BINOM.DIST.RANGE in Excel: Calculate Inclusive Binomial Count Ranges

=BINOM.DIST.RANGE(trials, probability_s, number_s, [number_s2])

trials is the nonnegative number of independent trials. probability_s is the success probability from zero through one. number_s is the required count or lower endpoint. number_s2 is the optional upper endpoint.

When the fourth argument is omitted, the function returns the probability of exactly number_s successes. When supplied, it returns the probability from number_s through number_s2 inclusive. Each count must lie between zero and trials; the upper endpoint must be at least the lower endpoint.

Notice the order: trials comes first here. In BINOM.DIST, the success count comes first. Copying arguments between the two functions without reordering them can produce an error or an entirely different calculation.

Enter 60 in A2, 0.75 in A3 and 48 in A4. In B2 use =BINOM.DIST.RANGE(A2,A3,A4).

The independent target is 0.08397496743, about 8.3975%. Microsoft’s displayed example rounds this to 0.084. The equivalent exact-count formula is =BINOM.DIST(A4,A2,A3,FALSE).

A fourth argument equal to 48 describes the same one-count range. It does not request the probability of at most 48; to include all lower counts, the lower bound must be zero.

Change A4 to 45, put 50 in A5, and enter =BINOM.DIST.RANGE(A2,A3,A4,A5). The independent target is 0.5236297935.

The cumulative equivalent is =BINOM.DIST(A5,A2,A3,TRUE)-BINOM.DIST(A4-1,A2,A3,TRUE). It subtracts the probability through 44 from the probability through 50. Subtracting through 45 would incorrectly exclude exactly 45.

This cumulative equivalent assumes the lower bound is positive. If the lower bound is zero, use only the upper cumulative result; a negative count is outside BINOM.DIST’s documented domain.

For ten independent trials with p=0.5, divide possible counts into 0–2, 3–5 and 6–10. Calculate the three ranges with BINOM.DIST.RANGE.

Independent results are 0.0546875, 0.568359375 and 0.376953125. Their sum is 1 because the intervals are disjoint and cover every possible count. This is a useful audit for a category table.

If the intervals were 0–3 and 3–10, count three would be included twice. If they were 0–2 and 4–10, count three would be omitted. Decide explicitly where each boundary belongs before summing range probabilities.

For the documented sixty-trial example, the expected success count is 60*0.75=45. The probability of the range 45–50 is not 100% merely because the range starts at the expectation. A mean summarizes the model; individual outcomes still vary.

The trials must be independent with a constant success probability. A collection of trials with different success chances is not automatically represented by substituting their average probability. These examples demonstrate the function under a single stated p, rather than estimating p from an observed dataset.

Microsoft documents #NUM! for inputs outside the stated constraints and #VALUE! for nonnumeric arguments. For example, a lower count above trials, a reversed range or a probability above one violates those constraints.

The reference also contains a broad sentence saying numeric arguments are truncated to integers. Read that cautiously: its own worked examples use probability 0.75, so it cannot consistently mean rounding the probability down to zero. This guide uses integer trial/count arguments and retains the stated fractional probability; fractional-count coercion is not relied on or native-verified.

Use percentage formatting for probability output and numeric formatting for counts. A result displayed as 0.524 is rounded, not exactly that decimal. No target-application boundary or numerical-precision testing was performed.

• 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.DIST.RANGE as introduced in Excel 2013. 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.DIST.RANGE 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.