What is the difference between cumulative TRUE and FALSE?

cumulative=TRUE returns the cumulative distribution function (CDF): the probability that a random value is less than or equal to your z-score—useful for percentile rankings. cumulative=FALSE returns the probability density function (PDF): the height of the bell curve at that point—useful for visualizing distribution shape. Always use TRUE for percentile questions.

Why must I convert my data to z-scores before using NORM.S.DIST?

NORM.S.DIST only works with the standard normal distribution, which has mean=0 and standard deviation=1. Any other data must be standardized using z = (value − mean) ÷ standard_deviation. This transforms your data into a universal scale so NORM.S.DIST can apply its pre-calculated probabilities.

What does a z-score of 2 mean, and what does NORM.S.DIST(2, TRUE) tell me?

A z-score of 2 means the value is 2 standard deviations above the mean. NORM.S.DIST(2, TRUE) returns approximately 0.9772, meaning about 97.72% of scores fall at or below this point. In other words, a score at z=2 is in the 97.72th percentile—exceptionally high.

Can NORM.S.DIST handle very large or very small z-scores?

Yes. NORM.S.DIST works for any real z-score, including extreme values like z=10 or z=−10. As z increases, cumulative probability approaches 1.0 (certainty below that score); as z decreases, it approaches 0. Very extreme values (e.g., z=±100) return probabilities so close to 0 or 1 that they are effectively 0 or 1 in practice.

NORM.S.DIST function

Returns the value of the standard normal distribution's probability density or cumulative probability at a given z-score.

=NORM.S.DIST(z, cumulative)

Generate a NORM.S.DIST formula

Describe what you need. The generator will reach for NORM.S.DIST where NORM.S.DIST is the right tool, and tell you when it is not.

Arguments

How NORM.S.DIST reads its arguments

Argument	Required	Description
z	Required	A numeric value representing the z-score (standard deviation units from the mean). Accepts any real number including negative values; edge cases like ±10 are handled gracefully.
cumulative	Required	A logical value: TRUE returns the cumulative distribution function (probability that a value is ≤ z); FALSE returns the probability density function (height of the curve at z). Must be boolean, not text.

Returns

A decimal number between 0 and 1 representing either the cumulative probability (cumulative=TRUE) or probability density (cumulative=FALSE).

Availability

Excel: All · Google Sheets: Supported

Worked examples

1. Find the percentile rank of a student's test score

Student	Subject	Assignment	Score	Max Score
Alice	Math	Quiz 1	85	100
Bob	Math	Quiz 1	72	100
Charlie	Math	Quiz 1	80	100
Diana	Math	Quiz 1	92	100

=NORM.S.DIST((85-80)/5, TRUE)

Result: 0.8413

Alice scored 85 on a test where the class mean is 80 and standard deviation is 5. Convert to z-score: (85−80)÷5 = 1. NORM.S.DIST(1, TRUE) returns 0.8413, meaning Alice performed better than 84.13% of the class. The cumulative probability tells you the percentile rank.

2. Calculate probability density at the mean

Student	Subject	Assignment	Score	Max Score
Alice	Math	Quiz 1	85	100
Bob	Math	Quiz 1	72	100
Charlie	Math	Quiz 1	80	100
Diana	Math	Quiz 1	92	100

=NORM.S.DIST(0, FALSE)

Result: 0.3989

When cumulative=FALSE, NORM.S.DIST returns the height of the standard normal curve at that z-score. At z=0 (exactly at the mean), the curve reaches its maximum height of 0.3989. This density value shows concentration—the mean is where most scores cluster in a normal distribution.

3. Determine the probability a student scores below a threshold

Student	Subject	Assignment	Score	Max Score
Alice	Math	Quiz 1	85	100
Bob	Math	Quiz 1	72	100
Charlie	Math	Quiz 1	80	100
Diana	Math	Quiz 1	92	100

=NORM.S.DIST((92-80)/5, TRUE)

Result: 0.9918

Diana scored 92, which is z = (92−80)÷5 = 2.4 standard deviations above the mean. NORM.S.DIST(2.4, TRUE) returns 0.9918, meaning Diana outperformed 99.18% of students. This cumulative probability shows how rare her score is under a normal distribution model.

Common errors

Which NORM.S.DIST error are you seeing?

Error	Why it happens	How to fix it
#VALUE!	The z argument contains text that cannot be converted to a number, such as =NORM.S.DIST("high", TRUE) or referencing a column header like =NORM.S.DIST(B1, TRUE) when B1 contains 'Score'.	Pass numeric values only. If using a cell reference, make sure it contains a number. Convert text numbers with VALUE(): =NORM.S.DIST(VALUE("1.5"), TRUE).
#VALUE!	The cumulative argument is text or a number that is not 0, 1, TRUE, or FALSE, such as =NORM.S.DIST(1, "true") or =NORM.S.DIST(1, 2).	Supply a logical constant: use TRUE (or 1) for cumulative distribution, FALSE (or 0) for density. For example, change =NORM.S.DIST(1.5, "yes") to =NORM.S.DIST(1.5, TRUE).
#NUM!	The z argument evaluates to NaN (not-a-number) or Infinity from an invalid computation, such as =NORM.S.DIST(0/0, TRUE) or from an error in a dependent calculation.	Check that the z calculation itself is valid—verify the mean and standard deviation values are correct numbers and that division by zero cannot occur. Wrap in IFERROR to suppress: =IFERROR(NORM.S.DIST(z, TRUE), "").

Tips and when to use something else

Always standardize your data first: z = (value − mean) ÷ standard deviation. NORM.S.DIST requires z-scores, not raw scores. Use AVERAGE to find the mean and reference it in the calculation.
cumulative=TRUE answers 'What percentage scored at or below?'; cumulative=FALSE is used for distribution visualization and density calculations. Choose based on your question.
For large datasets, use NORM.DIST() instead if your data has a non-standard mean and standard deviation—it accepts mean and std-dev parameters directly, avoiding manual z-score conversion.
NORM.S.INV is the inverse: it returns the z-score given a probability. Use NORM.S.INV(0.95, TRUE) to find the z-value where 95% of scores fall below.

Related functions

AVERAGEAVERAGE calculates the arithmetic mean of numbers, ignoring text and logical values; returns a single numeric value representing the average.MEDIANMEDIAN returns the middle value in a sorted list of numbers, or the average of the two middle values if the count is even.IFThe IF function returns one value if a condition is true and another (or nothing) if it is false, letting you branch logic in a cell.IFERRORIFERROR returns the result of a formula unless that formula generates an error, in which case it returns a user-specified alternative value.

Frequently asked questions

What is the difference between cumulative TRUE and FALSE?: cumulative=TRUE returns the cumulative distribution function (CDF): the probability that a random value is less than or equal to your z-score—useful for percentile rankings. cumulative=FALSE returns the probability density function (PDF): the height of the bell curve at that point—useful for visualizing distribution shape. Always use TRUE for percentile questions.
Why must I convert my data to z-scores before using NORM.S.DIST?: NORM.S.DIST only works with the standard normal distribution, which has mean=0 and standard deviation=1. Any other data must be standardized using z = (value − mean) ÷ standard_deviation. This transforms your data into a universal scale so NORM.S.DIST can apply its pre-calculated probabilities.
What does a z-score of 2 mean, and what does NORM.S.DIST(2, TRUE) tell me?: A z-score of 2 means the value is 2 standard deviations above the mean. NORM.S.DIST(2, TRUE) returns approximately 0.9772, meaning about 97.72% of scores fall at or below this point. In other words, a score at z=2 is in the 97.72th percentile—exceptionally high.
Can NORM.S.DIST handle very large or very small z-scores?: Yes. NORM.S.DIST works for any real z-score, including extreme values like z=10 or z=−10. As z increases, cumulative probability approaches 1.0 (certainty below that score); as z decreases, it approaches 0. Very extreme values (e.g., z=±100) return probabilities so close to 0 or 1 that they are effectively 0 or 1 in practice.

Need a different formula?

The full generator is not scoped to one function — describe any spreadsheet problem and it will pick.

Open the formula generator

Reviewed 2026-09-17