Zoho Sheet BETAINV Function: Percentile Thresholds and Beta Quantiles

BETAINV(p; α; β; [a]; [b])

The semicolon syntax is reproduced from Zoho’s English reference. Square brackets denote optional arguments and should not be entered. Use numerical probability 0.95, rather than the number 95, for a 95th-percentile request. Formatting the cell as 95% also stores 0.95 in an ordinary percentage-formatted spreadsheet cell; typing the number 95 does not. This is a mathematical input rule, not a tested claim about Zoho’s conversion of text. [Z1]

Documentation caveat: Zoho’s BETAINV page currently describes p as a “Probability density function” and uses 99 as its example input label. That description conflicts with the mathematical definition of inverse cumulative beta probability. Its error table also refers to an x not present in BETAINV’s signature. We therefore explain p as a cumulative probability and explicitly mark the precise treatment of p=0, p=1, p<0, p>1 as requiring native testing, rather than invent Zoho results. [Z1]

Enter the following into a blank worksheet area:

Type =BETAINV(A2;B2;C2) into F2. Expected answer: 0.5. An explicit-bounds version is =BETAINV(A2;B2;C2;D2;E2) and has the same independent expected answer.

Now check the inverse relation using the companion function:

=BETADIST(F2;B2;C2;D2;E2;TRUE)

Independently calculated expected result: 0.6875. The round trip is a useful consistency check if your actual Zoho workbook supports both functions, but we have not run either formula there. A mismatch could arise from accidental parameter reversal, a bound mismatch, numerical precision, or a distinct implementation detail not described in the help article.

Keep alpha=2 in B2 and beta=3 in C2. Place five cumulative probabilities into A5:A9: 0.05, 0.25, 0.50, 0.75, 0.95. In B5 enter:

=BETAINV(A5;$B$2;$C$2)

Copy the formula down through B9. The independent expected results are:

These points summarize a hypothesized probability model. They are not sample quantiles from A5:A9, which contains probabilities, or from an unrelated dataset. The mean of beta(2,3), calculated using the shape parameters, is 2/(2+3)=0.4; it need not equal its median, approximately 0.3857.

Suppose a hypothetical processing duration is modeled on 10 to 30 minutes, with the same beta(2,3) shape. To find the point at which the cumulative probability reaches 68.75%, use:

=BETAINV(0.6875;2;3;10;30)

Independent expected result: 20 minutes. The inverse maps the unit-interval quantile to a+(b-a)*u, where u is the standard beta quantile. With u=0.5, a=10 and b=30, this gives 10+20*0.5=20.

Use =BETAINV(0.95;2;3;10;30) for a hypothetical 95th-percentile completion time. Its expected result is 25.027907485 minutes, not simply 95% of 30. The interval’s location, width and beta shape all matter. Neither percentile is a measured delivery guarantee.

Suppose you observe 20 successes and 5 failures in independent binary trials, and explicitly choose a uniform Beta(1,1) prior for an unknown success probability. Under a Bernoulli likelihood, the posterior is beta(21,6) because you add observed successes and failures to the prior parameters.

Use these two formulas for the endpoints of a 90% equal-tailed posterior credible interval:

=BETAINV(0.05;21;6)
=BETAINV(0.95;21;6)

Independent expected outputs are approximately 0.637405138 and 0.894403551, respectively. Interpretation: given this prior, the stated likelihood model and the observations, the posterior assigns 90% probability to the unknown rate lying between the two endpoints. This is not a 90% frequentist confidence interval and is not automatically appropriate for dependent trials, biased samples or a changing process. The prior must be selected transparently rather than inferred from the function name.

For a quick decision threshold, the posterior probability that the success rate is below 0.70 would be modeled with =BETADIST(0.70;21;6); the companion function’s source is Zoho’s official BETADIST article. [Z2]

Excel: Microsoft’s BETA.INV(probability,alpha,beta,[A],[B]) uses the same conceptual argument roles, but its English reference describes specific boundary and error rules for Excel. Excel’s legacy BETAINV documentation is not interchangeable evidence of what Zoho executes. See Microsoft BETA.INV. [M1]

Google Sheets: Google’s function list contains both BETA.INV(probability,alpha,beta,lower_bound,upper_bound) and the alias-style BETAINV(probability,alpha,beta,lower_bound,upper_bound). This does not establish Zoho-to-Google numeric parity or exactly which optional-bound syntax a specific locale accepts. See Google Sheets function list. [G1]

Zoho Sheet: the five-argument signature is directly documented. The Zoho locale settings help explains how workbook locale can affect numeric and date presentation, but does not separately certify BETAINV parsing in all locales. We found no function-specific first-release date, tier, or parity matrix in the reference or the checked Zoho release listing; do not invent such conditions. [Z1, Z3, Z4]

See Zoho AVERAGE, which calculates an arithmetic mean from actual observations, and Zoho ROUND, which changes the numeric value to a specified number of digits; use number formatting instead when only the display should change.

• [Z1] Zoho Sheet, BETAINV reference — syntax/defaults/documentation ambiguity/errors; checked 2026-10-12.
• [Z2] Zoho Sheet, BETADIST reference — inverse/cumulative relationship and domains; checked 2026-10-12.
• [Z3] Zoho Sheet, locale and calculation settings — locale controls; checked 2026-10-12.
• [Z4] Zoho Sheet, What’s new — screened for releases, not proof of historical availability; checked 2026-10-12.
• [M1] Microsoft, BETA.INV — Excel syntax and version-specific coverage; checked 2026-10-12.
• [G1] Google, Sheets function list — Google-specific names/signatures; checked 2026-10-12.

Validation boundary: Statistical results were independently calculated using SciPy plus algebraic/round-trip checks, not from Zoho Sheet. In particular, malformed probabilities, endpoints, platform availability and display formats were not tested in Zoho Sheet.