CRITBINOM Function (LibreOffice Calc)
LibreOffice CRITBINOM finds lower-CDF binomial cutoffs, including accepted alpha endpoints, neighbor checks and threshold-count interpretation.
Verification status: Official release source and independently calculated examples for CRITBINOM were reviewed. No new LibreOffice Calc application execution is claimed for this guide; the stated version and example limits still apply. How formula examples are checked
Quick answer: =CRITBINOM(100;0.02;0.95) returns 5. With 100 independent trials and success probability 0.02, five is the smallest count whose cumulative probability reaches at least 95%.
Availability and version history
- Introduced: First release not established. The LibreOffice 3.3 appendix documents the name; that is evidence of presence, not its first introduction.
- Supported in: LibreOffice 26.8.1.1; no final supported release established.
- Scope: Desktop Calc. Argument contracts and boundaries below refer to the cited release.
- Checked: October 14, 2026. Documentation/source and independent mathematics checked; LibreOffice Calc was not run for this guide.
A discrete inverse, not an expected count
CRITBINOM is a binomial quantile. It chooses the smallest integer k with P(X≤k)≥Alpha, given Trials and a constant success probability. Because the distribution is discrete, the attained cumulative probability often exceeds Alpha. Official reference.
The expected count, Trials×Probability, is a different quantity. In the example it is 2, yet the 95th-percentile cutoff is 5. Neither number is a guarantee about the next set of trials.
Syntax and parameter ranges
=CRITBINOM(Trials; Probability; Alpha)
All three arguments are required. Trials must be nonnegative; the release evaluator floors it before calculation. Probability is between 0 and 1 inclusive. Alpha is the desired cumulative threshold, not the per-trial success probability.
LibreOffice 26.8.1.1 accepts 0≤Alpha≤1. Its explicit endpoint branches return 0 for Alpha=0; for Alpha=1 they return Trials, except that Probability=0 returns 0. Use an interior Alpha for cross-product worksheets.
Reproducible reference cases
The expected cutoffs are exact integers, independently calculated from binomial cumulative sums.
| Formula | Expected result, approximately |
|---|---|
=CRITBINOM(100;.5;.1) |
44 |
=CRITBINOM(100;.5;.9) |
56 |
=CRITBINOM(10;.5;.5) |
5 |
=CRITBINOM(100;.02;.95) |
5 |
=CRITBINOM(20;.1;.9) |
4 |
=CRITBINOM(0;.5;.5) |
0 |
=CRITBINOM(10;0;.9) |
0 |
=CRITBINOM(10;1;.9) |
10 |
=CRITBINOM(10;.5;0) |
0 |
=CRITBINOM(10;.5;1) |
10 |
Practical worksheet: a defect-count threshold
Assume a process produces independent items with a known defect probability of 2%. Put 100 in A2, 0.02 in B2 and 0.95 in C2. Use =CRITBINOM(A2;B2;C2) in D2. The expected cutoff is 5 defects.
This describes the stated binomial model, not a complete acceptance-sampling policy. Dependence between items, changing defect rates or estimating the probability from a small pilot sample adds uncertainty that this three-argument function does not account for.
Advanced check: prove the cutoff is the first one
For D2=5, =BINOMDIST(D2;A2;B2;1) is approximately 0.984516359358. At the preceding count, =BINOMDIST(D2-1;A2;B2;1) is approximately 0.949169554630. The first meets the 0.95 target; the second falls short, confirming minimality.
Do not replace this check with a rounded display of the CDF. Near a threshold, displaying 0.94917 as 0.95 can make the previous count look acceptable when its full value is below Alpha. Keep the underlying values for comparisons.
For a table of targets, keep Trials and Probability fixed with absolute cell references and vary only Alpha. Quantiles should be nondecreasing as Alpha increases, but several consecutive Alpha values can share the same integer cutoff.
Boundaries and numerical limits
Probability=0 makes every trial a failure, and Probability=1 makes every trial a success. With an interior Alpha, the corresponding outputs are 0 and Trials. A zero-trial experiment also has a zero count.
The current implementation contains fallback accumulation paths for small probability masses, but these examples are not an exhaustive large-trial precision test. Use explicit integer trial counts and avoid treating a numerical error as a valid cutoff of zero.