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Zoho Sheet BINOMDIST Function: Exact and Cumulative Probability Examples

Statistical Intermediate Zoho Sheet

Calculate probabilities of exact or at-most numbers of successes across independent trials in Zoho Sheet.

Verification status: See the evidence and test scope described in this guide. How formula examples are checked

Quick answer: =BINOMDIST(2;10;0.2;FALSE) gives the modeled probability of exactly two successes across ten independent trials when success probability is 0.2 on every trial. The independent expected result is 0.301989888 (about 30.20%). Use TRUE instead of FALSE for two or fewer successes, expected 0.6777995264 (about 67.78%). The distinction between exactly and at most is the most important choice in this function.

A binomial model applies when there are a fixed number of trials, each trial has two outcomes (success/failure), trials are independent, and the chance of success is the same on every trial. Examples can include pass/fail inspections or the count of shoppers who purchase, but a binomial distribution is not automatically justified if observations influence one another or probabilities vary. The official Zoho BINOMDIST guide documents its two calculation modes and the optional default. [Z1]

Availability and version history

  • Introduced: The original introduction version and date are not established by the checked sources.
  • Availability: Currently documented in Zoho Sheet’s rolling web-service help; no numbered release or retirement endpoint is established.
  • Scope: English-language web-service documentation. Mobile and offline-client parity is outside the verified scope.
  • Checked: October 14, 2026, against the official BINOMDIST reference. Documentation check; not a new native test.

Exact documented syntax and argument types

BINOMDIST(k; n; p; [mode])
Argument Required? Definition Documented default
k Yes Numeric count of successes to evaluate; intended as a discrete count from 0 through n None
n Yes Numeric number of independent trials, a nonnegative count None
p Yes Numeric chance of success on each trial, between 0 and 1 inclusive None
mode No 0/FALSE for exactly k successes (probability mass); 1/TRUE for at most k (cumulative) 0

The mode is fourth in Zoho’s English official syntax, and it is the only optional argument in that signature. Omitting mode requests the exact-count form, not the cumulative form. The semicolons follow the official article; locale-dependent workbook settings should not be conflated with a guarantee that another application’s comma-delimited formulas can be pasted unchanged. [Z1, Z4]

A count of successes is mathematically integer-valued. Zoho’s article does not state whether it truncates fractional k or n internally, so this guide intentionally uses whole numbers and marks fraction handling for native verification. Do not infer it from Excel’s documented integer truncation rule.

Worked example 1: quality checks on ten products

Hypothetical scenario: every unit independently has a 20% chance of failing inspection. Here, “success” in the binomial calculation means failure detected, to make the event count explicit. Enter:

Cell Value Meaning
A2 2 Exactly two failures to evaluate
B2 10 Number inspected
C2 0.2 Failure probability per unit

Enter =BINOMDIST(A2;B2;C2;FALSE) in D2. Expected output: 0.301989888.

Independently, the binomial mass calculation is COMBIN(10;2) * 0.2^2 * 0.8^8: there are 45 ways to place two failures among ten positions, and each particular arrangement has probability 0.2^2 * 0.8^8. These assumptions describe a model; you cannot conclude that an observed production line truly has independent, constant defect risk from the formula alone.

Enter =BINOMDIST(A2;B2;C2;TRUE) in E2. Expected output: 0.6777995264, which adds the probabilities of zero, one and two failures.

Event Formula Independent expected probability
Exactly two failures =BINOMDIST(2;10;0.2;FALSE) 0.3019898880
Zero failures =BINOMDIST(0;10;0.2;0) 0.1073741824
One failure =BINOMDIST(1;10;0.2;FALSE) 0.2684354560
At most two =BINOMDIST(2;10;0.2;TRUE) 0.6777995264
At least three =1-BINOMDIST(2;10;0.2;TRUE) 0.3222004736
At least one =1-BINOMDIST(0;10;0.2;TRUE) 0.8926258176

The complement 1 - P(X≤2) gives P(X≥3), not P(X>3). Be precise about inclusive boundaries. The same arithmetic can be evaluated using independent sums of binomial mass terms.

Worked example 2: an easy hand-check

For five independent trials with success probability 0.5, the probability of exactly two successes is:

=BINOMDIST(2;5;0.5)

Expected output: 0.3125. The mode argument is intentionally omitted to demonstrate Zoho’s documented default of zero. A by-hand check is C(5,2) * (0.5)^2 * (0.5)^3 = 10/32 = 0.3125. For two or fewer, use =BINOMDIST(2;5;0.5;TRUE), expected 0.5. The symmetric distribution makes this an especially useful cross-check when entering examples.

Advanced application: a probability-driven inspection rule

Suppose the acceptable limit is no more than two failures among ten, and a planning scenario assumes an independent 20% failure probability. The chance of the inspection passing under that scenario is:

=BINOMDIST(2;10;0.2;TRUE)

That is 67.77995264%, leaving a 32.22004736% probability of triggering an investigation for three or more failures under this model. If your threshold is three, you must change the k argument or use the correct complement. This is a planning probability, not a forecast with a verified manufacturing defect rate.

To compare risk across assumed failure rates, place 0.05, 0.10, 0.20, 0.30, 0.40 in A6:A10 and put:

=1-BINOMDIST(2;10;A6;TRUE)

in B6, then fill through B10. This yields the modeled probability of at least three failed units for each row’s probability. Keep n=10 and the cutoff k=2 fixed so the scenario comparison is meaningful. Such a table helps a manager see sensitivity to a disputed defect-rate estimate; it does not justify choosing a rate without empirical evidence.

For the smallest integer k whose cumulative probability meets a target, Zoho documents CRITBINOM, with syntax CRITBINOM(n; p; a). Use that documented function rather than guessing the correct inverse integer through rounding a normal approximation. [Z2]

Edge cases and diagnostics

Observation Check or action
#NUM! Official Zoho help specifically lists k<0, k>n, or p<0/p>1. Correct the input values. [Z1]
#VALUE! Inspect data types in k, n and p for text or invalid values. [Z1]
#NAME! Use BINOMDIST and the formula syntax applicable to your workbook. [Z1]
#REF! Repair a missing/deleted referenced cell or range. [Z1]
Unexpected cumulative result Ensure TRUE or 1 means at most k; FALSE, 0, or omitted means exactly k. [Z1]
A decimal result in a percentage-formatted cell 0.301989888 displays as about 30.20% when formatted as a percentage; it has not changed mathematically.
p entered as 20 Use 0.20 for 20% (or a numeric percentage-formatted 20% cell), not twenty.
Fractional k/n Article does not specify rounding/truncation of fractions. Use whole-number counts and flag native app verification.
n=0, p=0, p=1, very large n These are meaningful mathematical boundary cases, but exact Zoho handling, precision and error display are not established by this reference. Test before stating application-specific outcomes.
Independent trials assumption fails BINOMDIST may produce a number but not a reliable model. Consider a more appropriate sampling model; the output does not validate the assumptions.

The published table includes generic #N/A! explanations involving lookup operations; it does not substantiate a special BINOMDIST lookup error. [Z1]

Distinguishing Zoho from Excel and Google Sheets

  • Zoho Sheet: documents BINOMDIST(k; n; p; [mode]), with the last argument optional and default zero / FALSE. It explicitly accepts the logical and numeric modes described above. [Z1]
  • Microsoft Excel: modern BINOM.DIST documents BINOM.DIST(number_s,trials,probability_s,cumulative) with cumulative listed as required. It separately describes integer truncation for Excel inputs; Zoho’s help does not establish that same truncation behaviour. [M1]
  • Google Sheets: BINOMDIST documents BINOMDIST(num_successes,num_trials,prob_success,cumulative) with FALSE as the documented default, and its function index lists a BINOM.DIST spelling. Google documentation is not native Zoho execution evidence. [G1, G2]

Availability: The function is present in Zoho’s currently accessible English-language cloud-help documentation. No verified first-release version, paid-tier distinction, historical compatibility matrix or mobile parity statement has been found in this reference or the relevant Zoho update page, so none is asserted. [Z1, Z5] Zoho’s locale settings help documents workbook-level locale controls, not an exhaustive formula separator guarantee. [Z4]

For comparing probabilities with observed counts, see Zoho COUNT and Zoho SUM guides. For a related combinatorial calculation, Zoho COMBIN provides the count of combinations.

  • [Z1] Zoho Sheet, BINOMDIST reference — argument default, modes, errors; checked 2026-10-12.
  • [Z2] Zoho Sheet, CRITBINOM reference — inverse discrete threshold purpose and syntax; checked 2026-10-12.
  • [Z4] Zoho Sheet, locale settings — workbook locale scope; checked 2026-10-12.
  • [Z5] Zoho Sheet, What’s new — release review, not first-support certification; checked 2026-10-12.
  • [M1] Microsoft, Excel BINOM.DIST — required cumulative arg and Excel integer handling; checked 2026-10-12.
  • [G1] Google, Sheets BINOMDIST — Google-specific signature and default; checked 2026-10-12.
  • [G2] Google, Sheets function index — BINOM.DIST alias-style listing; checked 2026-10-12.

Validation boundary: exact and cumulative expected probabilities were calculated with Python/SciPy and independent combinatorial sums. No Zoho Sheet formula was run; there are no native screenshots, demonstrated mobile-version equivalence or validated service-tier claims.