BINOM.DIST function

Returns the probability of a specific number of successes occurring in a fixed number of independent binary trials with a known probability.

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

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Arguments

How BINOM.DIST reads its arguments
number_srequiredtrialsrequiredprobability_srequiredcumulativerequiredBINOM.DIST →
ArgumentRequiredDescription
number_sRequiredThe number of successes you want to find the probability for; must be a non-negative integer and cannot exceed trials.
trialsRequiredThe total number of independent trials; must be a positive integer representing the sample size.
probability_sRequiredThe probability of success on each individual trial; must be a decimal between 0 and 1 inclusive (e.g., 0.35 for 35%).
cumulativeRequiredIf TRUE, returns cumulative probability P(X ≤ number_s); if FALSE, returns the probability of exactly that count P(X = number_s).

Returns

A decimal probability value between 0 and 1, representing the likelihood of the outcome.

Availability

Excel: All · Google Sheets: Supported

Worked examples

1. Probability that exactly 5 vehicles need repairs

VehicleOdometerService DateCostGarage
Van-01450002024-01-15250MainGarage
Van-02670002024-02-20180SideGarage
Van-03330002024-01-10150MainGarage
Van-04780002024-03-05320MainGarage
Van-05520002024-02-14220SideGarage
Van-06890002024-03-18400MainGarage
Van-07410002024-01-22170SideGarage
Van-08950002024-04-01450MainGarage
=BINOM.DIST(5, 8, 0.35, FALSE)

Result: 0.2786

Out of 8 vehicles in the fleet, historical data shows 35% require repairs each service cycle. BINOM.DIST with cumulative=FALSE calculates the exact probability that exactly 5 vehicles will need repairs. This helps maintenance planners estimate parts inventory and crew scheduling.

2. Probability that at most 3 vehicles fail initial inspection

VehicleOdometerService DateCostGarage
Van-01450002024-01-15250MainGarage
Van-02670002024-02-20180SideGarage
Van-03330002024-01-10150MainGarage
Van-04780002024-03-05320MainGarage
Van-05520002024-02-14220SideGarage
Van-06890002024-03-18400MainGarage
Van-07410002024-01-22170SideGarage
Van-08950002024-04-01450MainGarage
=BINOM.DIST(3, 8, 0.4, TRUE)

Result: 0.5941

With a 40% failure rate on initial inspection and 8 vehicles to check, cumulative=TRUE sums the probabilities of 0, 1, 2, or 3 failures. The result 0.5941 means there's about a 59% chance that at most 3 will fail, informing whether today's maintenance window is adequate.

3. Probability that exactly 6 vehicles pass safety inspection

VehicleOdometerService DateCostGarage
Van-01450002024-01-15250MainGarage
Van-02670002024-02-20180SideGarage
Van-03330002024-01-10150MainGarage
Van-04780002024-03-05320MainGarage
Van-05520002024-02-14220SideGarage
Van-06890002024-03-18400MainGarage
Van-07410002024-01-22170SideGarage
Van-08950002024-04-01450MainGarage
=BINOM.DIST(6, 8, 0.8, FALSE)

Result: 0.2936

Based on an 80% historical pass rate and 8 vehicles being tested, this calculates the probability of exactly 6 passing. The non-cumulative result helps fleet managers assess whether a particular inspection run was typical or unusual.

Common errors

Which BINOM.DIST error are you seeing?
BINOM.DIST returned an error#NUM!
Use only decimal values between 0 and 1. Convert percentages: 35% becomes 0.35, not 35. Check for formula errors that might produce out-of-range results.
#NUM!
Ensure number_s ≤ trials and number_s ≥ 0. If you want to check 8 vehicles, number_s must be between 0 and 8 inclusive.
#VALUE!
Convert all arguments to numeric values. Use VALUE() if needed to convert text numbers, or ensure your data references point to actual numeric cells, not text-formatted cells.
ErrorWhy it happensHow to fix it
#NUM!The probability_s argument is outside the valid range [0, 1]. For example, using 1.5 (150%) or -0.2 (-20%) violates the mathematical definition of probability.Use only decimal values between 0 and 1. Convert percentages: 35% becomes 0.35, not 35. Check for formula errors that might produce out-of-range results.
#NUM!The number_s argument exceeds trials or is negative. You cannot have more successes than total trials; asking for 9 successes out of 8 trials is impossible.Ensure number_s ≤ trials and number_s ≥ 0. If you want to check 8 vehicles, number_s must be between 0 and 8 inclusive.
#VALUE!One or more arguments are text, dates, or other non-numeric types. For instance, passing "0.35" (text) instead of 0.35 (number), or a date in the probability_s position.Convert all arguments to numeric values. Use VALUE() if needed to convert text numbers, or ensure your data references point to actual numeric cells, not text-formatted cells.

Tips and when to use something else

  • Use cumulative=FALSE for 'exactly' questions ("what's the probability of exactly 5 repairs?") and cumulative=TRUE for 'at most' questions ("what's the probability of at most 3 failures?").
  • BINOM.DIST applies only to binary outcomes with constant probability across trials. For continuous data like repair costs, use NORM.DIST or AVERAGE instead.
  • If you only need to count how many vehicles passed or failed without calculating probability, use COUNTIF with a criterion (e.g., cost >250) rather than BINOM.DIST.
  • Results near 0 may display as 0 in cells with default formatting; increase decimal places to see the true small probability, or multiply by 1,000,000 to verify.

Related functions

COUNTIFCounts cells in a range that meet a specific criterion, returning a number — use it to tally matching rows like employee counts by department.COUNTIFSCOUNTIFS counts rows where all criteria are met across multiple ranges, useful for filtering inventory and finding matches across conditions.NORM.DISTReturns the probability of a value in a normal distribution, or the probability density at that specific value.AVERAGEAVERAGE calculates the arithmetic mean of numbers, ignoring text and logical values; returns a single numeric value representing the average.

Frequently asked questions

What's the difference between BINOM.DIST with cumulative=TRUE versus FALSE?
FALSE calculates P(X = number_s), the probability of exactly that count occurring. TRUE calculates P(X ≤ number_s), the cumulative probability of that count or fewer. For example, if checking 8 vehicles with FALSE, you get the probability of exactly 5 repairs; with TRUE, you get the probability of 0, 1, 2, 3, 4, or 5 repairs combined.
Can I use BINOM.DIST for maintenance categories like 'no repair,' 'minor repair,' or 'major repair'?
No. BINOM.DIST requires exactly two mutually exclusive outcomes per trial (success/failure, pass/fail, repair/no repair). If your fleet has three or more repair categories, use COUNTIFS to count each category separately, or consider a more complex statistical model.
How do I choose the right probability_s value for my fleet data?
Base it on historical rates from your maintenance log. If 140 out of 400 recent services resulted in repairs, set probability_s = 140/400 = 0.35. Alternatively, if you're testing a hypothesis (e.g., 'if my new maintenance schedule reduces repairs to 25%'), use that theoretical value directly as probability_s.
Why does my BINOM.DIST formula return 0 or a very tiny number?
Certain outcomes are mathematically very unlikely. If you request the probability of all 8 vehicles passing with only a 5% pass rate, the result is 0.05^8 ≈ 0.0000000039, which displays as 0 in standard cell formatting. Increase your cell's decimal places (right-click, Format Cells) to see the true value, or multiply by 10^8 to inspect it as an integer.

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Reviewed 2026-09-17