NORM.DIST in Google Sheets: Cumulative Probability and Density

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

Google’s NORM.DIST entry maps this spelling to the individual NORMDIST reference, with the same four argument positions.

All four arguments are shown as required. No omission default is established, so every example supplies the flag. Use a positive standard deviation for a nondegenerate normal model. Variance is the square of standard deviation, not a substitute for this parameter.

Assume processing times are modeled as normal with mean 30 minutes and standard deviation 4 minutes. Enter 26, 30, 34, 38 in A2:A5, mean 30 in D1 and standard deviation 4 in E1.

In B2, enter and fill down:

=NORM.DIST(A2,$D$1,$E$1,TRUE)

The middle result is a useful check: symmetry puts half the modeled values below the mean. The probability rises as the threshold rises. The input values are a constructed model, not evidence that a real process follows a normal distribution.

For the density at 30:

=NORM.DIST(30,30,4,FALSE)

Expected result: approximately 0.0997355701 per minute. This is the height of the density curve, not a 9.97% chance of exactly 30 minutes. A continuous distribution assigns zero probability to one exact point; interval probability comes from area.

The distinction follows the density and cumulative definitions in NIST’s normal-distribution reference. Google’s PHI reference also identifies the standard-normal density as NORMDIST with mean 0, standard deviation 1 and cumulative FALSE.

For a modeled processing time between 26 and 34 minutes:

=NORM.DIST(34,30,4,TRUE)-NORM.DIST(26,30,4,TRUE)

Expected result: 0.6826894921, about 68.27%. Subtract the cumulative value at the lower endpoint from the cumulative value at the upper endpoint. In this continuous model, including or excluding an exact endpoint does not change the probability.

For times above 38 minutes:

=1-NORM.DIST(38,30,4,TRUE)

Expected result: 0.0227501319, about 2.28%. Among 500 modeled cases, =500*(1-NORM.DIST(38,30,4,TRUE)) gives an expected count of 11.3750659741. An expected count can be fractional; it is not a promise that a particular run will contain that many cases.

A normal model is symmetric and extends across the whole number line. It can be unsuitable for strongly skewed, bounded or mixed-process data. Calculating a value successfully does not establish a good fit.

If the mean and spread are estimated from observations, record the sample definition and the choice of spread estimator. A distribution for individual observations is different from the sampling distribution of a mean. Dividing standard deviation by the square root of sample size changes the model and should not be done without that intended change.

Check that standard deviation is positive, that all units agree and that TRUE/FALSE matches the intended question. For “above,” subtract the CDF from 1; for an interval, subtract two CDFs. Do not format a density as a probability merely because both are numeric.

The reviewed NORMDIST page does not enumerate a complete native error-token, text/blank coercion or extreme-tail precision specification. Mathematical input requirements are not presented as observed native error mappings. For extremely small tails, subtracting a value close to 1 can lose precision; the examples intentionally avoid that regime.

The dotted and undotted spellings are linked by Google’s current documentation. No broader parity with other spreadsheet engines is assumed. Original introduction date, first supported version and last functioning numbered release were not established for rolling Sheets.

NOT_TESTED_IN_GOOGLE_SHEETS. Google references and the NIST mathematical definition were inspected on October 17, 2026. All example CDFs, densities and derived quantities were independently calculated with normal-distribution mathematics, without native execution or screenshots.

Related published guides: AVERAGE, STDEV.S, SQRT and ROUND.