# Google Sheets BETAINV Function: Syntax, Examples & Tips - URL: https://betteranalyst.com/google-sheets/betainv-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 cumulative beta distribution reaches a given probability. ``` =BETAINV(probability, alpha, beta, [lower_bound], [upper_bound]) ``` Generate FormulaExplain Formula One free generation or explanation per browser, shared across Excel and Google Sheets. Account usage limits apply afterward. Describe the BETAINV you need in plain EnglishGenerate Formula ## Parameters | Parameter | Required | Description | | - | - | - | | **probability** | Yes | The cumulative probability you want the value for. Must be between 0 and 1. | | **alpha** | Yes | The first shape parameter. Must be greater than 0. | | **beta** | Yes | The second shape parameter. Must be greater than 0. | | **lower\_bound** | No | The lower end of the interval. Defaults to 0. | | **upper\_bound** | No | The upper end of the interval. Defaults to 1. | ## What Is BETAINV? BETAINV is the inverse of the cumulative beta distribution. Where [BETADIST](https://betteranalyst.com/google-sheets/betadist-function) answers "what is the probability of being at or below this value?", BETAINV answers the reverse question: "below what value does this much of the probability lie?" In other words, it returns a **percentile** of the beta distribution. This is useful whenever you model a proportion or a bounded quantity with a beta distribution and want a cut-off point, such as the 5th and 95th percentiles of an uncertain conversion rate, or a pessimistic estimate of a task's duration. BETAINV is a legacy name. Its modern equivalent is **BETA.INV**, which takes the same arguments in the same order: `=BETA.INV(probability, alpha, beta, [lower_bound], [upper_bound])`. Both return the same result. ## How BETAINV Works You supply a cumulative probability between 0 and 1 and the distribution's shape parameters. Google Sheets searches for the value *x* such that BETADIST(*x*, alpha, beta) equals that probability. By default the answer lies between 0 and 1. If you pass **lower\_bound** and **upper\_bound**, the answer is scaled into that interval instead. ## Basic Examples ### Median of a beta distribution ``` =BETAINV(0.5, 2, 3) ``` Returns roughly 0.386, the point that splits the distribution in half. Note that this is a little below the mean of 0.4, because Beta(2, 3) is skewed. ### Round-trip check ``` =BETAINV(0.6875, 2, 3) ``` Returns 0.5, because `=BETADIST(0.5, 2, 3)` is 0.6875. ### Percentile on a custom scale ``` =BETAINV(0.9, 2, 5, 10, 40) ``` For a task modelled as taking between 10 and 40 hours, this returns the duration that 90% of outcomes will not exceed. ### A credible interval for a conversion rate With 40 conversions out of 400 visits and a flat prior, the rate follows Beta(41, 361): ``` =BETAINV(0.025, 41, 361) =BETAINV(0.975, 41, 361) ``` These give the lower and upper ends of a 95% interval, roughly 7.4% and 13.3%. ## Common Use Cases - **Experiment reporting**: credible intervals around a conversion or click-through rate - **Estimating**: optimistic and pessimistic durations or costs between known limits - **Simulation**: turn uniform random numbers into beta-distributed values with `=BETAINV(RAND(), alpha, beta)` - **Risk thresholds**: the proportion that will be exceeded only 5% of the time ## Common Errors - **#NUM! from probability**: The probability is below 0 or above 1. - **#NUM! from shape parameters**: alpha or beta is zero or negative. - **#NUM! from bounds**: **lower\_bound** is not less than **upper\_bound**. - **#VALUE!**: An argument is text that cannot be read as a number. ## Tips and Best Practices - Use BETA.INV in new spreadsheets; it is easier to recognise and matches the naming of other modern statistical functions. - Check your answer by feeding it back into BETADIST; you should get your original probability. - Format percentiles of rates as percentages for readability, and round them with [ROUND](https://betteranalyst.com/google-sheets/round-function). - Combine with RAND for Monte Carlo models, but remember that RAND recalculates on every edit. ## Related Functions - [BETADIST](https://betteranalyst.com/google-sheets/betadist-function): cumulative beta probability (the forward direction) - [BINOM.INV](https://betteranalyst.com/google-sheets/binominv-function): inverse for counts of successes - [AVERAGE](https://betteranalyst.com/google-sheets/average-function): the mean of a data set - [ROUND](https://betteranalyst.com/google-sheets/round-function): tidy up probability results - [IF](https://betteranalyst.com/google-sheets/if-function): turn a probability into a decision ## Example use case A product team ran a test that produced 40 sign-ups from 400 visitors. Using =BETAINV(0.025, 41, 361) and =BETAINV(0.975, 41, 361), they report a 95% range for the true sign-up rate instead of a single number. ## 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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