ERFC in Calligra Sheets: Complementary Error Function and Interval Pitfall

=ERFC(1) has an independently expected result of 0.157299207050. Beware: the source branch for two arguments makes =ERFC(0;1) expect −0.842700792950, not a positive probability. 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.

=ERFC(x)
=ERFC(lower;upper)

The pinned registration permits one or two arguments, with an explicit alternate compatibility name COM.SUN.STAR.SHEET.ADDIN.ANALYSIS.GETERFC. 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.

The complementary error function is erfc(x) = 1 − erf(x). With one argument the pinned implementation returns calc->erfc(x). Independently, ERFC(0) is expected 1, ERFC(1) approximately 0.157299207050, and ERFC(-1) approximately 1.842700792950. Values above 1 for negative x are normal mathematically; erfc is not inherently a probability for every x.

Important source-code finding: For two arguments the inspected Calligra 26.08.2 implementation returns erfc(upper) − erfc(lower), not erfc(lower) − erfc(upper). Because erfc decreases with x, =ERFC(0;1) is expected from the code to be −0.842700792950. This is the negative of =ERF(0;1). It is not a probability and can surprise users expecting the positive area under an integrand. The XML documentation says only that ERFC returns the complementary error function; it does not spell out this two-bound sign choice. Native execution has not been performed, so the release-pinned branch is strong source evidence but not a screenshot-confirmed application result. KDE code; KDE XML metadata.

One versus two arguments: XML renders both parameter nodes without optional=true, while the C++ registration allows 1–2, and the handbook includes ERFC(0.4) as a one-input example. Both forms are documented in the guide with this inconsistency prominently flagged; the actual function-dialog behavior still requires a native run. Registration; handbook.

Calculate a one-sided Gaussian tail without subtracting nearly equal numbers

Mathematically, the standard-normal upper-tail probability is 0.5*erfc(z/√2). For z=2, the conceptual Calligra expression =0.5*ERFC(2/SQRT(2)) has an independently calculated expected value 0.022750131948. It uses one input to ERFC and a separate documented SQRT; the full combined formula has not been run in Calligra. The one-input ERFC form is often preferable to subtracting a CDF extremely close to 1, though native numerical accuracy is not established. KDE SQRT handbook.

Cross-check the complement identity for a single input

For x=0.4, =ERF(0.4) is independently expected 0.428392355047 and =ERFC(0.4) 0.571607644953. Adding them mathematically gives exactly 1 within floating-point rounding. This comparison is evidence-based from the two C++ branches and the standard mathematical definitions; it is not an executed worksheet test.

Beware the two-input sign trap

The independent predictions are =ERFC(0;1) −0.842700792950 and =ERFC(1;0) +0.842700792950. The two-input ERF branch has the opposite sign in the corresponding order. If your intent is a positive interval integral, use =ERF(lower;upper) based on the signed interval of erf (with the appropriate model scaling), rather than silently assuming ERFC(lower;upper) returns the same sign. Confirm with the actual application before using in operational analysis.

ERFC is explicitly listed as related to ERF in KDE’s XML function description. For a single x, ERFC(x)=1-ERF(x) is reliable mathematical reasoning. For two bounds, subtracting two complements cancels 1 and reverses the ERF difference; the exact source branch is critical. This is a concrete reason not to port a similarly named function’s calling convention from Excel, LibreOffice or Google Sheets without verifying Calligra itself.

• Official ERFC 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.