probability from the left, a probability of 0.95 returns a value near the upper end of the distribution, and 0.05 returns a value near the lower end. For right-tail critical values used in most tests, [CHISQ.INV.RT](https://betteranalyst.com/google-sheets/chisqinvrt-function) is more convenient: `CHISQ.INV(1 - α, df)` equals `CHISQ.INV.RT(α, df)`. ## Basic Examples ### 95th percentile with 1 degree of freedom ``` =CHISQ.INV(0.95, 1) ``` Returns about 3.841. ### 5th percentile with 5 degrees of freedom ``` =CHISQ.INV(0.05, 5) ``` Returns about 1.145. Only 5% of the distribution lies below this value. ### The median with 2 degrees of freedom ``` =CHISQ.INV(0.5, 2) ``` Returns about 1.386 (that is, 2 × ln 2). ### Round-trip check ``` =CHISQ.DIST(CHISQ.INV(0.9, 7), 7, TRUE) ``` Returns 0.9. ## Confidence Interval for a Variance A standard use of CHISQ.INV is building a confidence interval for a population variance from a sample. With the sample variance in B1 and sample size in B2, a 95% interval is: ``` Lower: =(B2-1)*B1 / CHISQ.INV(0.975, B2-1) Upper: =(B2-1)*B1 / CHISQ.INV(0.025, B2-1) ``` Take square roots of both limits for an interval on the standard deviation. This assumes the data comes from a roughly normal population. ## Common Use Cases - **Variance and standard deviation intervals**: as shown above - **Lower-tail tests**: is a process less variable than a target? - **Critical values**: when a textbook or method specifies left-tail percentiles - **Simulation**: `=CHISQ.INV(RAND(), df)` generates chi-square random values ## Common Errors - **#NUM!**: **probability** is outside the range 0 to 1, or **degrees\_freedom** is less than 1. - **#VALUE!**: An argument is text. - **Using the wrong tail**: For a 5% significance test on the right tail, use `CHISQ.INV(0.95, df)` or `CHISQ.INV.RT(0.05, df)`, not `CHISQ.INV(0.05, df)`. - **Mixing up probability and significance level**: α = 0.05 corresponds to a left-tail probability of 0.95. ## Tips and Best Practices - Keep the confidence level in a cell and derive the tail probabilities from it, so the whole interval updates when you change it. - Round critical values to three decimals to match printed tables. - Check results against the forward function as a quick audit. ## Related Functions - [CHISQ.DIST](https://betteranalyst.com/google-sheets/chisqdist-function): left-tailed probability or density - [CHISQ.INV.RT](https://betteranalyst.com/google-sheets/chisqinvrt-function): critical value from a right-tail probability - [CHIINV](https://betteranalyst.com/google-sheets/chiinv-function): legacy inverse right-tailed function - [CHISQ.DIST.RT](https://betteranalyst.com/google-sheets/chisqdistrt-function): right-tailed probability (p-value) - [ROUND](https://betteranalyst.com/google-sheets/round-function): round results for reporting ## Example use case A lab manager has 20 measurements with a sample variance of 0.8. Using =(19\*0.8)/CHISQ.INV(0.975, 19) and =(19\*0.8)/CHISQ.INV(0.025, 19), they build a 95% confidence interval for the instrument's true variance. ## 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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