Google Sheets BETAINV Function: Syntax, Examples & Tips

What Is BETAINV?

BETAINV is the inverse of the cumulative beta distribution. Where BETADIST 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.
• Combine with RAND for Monte Carlo models, but remember that RAND recalculates on every edit.

Related Functions

• BETADIST: cumulative beta probability (the forward direction)
• BINOM.INV: inverse for counts of successes
• AVERAGE: the mean of a data set
• ROUND: tidy up probability results
• IF: turn a probability into a decision