BINOM.DIST in Google Sheets: Exact and Cumulative Probability
Use BINOM.DIST in Google Sheets for exact counts, cumulative probabilities and upper tails, with an eight-trial example and independent answer checks.
Verification status: See the evidence and test scope described in this guide. How formula examples are checked
Quick answer: =BINOM.DIST(2,8,0.25,FALSE) gives the probability of exactly two successes in eight independent trials, each with success probability 25%: approximately 0.3114624023. Change the final argument to TRUE to get the probability of two or fewer, approximately 0.6785430908.
Syntax, aliases and the cumulative switch
=BINOM.DIST(num_successes, num_trials, prob_success, cumulative)
| Argument | Meaning |
|---|---|
num_successes |
Count whose probability is required, or the inclusive upper count in cumulative mode |
num_trials |
Fixed number of independent trials |
prob_success |
Same success probability for each trial |
cumulative |
FALSE for exactly the count; TRUE for that count or fewer |
Google’s function catalogue routes BINOM.DIST to BINOMDIST, with the same four argument positions. The latter help page documents FALSE as the default for cumulative; all examples here specify the switch explicitly to make the event unambiguous.
Use numeric whole counts, with 0 ≤ successes ≤ trials, and a probability between 0 and 1. These are the mathematical input requirements of this model. The retrieved help does not give a full rule for fractional-count coercion or every invalid-input error token; do not depend on undocumented rounding.
Set up an eight-contact response model
For this teaching scenario, assume eight independent contacts each have a fixed 25% response chance. Enter:
| Cell | Meaning | Value |
|---|---|---|
| A1 | Parameter | text heading |
| B1 | Value | text heading |
| A2 / B2 | Success count | 2 |
| A3 / B3 | Contact count | 8 |
| A4 / B4 | Response probability | 0.25 |
The numeric inputs go in B2:B4; labels go in A2:A4. Use D2 and D3 for formulas:
=BINOM.DIST(B2,B3,B4,FALSE)
=BINOM.DIST(B2,B3,B4,TRUE)
Expected results:
- D2: 0.31146240234375, or about 31.14624%.
- D3: 0.6785430908203125, or about 67.85431%.
A percentage format changes display, not the stored probability. Do not type 25 into B4 when you intend 25%; enter 0.25 or 25%.
Check the exact probability independently
The number of ways to place two successes among eight trials is 28. Each specific arrangement has probability 0.25² × 0.75⁶. Therefore:
=COMBIN(8,2)*0.25^2*0.75^6
Expected result: 0.31146240234375, matching the documented binomial calculation. This is a mathematical cross-check, not a second execution engine’s certification of Sheets behavior.
Two useful boundary cases within the same model are:
=BINOM.DIST(0,8,0.25,FALSE)
=BINOM.DIST(8,8,0.25,FALSE)
Expected answers: 0.1001129150390625 and 0.0000152587890625. They correspond to eight failures and eight successes, respectively.
Advanced application: at least three responses
“At least three” includes counts 3, 4, 5, 6, 7 and 8. Its complement is at most two:
=1-BINOM.DIST(2,8,0.25,TRUE)
Expected result: 0.3214569091796875, about 32.14569%. Subtracting the cumulative probability at 3 instead would calculate more than three, excluding the count 3 itself.
For an inclusive interval from two through four responses:
=BINOM.DIST(4,8,0.25,TRUE)-BINOM.DIST(1,8,0.25,TRUE)
Expected result: 0.605621337890625. Subtracting the cumulative value at 2 would omit exactly two, an easy off-by-one error.
If a tail probability is extremely small, subtraction from 1 can lose useful floating-point precision. Avoid claiming more reliable digits than the situation supports, and check a suitable direct-tail or specialized numerical method for demanding work.
When the binomial model does not fit
The number of trials is fixed in advance, each trial has two classified outcomes, and the probability stays the same. “Success” can mean an unwanted event such as a defect; it is simply the outcome being counted.
Sampling from a finite stock without replacing items can change the success probability after each draw. Google distinguishes that case through HYPGEOMDIST. Likewise, contacts influenced by one another or trials with substantially different response rates do not meet this simple independent, constant-probability model.
BINOM.DIST does not estimate the 25% input from these eight trials. That estimate must come from a justified source. A precise formula result cannot repair an unjustified probability assumption.
Troubleshooting and error boundaries
- Check whether the question asks for exactly, at most, at least or a range of counts.
- Confirm the trials and successes were not interchanged. Successes cannot exceed trials in the model.
- Enter the probability on the 0–1 scale and use an explicit Boolean switch.
- Keep counts as intentional whole numbers. Do not rely on another product’s truncation behavior.
- If the formula is rejected before calculation, check English function names, the dot in BINOM.DIST, local separators and numeric cell contents.
The official page reviewed does not enumerate precise native errors for every bad input. No particular Sheets error code is asserted here for negative counts, text, fractions or out-of-range probabilities. Validate those inputs and read the cell’s error detail when testing in the target spreadsheet.
Availability and evidence
Both BINOM.DIST and the BINOMDIST spelling are listed for the rolling Google Sheets service as checked October 17, 2026. The reviewed records do not establish an original introduction date or a last functioning numbered version. Do not infer a function’s launch year from the age of a help URL.
NOT_TESTED_IN_GOOGLE_SHEETS: Individual Google help and its catalogue alias mapping were inspected. Worked values were calculated independently with the binomial formula and exact rational arithmetic; no native Sheets session was executed. Exported workbook behavior and invalid-input coercions need separate testing in the destination program.