PlanMaker PHI: Standard Normal Density and Historical Caveats

• Introduced: Documented by the PlanMaker 2010 manual; the first introduction release is not established.
• Availability: Documented in PlanMaker 2026; this does not establish a final working-version endpoint.
• Scope: The current reference belongs to the 2026/NX manual family. Individual FreeOffice and mobile builds are not verified here.
• Checked: October 14, 2026, against the official function reference. Examples use vendor rules and independent calculations; no native PlanMaker test was performed.

=PHI(x)

The current official entry specifies one input and explicitly identifies the density function. For a standard normal distribution, the mean is 0 and the standard deviation is 1. Its mathematical density at x is:

exp(-x^2/2) / sqrt(2*pi)

The input is a standardized coordinate. The density’s height at a single point is not the probability of obtaining exactly that point. For a continuous distribution, probabilities concern areas over intervals, not individual density heights.

In particular, PHI(0) is about 0.39894, while the cumulative probability at zero is 0.5. Confusing those two values changes the statistical calculation.

On a blank worksheet, put Standardized x, Density, Exponential check and Difference in A1:D1. Enter -2, -1, 0, 1, 2 in A2:A6.

Enter =PHI(A2) in B2, =EXP(-(A2^2)/2)/SQRTPI(2) in C2 and =B2-C2 in D2. Fill B2:D2 through row 6.

The numbers are independently calculated from the density formula. D has a mathematical target of zero, but equivalent floating-point paths need not agree in every last digit.

EXP provides the exponential term and SQRTPI supplies √(2π). Squaring x inside the exponent makes the density equal at x and −x. A negative input does not produce a negative density.

SoftMaker gives the identity PHI(x)=NORMDIST(x,0,1,FALSE) and notes that PHI is unavailable in Excel versions before 2013. On the same worksheet, put =NORMDIST(A2,0,1,FALSE) in E2 and fill to E6. The current PlanMaker reference identifies these as equivalent density calculations.

The final FALSE is essential: it selects density. With TRUE, NORMDIST instead returns a cumulative value. Do not omit or change that flag while translating the formula.

This is a documented alternative, not a claim that a workbook was round-trip tested in every Excel version. Check formulas after exporting rather than relying only on an initially displayed result.

On the worksheet, put =NORMSDIST(A2) in F2 and fill to F6. The NORMSDIST reference specifically defines the standard normal cumulative function.

Unlike the density column, cumulative values increase from left to right. They measure the modeled probability at or below the chosen coordinate.

To calculate the modeled probability between −1 and 1, enter =NORMSDIST(1)-NORMSDIST(-1) in H2. The independent expected value is approximately 0.6826894921, or 68.26894921%. Subtracting PHI(-1) from PHI(1) would instead give zero because those density heights are equal; it would not calculate the interval’s probability.

The 2010 manual, pages 567–568, calls PHI a PlanMaker 97 compatibility function. Its description says “cumulative,” yet its proposed replacement is the FALSE, density form of NORMDIST. Those two statements conflict.

The 2026 entry explicitly says density and retains the same FALSE replacement, so this guide follows the clear current definition. The historical wording does not establish that a calculation engine changed behavior, identify a change release, or prove a retirement date. Current PHI is still documented.

The short entry does not define every blank, text, source-error or extreme-input outcome. These examples use ordinary numeric coordinates and do not establish all native precision boundaries.

A normal-distribution model must suit the data before its density or probabilities are useful. PHI does not estimate a mean, standard deviation or distribution fit from a range. GAUSS is another standard-normal function, returning cumulative probability minus 0.5; PI is the unrelated circle constant.