NORMSDIST Function (LibreOffice Calc)
LibreOffice NORMSDIST converts z-scores to cumulative standard-normal probabilities. Work through interval, complement and tail examples.
Verification status: Official release source and independently calculated examples for NORMSDIST 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: =NORMSDIST(1) returns approximately 0.841344746069. It gives the area to the left of z=1 under a normal distribution with mean 0 and standard deviation 1.
Availability and version history
- Introduced: First release not established. This name is documented in the LibreOffice 3.3 function appendix; that establishes historical presence, not introduction.
- Supported in: LibreOffice 26.8.1.1. The NORMSDIST/NORMSINV spellings are retained legacy functions, not proven retired functions.
- Scope: Desktop Calc. These examples use English function names, semicolon separators and decimal points.
- Checked: October 14, 2026. Official source/documentation and independent mathematical examples checked; LibreOffice Calc was not run for this guide.
What the standard-normal CDF means
NORMSDIST expects a z-score, which expresses a value’s distance from the mean in standard-deviation units. Negative scores are valid. The CDF increases from 0 toward 1; the midpoint z=0 gives 0.5. Official reference.
The mathematical relationship is Φ(z)=erfc(−z/√2)/2. Symmetry gives Φ(−z)=1−Φ(z), though numerically subtracting a value extremely close to 1 can lose a small tail. A cumulative probability is an area, not the height of the bell curve.
Syntax and equivalent formula
=NORMSDIST(Number)
There is one required argument and no density selector. Use =NORMDIST(Number;0;1;1) for the equivalent general-distribution CDF. To evaluate standard-normal density instead, use =NORMDIST(Number;0;1;0); do not append a second argument to NORMSDIST.
The pinned evaluator calls its cumulative-normal helper with the supplied number. The legacy spelling remains implemented; a preference for a more general function does not establish that NORMSDIST has been retired.
Reproducible reference cases
Enter each formula in a separate cell. The table shows independently calculated values rounded to twelve decimal places.
| Formula | Expected result, approximately |
|---|---|
=NORMSDIST(-3) |
0.001349898032 |
=NORMSDIST(-2) |
0.022750131948 |
=NORMSDIST(-1.96) |
0.024997895148 |
=NORMSDIST(-1) |
0.158655253931 |
=NORMSDIST(0) |
0.5 |
=NORMSDIST(1) |
0.841344746069 |
=NORMSDIST(1.96) |
0.975002104852 |
=NORMSDIST(3) |
0.998650101968 |
Practical worksheet: standardize a measurement
Put an observation of 12 in A2, mean 10 in B2 and SD 2 in C2. In D2 calculate =(A2-B2)/C2, giving z=1. Then use =NORMSDIST(D2) in E2, expected 0.841344746069. C2 must be positive; a zero denominator fails before NORMSDIST receives an input.
This two-step arrangement makes the units and model parameters visible. You can combine it as =NORMSDIST((A2-B2)/C2), but keep the source columns. Do not standardize the mean or SD a second time, and do not pass the raw measurement 12 as though it were already a z-score.
Advanced example: select one or two tails
For z=2, =1-NORMSDIST(2) gives an upper-tail probability of approximately 0.022750131948. The probability beyond either −2 or +2 is =2*(1-NORMSDIST(2)), approximately 0.045500263896. Doubling is justified here by symmetry and by specifying two equally distant tails, not by a universal rule for statistical tests.
The area from −1.96 to 1.96 is =NORMSDIST(1.96)-NORMSDIST(-1.96), approximately 0.950004209704. It is slightly above 0.95 because 1.96 is a rounded cutoff. For a more exact central-95% endpoint, use NORMSINV(0.975).
Numerical history and limits
The release helper directly evaluates an erfc-based normal CDF. A successful ordinary-range comparison does not establish accuracy at every extreme z-score. Versioned cumulative helper.
A displayed 0 or 1 at an extreme score can reflect finite numerical precision. Keep the actual inputs and distinguish a tiny modeled probability from a logically impossible event. The guide’s reference values are mathematical targets, not evidence that the application accepts every text value, locale format or nonfinite input.