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BINOM.INV Function (LibreOffice Calc)

Statistical Intermediate LibreOffice Calc LibreOffice 4.2

The BINOM.INV function returns the smallest integer x such that the cumulative binomial distribution is greater than or equal to a given probability. It is used for quantile calculations, quality control thresholds, and reliability modeling.

Verification status: Consult the documentation, examples and any stated test scope below. How formula examples are checked

Availability and version history

  • Introduced: LibreOffice 4.2.
  • Availability: Supported in LibreOffice 26.8.1.1, verified against its function registry. This identifies a supported release, not a final working version.
  • Scope: Desktop Calc, using the English function name. Availability in other spreadsheet applications is separate.
  • Checked: 2026-10-14 — function reference; versioned support. Documentation/source check; not a new native test. Existing example-specific test claims below retain their stated scope.
The **BINOM.INV** function returns the **inverse binomial distribution**, meaning it finds the smallest integer *x* such that the cumulative binomial probability **P(X ≤ x)** is at least a given probability *p*. It is widely used in quality control, reliability engineering, and statistical threshold calculations.

What the BINOM.INV Function Does

  • Computes the quantile of a binomial distribution
  • Finds the smallest x where CDF ≥ probability
  • Useful for thresholding, acceptance sampling, and reliability modeling
  • Inverts BINOM.DIST to determine required success counts

Syntax

BINOM.INV(trials; probability_s; alpha)

Arguments

  • trials:
    Number of trials (integer ≥ 0).

  • probability_s:
    Probability of success on each trial (0–1).

  • alpha:
    Target cumulative probability (0–1).

Basic Examples

Find the smallest x such that P(X ≤ x) ≥ 0.5

=BINOM.INV(10; 0.5; 0.5)

Find the 95th percentile of a binomial distribution

=BINOM.INV(20; 0.3; 0.95)

Using cell references

=BINOM.INV(A1; B1; C1)

Advanced Examples

Quality control: maximum acceptable defects

=BINOM.INV(100; 0.01; 0.95)

Reliability: threshold for failure probability

=BINOM.INV(n; p; 0.99)

Compute two‑sided confidence interval

=BINOM.INV(n; p; 0.975) - BINOM.INV(n; p; 0.025)

A/B testing: minimum successes to exceed probability threshold

=BINOM.INV(trials; p; 0.9)

Validate inversion using BINOM.DIST

=BINOM.DIST(BINOM.INV(n; p; α); n; p; TRUE)

Compute quantile for rare‑event approximation

=BINOM.INV(n; p; α)

Edge Cases and Behavior Details

BINOM.INV returns an integer between 0 and trials

Accepts:

  • Integer trials
  • 0 ≤ probability_s ≤ 1
  • 0 ≤ alpha ≤ 1

Behavior details

  • If alpha = 0 → returns 0
  • If alpha = 1 → returns trials
  • Quantile is the smallest x where CDF ≥ alpha
  • Equivalent to scanning cumulative probabilities until threshold is reached

Invalid input → Err:502

BINOM.INV of an error → error propagates

Common Errors and Fixes

Err:502 — Invalid argument

Cause:

  • Non-integer trials
  • probability_s or alpha outside 0–1
  • Non-numeric input

Fix:

  • Wrap with INT()
  • Clamp probability_s and alpha to [0,1]
  • Validate numeric input

Unexpected quantile values

Cause:

  • Misinterpreting CDF vs. PMF
  • alpha too small or too large

Fix:

  • Confirm alpha definition
  • Use BINOM.DIST to inspect CDF

Best Practices

  • Use BINOM.INV for threshold and quantile calculations
  • Validate integer inputs
  • Use BINOM.DIST to verify cumulative behavior
  • Use BINOM.DIST.RANGE for multi‑value probabilities
  • Use POISSON.DIST for rare‑event approximations
BINOM.INV is essential for quality control, reliability thresholds, and any model requiring binomial quantiles or acceptance criteria.
  • Use BINOM.DIST for PMF/CDF
  • Use BINOM.DIST.RANGE for multi‑value ranges
  • Use POISSON.DIST for rare‑event approximations
  • Use NORMINV for normal‑approximation quantiles

By mastering BINOM.INV, you can build precise, reliable statistical and probability‑driven models in LibreOffice Calc.