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In Excel, the z distribution (the standard normal distribution) is handled by three functions: STANDARDIZE turns a raw value into a z-score, NORM.S.DIST turns a z-score into a probability or density, and NORM.S.INV turns a probability back into a z-score. This guide chains the three on one data point, using the example values from Microsoft’s own function pages, so you can check your worksheet against known results.
What it is used for in research
The z distribution is the normal distribution rescaled to mean 0 and standard deviation 1. Analysts use it to place a value on a common scale, to find the share of a normal population below a value, and to look up the z cutoff for a chosen probability. For the background see normal and standard normal distribution; for the table-based equivalent see how to use a z table.
Which function answers which question
| Question | Excel formula | Returns |
|---|---|---|
| How many standard deviations is x from the mean? | =STANDARDIZE(x, mean, standard_dev) |
The z-score |
| What proportion of the standard normal lies below z? | =NORM.S.DIST(z, TRUE) |
The cumulative probability (left tail) |
| How high is the standard normal curve at z? | =NORM.S.DIST(z, FALSE) |
The density at z |
| Which z has a given cumulative probability below it? | =NORM.S.INV(probability) |
The z-score |
| What proportion lies above z? | =1-NORM.S.DIST(z, TRUE) |
The complement of the cumulative probability (right tail) |
The last row is arithmetic on the cumulative result, not a separate Excel function.
Where the functions are available
Microsoft’s documentation lists NORM.S.DIST as applying to Excel for Microsoft 365 (Windows and Mac), Excel 2024, 2021, 2019 and 2016. NORMSDIST is the older compatibility form of the same calculation; use NORM.S.DIST in new work because it lets you choose cumulative or density output. Nothing needs to be installed: the functions are built in and are typed into a cell like any formula.
Step by step: from a raw value to a z probability and back
This sequence uses Microsoft’s example values: a value of 42 from a distribution with mean 40 and standard deviation 1.5.
- Enter the inputs. Put 42 in A2, 40 in A3 and 1.5 in A4.
- Standardize. In B2 type
=STANDARDIZE(A2,A3,A4). Microsoft’s page gives the result as 1.33333333. - Get the cumulative probability. In B3 type
=NORM.S.DIST(B2,TRUE). For z = 1.333333 Microsoft’s page gives 0.908788726, so about 90.9% of the standard normal lies below this value. - Get the density if you need the curve height.
=NORM.S.DIST(B2,FALSE)gives 0.164010148 for the same z on Microsoft’s page. - Get the right tail.
=1-B3gives 1 – 0.908788726 = 0.091211274. - Invert.
=NORM.S.INV(0.908789)returns 1.3333347 on Microsoft’s page, which recovers the z-score from step 2 to about five decimal places.
Output and how to read it
- STANDARDIZE output is a z-score. Here 1.3333 means the value 42 lies 1.3333 standard deviations above the mean of 40.
NORM.S.DIST(z, TRUE)is a probability between 0 and 1: the proportion of the standard normal at or below z.NORM.S.DIST(z, FALSE)is a density, the height of the bell curve at z. It is not a probability. Microsoft’s page labels it the probability mass function; for a continuous variable read it as curve height.- NORM.S.INV output is a z-score. Microsoft notes it uses an iterative search whose precision depends on
NORM.S.DIST, which is why 0.908789 returns 1.3333347 rather than exactly 1.333333.
To turn a z-score into a p-value for a test, see how to find the p-value from a z-score. For critical values from a chosen significance level see z alpha and the inverse normal distribution.
Troubleshooting
| Error | Function | Cause (per Microsoft) |
|---|---|---|
| #VALUE! | NORM.S.DIST | z is non-numeric |
| #VALUE! | NORM.S.INV | probability is non-numeric |
| #NUM! | NORM.S.INV | probability is 0 or less, or 1 or greater |
| #NUM! | STANDARDIZE | standard_dev is 0 or less |
Because NORM.S.INV needs a probability strictly between 0 and 1, it cannot return a z for exactly 0 or 1.
Related Excel guides
To draw the bell curve itself, see how to construct a normal distribution curve in Excel. For summary statistics to feed STANDARDIZE, see descriptive statistics in Excel.
Frequently asked questions
What is the z distribution in Excel?
It is the standard normal distribution, mean 0 and standard deviation 1, accessed through NORM.S.DIST (probability or density from z) and NORM.S.INV (z from probability).
What does the TRUE or FALSE argument in NORM.S.DIST do?
TRUE returns the cumulative distribution function; FALSE returns the density (Microsoft calls it the probability mass function).
How do I get a z-score for my own data?
Use STANDARDIZE(x, mean, standard_dev) with your value, the mean and the standard deviation.
Is NORMSDIST the same as NORM.S.DIST?
NORMSDIST is the older compatibility version of the cumulative calculation. NORM.S.DIST is the current function and adds the cumulative argument.
Sources
- Microsoft Support, NORM.S.DIST function, read 2026-11-08.
- Microsoft Support, STANDARDIZE function, read 2026-11-08.
- Microsoft Support, NORM.S.INV function, read 2026-11-08.
