BINOM.DIST in Excel: Exact Counts, Cumulative Probabilities and Tails

=BINOM.DIST(number_s, trials, probability_s, cumulative)

All four arguments are required. number_s is the success count, trials the fixed number of trials, and probability_s the success probability on each trial. cumulative selects TRUE for P(X≤number_s) or FALSE for P(X=number_s).

Microsoft describes a fixed number of independent, two-outcome trials with constant success probability. Define success before calculating: it could mean a passing item, an event being observed, or a selected category. A probability of 0.5 means fifty percent; entering 50 does not mean the same thing.

For integer k from zero through n, the mathematical mass is COMBIN(n,k)*p^k*(1-p)^(n-k). The cumulative result sums those masses from zero through k. These equations explain the examples; Excel’s internal implementation was not inspected or executed.

Enter 6 in A2, 10 in A3 and 0.5 in A4. In B2 enter =BINOM.DIST(A2,A3,A4,FALSE) and in B3 enter =BINOM.DIST(A2,A3,A4,TRUE).

The independent targets are 0.205078125 and 0.828125. The first is one outcome count. The second includes counts zero, one, two, three, four, five and six. A percentage format displays about 20.51% and 82.81% without changing the underlying probabilities.

The official example prints the first result rounded to 0.2050781. Retain the full calculated cell value when using it elsewhere instead of retyping the displayed rounded number.

For at least six successes, use =1-BINOM.DIST(5,10,0.5,TRUE). The independent target is 0.376953125. Subtracting the cumulative probability through five leaves six through ten.

For more than six successes, use =1-BINOM.DIST(6,10,0.5,TRUE), targeting 0.171875. The one-count difference matters because a discrete distribution assigns positive probability to exactly six.

Write the verbal event beside the formula. “At least,” “more than” and “at most” are different conditions and should not share an unlabeled generic probability column.

For three through five successes inclusive, use =BINOM.DIST(5,10,0.5,TRUE)-BINOM.DIST(2,10,0.5,TRUE). Its independent target is 0.568359375.

The lower subtraction stops at two, immediately before the desired lower bound. Subtracting the cumulative result at three would remove the probability of exactly three. When the desired lower limit is zero, use the upper cumulative result directly; do not call BINOM.DIST with a negative count.

To audit a distribution, put counts 0 through 10 in D2:D12 and =BINOM.DIST(D2,$A$3,$A$4,FALSE) in E2, filling down. The independent sum is 1, and the weighted count sum is 5, agreeing with n*p. Those checks catch many reference and parameter mistakes.

Microsoft documents truncation of number_s and trials to integers. Use validated integer counts rather than relying on truncation to repair fractional data. A count outside zero through trials or a probability outside zero through one produces documented #NUM!; nonnumeric count, trials or probability produces documented #VALUE!.

If the outcome probabilities change between trials, or one trial affects another, this simple binomial model is not justified merely because Excel returns a number. Sampling without replacement from a small finite population is a different situation. A formula checks arithmetic, not whether the experiment matches the assumptions.

For very small upper tails, subtracting a cumulative value near one can lose displayed precision. Do not replace such a result with an unsupported exact zero. Extreme-tail numerical accuracy and native coercion were not tested here.

• 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 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.DIST 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.