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PHI Function
Summary
The PHI function calculates the value of the probability density function for a standard normal distribution (mean 0, standard deviation 1) at a given point. This is essential for statistical analysis, probability calculations, and financial modeling involving normal distributions.
Syntax
PHI(x)Parameters
| Parameter | Type | Required | Description |
|---|---|---|---|
| x | Number |
Yes | Numerical input for which to compute the standard normal density |
Using the PHI Function
Use PHI to obtain the height of the standard normal curve at specific points. This is valuable in statistics for understanding distribution shapes, hypothesis testing, confidence intervals, and risk assessment models.
Common PHI Examples
Basic Density Calculation
=PHI(0.75)Returns the density value at z=0.75 (approximately 0.3011), representing the curve height at that point.
Z-Score Analysis
=PHI((A1-B1)/C1)Calculates density at standardized z-score from sample data, useful for statistical testing.
Multiple Evaluations
=PHI(A1:A10)Array calculation of densities across multiple z-scores for distribution visualization.
Frequently Asked Questions
Common Errors and Solutions
#NUM!
Cause: Invalid numeric input or non-number value
Solution: Ensure x is a valid number; use IFERROR for handling if needed
#VALUE!
Cause: Non-numeric data type passed to x
Solution: Verify input data types are numeric
Notes
- Maximum value is approximately 0.3989 at x=0
- PHI(x) approaches 0 as |x| increases
- Useful for p-value approximations and statistical tables
- Part of Excel's statistical function suite
Compatibility
Available in: Excel 2013, Excel 2016, Excel 2019, Excel 2021, Excel 365
Not available in: Excel 2010, Excel 2007, Excel 2003 and earlier
Content last reviewed: December 9, 2025
Update frequency: As needed
Excel versions tested: Excel 2013+