NORM.S.DIST in ONLYOFFICE: Standard Normal Probabilities and Density

Create a sheet named PackingModel. These are assumed model parameters, not measurements or a fitted dataset. Put Parameter in A1 and Value in B1, then enter:

Keep this input block unchanged while adding formulas in D2 onward. Enter 0.95 as a number, or 95% with percentage formatting, rather than the number 95. The numeric value 0.95 and the percentage 95% represent the same probability; the plain number 95 does not.

A normal model is symmetric and continuous. It is an assumption about a distribution, not proof that actual packing data are normal, independent or stable. The parameters must be chosen or estimated separately. In particular, a standard deviation is not a standard error of a sample mean; substituting one for the other changes the modeled quantity.

The official syntax requires both z and cumulative. TRUE returns the left-tail CDF Φ(z); FALSE returns the density φ(z). A z-score has no units because it divides a difference by a standard deviation measured in the same units.

Although the help describes FALSE as a “probability mass function”, the inspected code computes exp(−z²/2)/√(2π), the continuous normal density. This is not the probability of an exact z value. The area over an interval, obtained from CDF differences, is a probability. Density and CDF answer different questions even when both happen to lie between 0 and 1 for the standard distribution.

In D2 put =(B5-B2)/B3 for z=1. In D3 put =(B4-B2)/B3 for z=−1. Do not pass 510 directly as a z-score; that would mean 510 standard deviations above the mean rather than 510 grams.

The equal densities at −1 and 1 illustrate symmetry. Their CDFs differ because a CDF counts all mass to the left, not just the local height. D6 is the central one-standard-deviation interval probability, approximately 68.27%.

For z=1.96, the independent left-tail target is approximately 0.975002104851780. The upper tail =1-NORM.S.DIST(1.96,TRUE) is about 0.0249978951482204. A two-sided tail outside ±1.96 has target =2*(1-NORM.S.DIST(ABS(1.96),TRUE)), approximately 0.0499957902964409.

The absolute value ensures the threshold is interpreted by distance from zero. Without it, a negative input would give a large upper-tail area and doubling could exceed 1. This formula describes a standard-normal model; calling it a test p-value additionally requires a valid test statistic, null model and appropriate assumptions.

For original units, =NORM.DIST(B5,B2,B3,TRUE) is mathematically the same CDF as D4. For density in grams, divide D9 by B3. The general-normal implementation follows a different numerical helper, so mathematical identity does not imply identical floating-point results in every tail.

NORMSDIST accepts only z and always returns a CDF. It has no FALSE argument for density. NORM.S.DIST is a separate implementation with a mode argument, not simply a punctuation alias. The tagged source uses 0.5+gauss(z) for the cumulative branch and an exponential expression for density. It converts both arguments numerically internally; use explicit logical TRUE/FALSE to match documented intent rather than depending on undocumented numeric mode coercion.

Negative z values are valid. Errors converting arguments propagate. No mean or scale argument exists here, so a zero standard deviation error belongs to the caller’s standardization formula, not to this two-argument syntax itself. If B3 is zero, fix the model rather than interpreting a failed division as a standard-normal result.

The common source comment warns that 0.5+gauss has cancellation trouble in negative tails below −4, whereas NORM.DIST uses an erfc-based CDF helper. Avoid claims of high relative accuracy from these moderate-z examples. Rounding a tiny tail to zero is not evidence that an event is impossible. Array-oriented helpers in the code are not proof of any particular native spill or UI workflow.

These notes were checked on October 18, 2026 against the linked official help and SDKJS tag v10.0.0.169, commit 3679e0375a758d7dc59d31337a45461be3525ed8. The original introduction date and final supported-version endpoint are not established. Current help is not a complete historical compatibility table; Desktop Editors, Docs and mobile releases need separate verification.

Neither the ONLYOFFICE application nor its calculation engine was executed for this guide. Numerical targets in this guide were independently calculated from normal-distribution mathematics; source observations come from reading the pinned implementation. Rounded targets are not promises of identical displayed digits. There are no new native screenshots or observed workbook results.

Examples use English names and comma separators. Adapt separators to the actual editor without changing argument order. Scalar examples do not establish dynamic-array spill, imported-workbook parity, every coercion rule or behavior in older releases. Retain unrounded probabilities for later calculations and format cells for display rather than replacing stored values with rounded text.

• Official NORM.S.DIST help, checked October 18, 2026.
• Pinned calculation and name definitions.
• Pinned normal-distribution helpers.
• NORM.DIST.
• NORM.INV.
• NORM.S.INV.
• NORMSDIST.