BINOM.DIST Function

Excel Functions › Statistical

Excel 2010+ Statistical

The Excel BINOM.DIST function returns the binomial probability — the chance of a given number of successes in a fixed number of independent yes/no trials, each with the same success probability.


Quick answer:
=BINOM.DIST(6,10,0.5,FALSE) P(exactly 6 of 10) ≈ 0.2051

Syntax

=BINOM.DIST(number_s, trials, probability_s, cumulative)
ArgumentDescription
number_sRequiredThe number of successes you are interested in.
trialsRequiredThe total number of independent trials.
probability_sRequiredThe probability of success on any single trial (0 to 1).
cumulativeRequiredTRUE for the probability of up to number_s successes; FALSE for exactly number_s.

How to use it

BINOM.DIST models repeated yes/no trials — coin flips, pass/fail tests, defect checks. The cumulative switch decides whether you want the chance of an exact count or a running total.

=BINOM.DIST(6,10,0.5,FALSE) // exactly 6 of 10 ≈ 0.2051
=BINOM.DIST(6,10,0.5,TRUE) // 6 or fewer of 10 ≈ 0.8281

With FALSE you get the probability mass at exactly number_s successes; with TRUE you get the cumulative probability of 0 through number_s successes added together.

Need a range of successes? Use BINOM.DIST.RANGE to get the probability of, say, between 4 and 6 successes directly — no subtracting two cumulative values by hand.

Try it: interactive demo

Live demo

Pick a BINOM.DIST example to see the formula and its result.

Result:

Practice workbook

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Frequently asked questions

What does the cumulative argument control?
FALSE returns the probability of exactly number_s successes. TRUE returns the probability of at most number_s successes (0 through number_s, summed).
What is a binomial trial?
An independent experiment with two outcomes (success/failure) and a constant success probability — like a coin flip or a pass/fail inspection. BINOM.DIST assumes every trial is independent and identical.
How do I find the chance of a range of successes?
Either subtract two cumulative BINOM.DIST values, or use BINOM.DIST.RANGE, which takes a lower and upper success count directly.
How is BINOM.DIST different from BINOMDIST?
BINOM.DIST (Excel 2010+) is the modern name; BINOMDIST is the legacy compatibility version. They compute the same probabilities.

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Related functions: BINOM.INV · BINOM.DIST.RANGE · NEGBINOM.DIST · POISSON.DIST · BETA.DIST