NORM.DIST in Excel: Separate Normal Probabilities From Density Heights

=NORM.DIST(x, mean, standard_dev, cumulative)

All four arguments are required. x is the evaluation point, mean the arithmetic mean, and standard_dev a positive standard deviation. These three quantities must use compatible units. cumulative selects TRUE for the lower-tail probability P(X≤x), or FALSE for the probability density.

The standardization is z=(x−mean)/standard_dev. The cumulative result is the standard normal cumulative probability at z. The density includes an additional division by standard_dev, so changing scale changes the height as well as the position of the curve.

A continuous normal model assigns zero probability to any one exact value. Probabilities are areas over intervals, not individual density heights. The official example table uses the phrase “probability mass” for its FALSE row; its syntax and density definition establish that this is a density function instead.

Enter 42 in A2, 40 in A3 and 1.5 in A4. In B2 enter =NORM.DIST(A2,A3,A4,TRUE). In B3 use the same formula with FALSE.

Independent targets are 0.9087887803 and 0.1093400498. About 90.8789% of the modeled values lie at or below 42. The second output is a density measured in reciprocal x-units; it is not a 10.934% chance of exactly 42.

The z-score is 1.3333333333. Computing the standard normal cumulative probability at that z gives the same mathematical lower-tail target. Keep the unrounded z-score in a cell if carrying out that cross-check.

For mean 100 and standard deviation 15, use =NORM.DIST(115,100,15,TRUE)-NORM.DIST(85,100,15,TRUE). The independent target is 0.6826894921, the probability of falling within one standard deviation of the mean.

For a continuous model, including or excluding the exact endpoints does not change the probability. This differs from discrete count distributions, where removing one endpoint can remove a positive mass.

The upper-tail probability above 115 is =1-NORM.DIST(115,100,15,TRUE), independently 0.1586552539. Do not use FALSE as an upper-tail switch; it changes the output to density.

Suppose x, mean and standard deviation are all converted from meters to centimeters by multiplying by 100. The cumulative probability remains unchanged because z is unchanged. The density per centimeter becomes one hundredth of the density per meter.

For example, the original 42,40,1.5 calculation and =NORM.DIST(4200,4000,150,TRUE) have the same cumulative target. The corresponding FALSE result becomes approximately 0.001093400498. This check explains why a density height cannot be interpreted as a unit-free probability.

A normal calculation needs a stated mean and standard deviation. Supplying estimates from observations does not prove that their population is normally distributed or that the estimates are sufficiently precise for a decision.

Label a parameter table with its source and units. Keep a graph or separate diagnostic analysis if shape matters. A normal distribution extends without bound in both directions, which may be inappropriate for some strictly positive measurements, even if the central part of the data looks symmetric.

Microsoft documents #VALUE! for nonnumeric mean or standard_dev and #NUM! for standard_dev≤0. A zero standard deviation is not a valid input to this function. Its dedicated remarks do not enumerate every possible coercion of x or cumulative; those cases were not native-tested.

Check parentheses in a manual z-score: (x-mean)/standard_dev is not x-mean/standard_dev. A wildly small tail can result from mixing units. Subtracting a cumulative value near one may also lose numerical precision; this guide does not establish extreme-tail accuracy for any Excel build.

• Current documentation: the dedicated Microsoft reference lists Excel for Microsoft 365, Excel for Microsoft 365 for Mac, Excel 2024, Excel 2024 for Mac, Excel 2021, Excel 2021 for Mac, Excel 2019, Excel 2016.
• Introduced: Microsoft’s alphabetical catalog marks NORM.DIST as introduced in Excel 2010. Exact first build and platform-specific introduction dates remain unverified.
• Last functioning version: unknown; a current help listing is not a last-working-build test.
• Evidence checked: October 15, 2026. Official documentation was freshly retrieved; examples were independently calculated. No native Excel, Mac or web-client execution was performed.

• Microsoft NORM.DIST reference.
• Microsoft function catalog and introduction-marker explanation.
• Editorial testing standards.

Examples use English function names and comma separators. Expected numbers are rounded independent mathematical calculations; documented error expectations are labeled as such. They are not captured Excel output. All illustrative data and policies are fictional.