ERFC Function (OpenOffice Calc)

• Introduced: First release not established; documented by OpenOffice.org 3.3.
• Supported in: Apache OpenOffice 4.1.16; this identifies a verified release, not a final supported version.
• Scope: Desktop Calc with its Analysis add-in, English function names and semicolon-separated formulas.
• Checked: October 14, 2026. Eight reference formulas and the listed diagnostics were recalculated after XLSX import in 4.1.16 on Linux x86-64, Build 9816. Source and independent reference calculations were also checked.

ERFC evaluates the complementary error function. Mathematically ERFC(x)=1−ERF(x), but a direct complementary calculation can retain a small positive tail that subtraction from 1 loses. It takes one endpoint, not two interval bounds. Release entry.

=ERFC(X)

Exactly one numeric argument is used. Negative X is accepted. The exact mathematical value is between 0 and 2 for finite real arguments, and ERFC(0)=1. The add-in calls the dedicated complementary helper rather than computing 1−ERF(X) itself.

The native column records the saved 4.1.16 results. Ordinary numeric values are rounded to twelve decimal places, with scientific notation for tiny values. Stored values and display text were inspected separately; a twelve-decimal cell display can hide a tiny nonzero number.

At x=1, =ERFC(1) gives approximately 0.157299207050. At x=−1 it gives approximately 1.842700792950. The value above 1 is valid for a complementary error function; it is not already a standard-normal right-tail probability.

For a standard-normal cutoff z, the right-tail probability is ERFC(z/SQRT(2))/2. This transformation is derived from the normal density and requires the same normal-model assumptions as other normal probability calculations.

The far-tail row ERFC(6) has a mathematical reference near 2.151973671250×10⁻¹⁷. Use scientific notation when displaying it; a fixed twelve-decimal format can hide a nonzero stored value as zero.

The symmetry ERFC(−x)=2−ERFC(x) explains the paired positive and negative examples. The identity ERF(x)+ERFC(x)=1 is a useful ordinary-input check, but it does not establish relative accuracy of an extremely small complement by itself.

For a positive interval in the tail, ERFC(a)−ERFC(b) corresponds to ERF(b)−ERF(a) when a≤b. It avoids subtracting two values already close to 1, although very narrow intervals can still encounter cancellation.

The tested extreme endpoints at ±30 are finite-precision outcomes. The exact positive tail at 30 is nonzero but below ordinary binary64’s representable range, so zero does not mean a mathematically impossible event.

A second argument is not supported in this program’s ERFC contract. Do not copy a two-argument form from a different spreadsheet product. Keep a native error as an error rather than substituting a plausible-looking probability.

These additional formulas were recalculated through the same import path. Error displays are retained as errors, even when an ODS numeric attribute stores zero.

The ERFC guide for Gnumeric documents that product’s own syntax and tested behavior. A shared function name does not guarantee the same argument conversion, text parsing, branch or precision rules.

• Function-specific release entry
• Numeric algorithm or complex parser/formatter

The saved ODS retained every tested formula identity. A deliberately stale SUM cache changed from 999999 to 3, and an uncached SUM returned 7 after hard recalculation. Native evidence covers the eight reference formulas and listed diagnostics only. Other explanatory compositions are independent mathematical checks; other releases, locales and extreme-value behavior were not established by this run.