BINOM.INV in Excel: Find the Smallest Binomial Count Meeting a Probability

=BINOM.INV(trials, probability_s, alpha)

All three arguments are required. trials is the number of Bernoulli trials, probability_s is the success probability on each trial, and alpha is the cumulative probability criterion.

The output is a count, not a probability. It finds the smallest integer k satisfying P(X≤k)≥alpha for the binomial distribution. Because the distribution changes in steps, the cumulative probability at the returned count will often exceed alpha. It is not generally possible to obtain equality.

The same binomial assumptions apply: a fixed number of independent trials, two outcomes per trial and constant success probability. The mathematical definition is independently checked here; it is not a claim about a particular Excel solver algorithm.

Put 6 in A2, 0.5 in A3 and 0.75 in A4. Enter =BINOM.INV(A2,A3,A4) in B2. The documented result and independent target are 4.

Check the two neighboring cumulative values with =BINOM.DIST(3,A2,A3,TRUE) and =BINOM.DIST(4,A2,A3,TRUE). Independent targets are 0.65625 and 0.890625. The first is below 0.75, while the second meets or exceeds it. That pair explains why four, rather than three, is the answer.

The mean count n*p is three. A 75th-percentile count need not equal that mean. Keep expected-count and quantile-count fields separately labeled.

For ten trials with success probability 0.5, place 0.75, 0.90, 0.95 in D2:D4. In E2 enter =BINOM.INV(10,0.5,D2) and fill down.

The independent outputs are 6, 7, 8. The cumulative probabilities at those counts are 0.828125, 0.9453125, 0.9892578125. They meet the respective criteria even though they do not equal them.

Do not interpolate between those integer outputs to invent a fractional number of observed successes. A discrete quantile is deliberately a stepwise result.

Build a table with candidate counts zero through n and cumulative BINOM.DIST values. For a selected alpha, find the first row reaching alpha and compare its count with BINOM.INV. This makes the threshold rule inspectable without treating the inverse as a black box.

For n=10, p=0.5 and alpha=0.95, the cumulative value at seven is 0.9453125, just below the criterion; at eight it is 0.9892578125, above it. A rule using a rounded display of 0.95 at seven would choose the wrong threshold. Compare the unrounded cell values.

If the returned count is zero, there is no valid negative-count predecessor to pass to BINOM.DIST. Treat P(X≤−1)=0 as a mathematical boundary convention for the audit, rather than executing an invalid negative-count formula.

The current Microsoft reference documents #VALUE! for nonnumeric arguments, truncation of noninteger trials and #NUM! for negative trials. Its remarks also state that probability_s and alpha must lie strictly between zero and one, with #NUM! at the endpoints.

This guide’s formulas deliberately use interior probabilities. Endpoint behavior was not native-tested; the reference’s stated restriction is documentation evidence, not a captured Excel result. If a workbook needs deterministic probabilities of zero or one or an endpoint alpha, verify that case in its actual Excel version instead of silently extending these controls.

Validate nonnegative integer trial counts before calculation. Truncating an accidental 10.9 to ten can produce a plausible but unintended result. If a larger alpha appears to give a smaller threshold in an ordinary fixed-parameter table, inspect changed trial/probability references and text-versus-number inputs.

These quantiles describe the selected probability model. They do not guarantee that an operational process will meet a service level or validate an estimated success probability.

• Current documentation: the dedicated Microsoft reference lists Excel for Microsoft 365, Excel for Microsoft 365 for Mac, Excel 2024, Excel 2024 for Mac, Excel 2021, Excel 2021 for Mac, Excel 2019, Excel 2016.
• Introduced: Microsoft’s alphabetical catalog marks BINOM.INV as introduced in Excel 2010. Exact first build and platform-specific introduction dates remain unverified.
• Last functioning version: unknown; a current help listing is not a last-working-build test.
• Evidence checked: October 15, 2026. Official documentation was freshly retrieved; examples were independently calculated. No native Excel, Mac or web-client execution was performed.

• Microsoft BINOM.INV reference.
• Microsoft function catalog and introduction-marker explanation.
• Editorial testing standards.

Examples use English function names and comma separators. Expected numbers are rounded independent mathematical calculations; documented error expectations are labeled as such. They are not captured Excel output. All illustrative data and policies are fictional.