ERF in Calligra Sheets: Error Function and Bounded Differences

=ERF(1) has an independently expected result of 0.842700792950. The two-input =ERF(0;1) expects the same value because the inspected source computes erf(upper) - erf(lower). All results here are independent arithmetic expectations, not Calligra runtime observations. The exact function name and 1–2-argument registration appear in KDE’s pinned 26.08.2 source; details are confirmed with the calculation branch, XML function definition and official handbook. Source consultation: 2026-10-13.

• First introduced: Introduction version not established.
• Current support: Registered in Calligra Sheets 26.08.2; see the function-specific source and official release listing. This is support evidence for that release, not a final supported version.
• Platform and retirement: The KDE application listing provides Linux installation. Other packaged platforms/builds and a retirement endpoint have not been established.
• Checked: October 14, 2026. Native test: Not executed in Calligra Sheets.

Examples use semicolons and decimal points, matching the English formula handbook. Numerical results were checked independently against the published implementation. Calligra itself was not run, so packaged-build behavior, locale handling and displayed errors remain untested.

=ERF(x)
=ERF(lower;upper)

The pinned registration permits one or two arguments, with an explicit alternate compatibility name COM.SUN.STAR.SHEET.ADDIN.ANALYSIS.GETERF. This is a compatibility spelling of the same registered function; use the shorter name in ordinary formulas. KDE’s engineering XML and C++ registration were checked separately.

Documentation mismatch: The XML’s second parameter is not marked optional, yet the pinned C++ accepts one argument and the handbook shows a one-argument example. Treat one-input support as documented/source-backed, not native-executed. Do not invent a default upper bound: a one-input call uses a distinct calculation branch rather than supplying an upper value.

1. Open a blank Calligra Sheets document. Enter First input / value in A1, Second input / bound (optional) in B1, and Formula result in C1. Use D1 for notes if recording native observations later. Confirm the formula editor recognizes the = prefix and ; separator in your locale.
2. Type the numeric values below into A2:B14. Rows labelled omit optional argument are intentionally single-argument formulas; leave the B cell blank and do not pass B in that row’s formula. The blank column cell alone is not a demonstrated default.
3. Copy the displayed formula text for each row into the corresponding C cell. Each example uses its own references. Do not simply fill down a two-argument formula across single-argument rows.
4. Format the output column to about 12 decimal places. Compare with the independent expected output column. The values are predictions derived outside Calligra, not screenshots or logs of native runs.
5. If running the test independently, note Calligra version, operating system, locale and any observed errors; do not treat source predictions as proof that the application returned them.

For a real number x, the mathematical error function is erf(x) = (2/√π) ∫₀ˣ exp(-t²) dt. When the function receives one argument, the pinned source calls calc->erf(x); this is the ordinary error function. The independent values erf(0)=0, erf(1)≈0.842700792950 and erf(-1)≈-0.842700792950 illustrate symmetry around zero.

For two arguments, Calligra’s pinned source computes erf(upper) − erf(lower). Thus =ERF(0;1) has an independently calculated expected result of +0.842700792950, while =ERF(1;0) has the negative. It is a difference of error-function values, not just a call with a redundant parameter. Note this distinction when comparing against a probability model. KDE C++ branch.

Source versus manual nuance: The handbook and XML show ERF(Lower limit; Upper limit) and XML lists two required-looking <Parameter> nodes. Nonetheless, the same release C++ registers setParamCount(1,2) and the handbook explicitly gives a single-argument example ERF(0.4). The guide therefore accepts one or two arguments on the evidence of registration and example, but flags the XML’s missing optional marker; native formula-dialog acceptance remains untested. Function metadata; registration; manual.

Convert a standard-normal z-score into a CDF

The standard-normal CDF identity is Φ(z) = (1 + erf(z/√2))/2. To model z=1 using functions documented in Calligra Sheets, enter the conceptual expression =(1+ERF(1/SQRT(2)))/2. The independent mathematical result is 0.841344746069. This is a cross-check against probability mathematics, not a spreadsheet-executed combined-formula test. SQRT is documented separately; verify the entire formula in the installed application before relying on it. KDE SQRT handbook.

Compute a signed interval and reverse it

Using bounds from 0 to 1, =ERF(0;1) has an independent expected output of 0.842700792950. Reversing the limits to =ERF(1;0) gives −0.842700792950. This makes ERF useful for signed differences in the transformed error-function scale, but the sign is not automatically a probability.

Symmetric interval about zero

The mathematical identity erf(a)-erf(-a)=2erf(a) gives =ERF(-1;1) independently expected 1.685401585899. This can exceed 1; an interval difference of error-function values is not a probability until divided by an appropriate normalization such as 2 for a particular transformed-normal model. Avoid labeling every two-input ERF output a probability.

For a single argument x, erf(x) + erfc(x) = 1. Thus =ERF(1) is independently expected 0.842700792950 and =ERFC(1) 0.157299207050. The two-argument source branch for ERFC has a different sign convention from ERF; do not assume every two-input ERF and ERFC pair sums to 1. See the ERFC reference and the pinned implementation before importing a two-input formula.

• Official ERF function entry
• 26.08.2 registration and argument count
• Function-specific parameter metadata
• Numerical helper: standard-library erf and erfc

These are documentation and source checks. All displayed results are independent expectations, not claims of an executed Calligra worksheet.