PHI in ONLYOFFICE Spreadsheet Editor

• Introduced: Original introduction release is not established by the checked sources.
• Available: Listed in current unversioned ONLYOFFICE help, checked October 18, 2026.
• Implementation inspected: Official SDKJS v10.0.0.169, commit 3679e0375a758d7dc59d31337a45461be3525ed8. The snapshot does not prove identical behavior in every installed editor.
• Retired or deprecated: These sources do not establish retirement or formal deprecation. A legacy name alone does not mean the function has been removed.
• Testing: Numerical examples are independent mathematical expectations, and implementation discrepancies are labeled source predictions. No ONLYOFFICE application or calculation-engine execution was performed.

The examples use English function names and commas. Use your locale’s argument separator if different. Retain full precision in formulas; round only the displayed result. The examples describe function mechanics under the stated model, rather than establishing that your observations follow that model.

=PHI(x)

One numeric argument is required. x is a standardized position on the standard normal distribution, whose mean is 0 and standard deviation is 1. The mathematical density is EXP(-(x^2)/2)/SQRT(2*PI()). PHI has no cumulative flag and does not return a lower-tail probability.

The standard-normal density is symmetric: PHI(−x) equals PHI(x). Its peak occurs at zero. The total area over the real line is 1, but the height at any single point is not that point’s probability. In a continuous distribution, the probability of one exact value is zero. Interval probabilities require integrating density, or subtracting CDF values.

Do not confuse PHI’s density with GAUSS’s signed area or a normal CDF. For example, at x = 1 the density is about 0.241971, the signed area from zero is about 0.341345, and the lower-tail probability is about 0.841345. These answer different questions.

1. Put -1, 0, 1 and 2 in A2:A5.
2. Enter =PHI(A2) in B2 and copy down.
3. Label the second column “standard-normal density,” rather than “probability.”
4. Independently compare the results with the exponential formula above.

The value at zero is 1/SQRT(2*PI()). At one standard deviation it is that value multiplied by EXP(-0.5). At two it is multiplied by EXP(-2). These identities show why negative and positive inputs of equal magnitude give the same result.

For a chart of the density curve, make a separate column of x values at regular intervals and evaluate PHI for each. A sum of those density values alone is not a probability: numerical integration also needs interval widths and a suitable quadrature rule.

Suppose a variable is modeled as normal with mean 50 units and standard deviation 4 units. The density at a raw value 54 is =PHI((54-50)/4)/4, independently 0.060492681130 per unit. Dividing by standard deviation is essential; standardizing only the argument gives the standard-normal density, not the density per original unit.

On a fresh sheet put raw value 54 in A2, mean 50 in B2 and positive standard deviation 4 in C2. Use =PHI((A2-B2)/C2)/C2. If measurements are rescaled by a factor of 10, the numerical density per new unit changes inversely, even though the underlying probability of the same physical interval does not. A model with a narrow standard deviation can have a density above 1 without violating probability rules.

For a small interval from z = 0.9 to 1.1, a midpoint approximation is =PHI(1)*0.2, approximately 0.048394144904. The independent normal-area value is about 0.048394064400. The approximation is useful for understanding area, but it is not an exact probability formula and becomes unreliable for wider intervals or rapidly changing density. A CDF difference is preferable when an accurate interval probability is required.

Negative numeric x values are valid. The inspected wrapper converts its argument to a number and propagates conversion errors. Its helper multiplies a fixed approximation to 1/SQRT(2*PI()) by EXP(-x*x/2); a NaN helper result is mapped to internal not_available, conventionally #N/A. This does not establish how every unusual text or nonfinite input will be displayed by an application.

Very large absolute x can cause the exponential to underflow to zero. That zero is a numerical limit, rather than proof that a finite mathematical normal density is exactly zero. Report an appropriate precision and do not infer a tail probability from a density that rounds to zero.

The function does not fit a distribution or validate assumptions. When transforming a raw measurement, use a strictly positive standard deviation and matching units for x, mean and standard deviation. A raw negative measurement need not imply negative standardized x; standardization depends on its position relative to the mean.

Recalculate representative formulas when moving a workbook between editors. Matching names do not guarantee identical argument coercion, array behavior, numerical precision or error handling. The scalar formulas here do not establish automatic spill behavior or a general import/export guarantee.

• STANDARDIZE
• EXP

• ONLYOFFICE PHI help, checked October 18, 2026.
• Official SDKJS implementation, 10449–10483, tag v10.0.0.169 and exact commit above.