BETA.INV in Google Sheets: Quantiles With Explicit Bounds

=BETA.INV(probability, alpha, beta, lower_bound, upper_bound)

The Google BETA.INV reference documents the probability, two shape parameters and two domain bounds. Supply all five arguments in this guide’s formulas.

• probability: cumulative probability, documented from 0 to 1 inclusive. For example, 25% is 0.25.
• alpha: positive first shape parameter.
• beta: positive second shape parameter, not an interval endpoint.
• lower_bound: lower endpoint of the modeled interval.
• upper_bound: upper endpoint of the modeled interval.

Use an increasing, nonzero-width interval. The mathematical distribution needs its upper endpoint above its lower endpoint.

Omitted bounds remain unresolved: the reviewed Google page lists 1 as the default for both bounds while also showing an example that omits them. Those statements do not identify a usable nondegenerate default interval. This guide does not choose replacement defaults. Every example explicitly provides both bounds, including 0 and 1 for a standard beta distribution.

Suppose a synthetic model for a proportion uses alpha 2 and beta 1. Enter the probabilities 0.04, 0.25 and 0.81 in A2:A4. Put 2 in D1, 1 in E1, 0 in F1 and 1 in G1.

In B2, enter and fill down:

=BETA.INV(A2,$D$1,$E$1,$F$1,$G$1)

A probability of 0.81 does not request an 81% output. It asks for the value below which 81% of the modeled distribution lies. Here that value is 0.9.

The original inputs are deliberately simple enough to check without another spreadsheet function. With these shapes on [0,1], the cumulative probability at x is x squared, so the quantile is the square root of p. The table is therefore checked by =SQRT(A2) filled down. This is a mathematical special case, not a general replacement for BETA.INV.

Consider a bounded synthetic duration model from 10 to 30 minutes. For the same shapes:

=BETA.INV(0.81,2,1,10,30)

Expected result: 28 minutes, because 10+(30-10)*SQRT(0.81) equals 28. The probability and shapes have no time units; the bounds determine the output units.

For comparison, alpha 1 and beta 1 describe a uniform distribution on the interval. These formulas have expected results 15, 20 and 28:

=BETA.INV(0.25,1,1,10,30)
=BETA.INV(0.5,1,1,10,30)
=BETA.INV(0.9,1,1,10,30)

Each follows the independent linear check 10+20*p. Do not assume all beta models have evenly spaced quantiles; the shape-2 example clearly does not.

For a central 80% interval under the shape-2, shape-1 model on [0,1], use:

=BETA.INV(0.1,2,1,0,1)
=BETA.INV(0.9,2,1,0,1)

Expected endpoints are approximately 0.3162277660 and 0.9486832981. The remaining probability is split into 10% in each tail. This is a distribution interval for the chosen model, not automatically a confidence interval for a measured population parameter.

The transformations and special cases follow the bounded beta definition in NIST’s beta-distribution reference. Choosing or estimating the shapes is a separate modeling decision.

Check probability scaling, positive shapes and endpoint order. A value such as 25 is not a valid way to request the 25th percentile. Reversed bounds, identical bounds or nonnumeric inputs need correction before interpreting a result. Exact native error tokens and blank/text coercion were not established by the reviewed help page.

Avoid reducing the argument list when moving this formula between workbooks. The explicit bounds are intentional. Do not substitute another product’s omitted-argument behavior to resolve Google’s documentation conflict.

BETA.INV is currently documented for rolling Google Sheets. Its original introduction date, first release and last functioning numbered version were not established.

NOT_TESTED_IN_GOOGLE_SHEETS. Google and NIST references were inspected on October 17, 2026. All original outputs were independently checked with square-root or linear equations and numerical beta quantiles. No native calculation or UI result is claimed.

Related published guides: SQRT, POWER and ROUND.