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NORM.S.DIST Function

Excel 2010+

Summary

The NORM.S.DIST function calculates values for the standard normal distribution (mean=0, standard deviation=1). It provides either the cumulative probability (area under the curve to the left of z) or the probability density at a specific z-value, serving as a digital replacement for Z-tables in statistics.

Syntax

NORM.S.DIST(z, cumulative)

Parameters

Parameter	Type	Required	Description
z	`Number`	Yes	The z-score or standard deviate value
cumulative	`Boolean`	Yes	Logical value: TRUE=CDF, FALSE=PDF

Using the NORM.S.DIST Function

NORM.S.DIST is crucial for statistical analysis involving Z-scores. Use TRUE for finding probabilities less than a z-value (left-tail), or FALSE for the height of the density curve at exactly that z-value. This function powers confidence intervals, p-values, and quality control charts.

Common NORM.S.DIST Examples

Cumulative Distribution (Left-Tail Probability)

=NORM.S.DIST(1.333333,TRUE)

Returns 0.9088 - probability that a standard normal variable is less than 1.333

Probability Density Function

=NORM.S.DIST(1.333333,FALSE)

Returns 0.1640 - height of the standard normal curve at z=1.333

Negative Z-Score Example

=NORM.S.DIST(-1.96,TRUE)

Returns 0.025 - left-tail probability for 95% confidence level

Z-Score from Percentile

=NORM.S.DIST(0.975,TRUE)

Verifies that 97.5th percentile = z=1.96 for two-tailed 95%

Frequently Asked Questions

TRUE returns the area under the curve to the left of z (CDF). FALSE returns the density/height at exactly z (PDF).

Yes, NORM.S.DIST handles negative values correctly, returning values between 0 and 1 for CDF.

NORM.S.DIST is the modern replacement (Excel 2010+). Both work identically.

Common Errors and Solutions

#VALUE!

Cause: z or cumulative argument is text/non-numeric

Solution: Ensure z is a number and cumulative is TRUE/FALSE

#NUM!

Cause: Invalid cumulative value (not TRUE/FALSE)

Solution: Use TRUE or FALSE explicitly

Notes

Standard normal only (μ=0, σ=1) - use NORM.DIST for custom distributions
CDF output always between 0 and 1
PDF output represents curve height (maximum ~0.4 at z=0)
Perfect complement to NORM.S.INV for two-way conversions

Compatibility

Available in: Excel 2010, Excel 2013, Excel 2016, Excel 2019, Excel 2021, Microsoft 365

Not available in: Excel 2007 and earlier

Content last reviewed: December 9, 2025
Update frequency: As needed
Excel versions tested: Excel 2010+