ERF in ONLYOFFICE: One- and Two-Limit Error Integrals

The mathematical error function is erf(x)=(2/sqrt(pi))*integral_0^x exp(-t^2) dt. In the two-bound form, the value is erf(upper_limit)-erf(lower_limit). The normalization is essential: the plain integral of exp(-t²) without the factor 2/sqrt(pi) is not an ERF result. ERF is useful in probability models, diffusion equations, signal processing and Gaussian-integral calculations; it is not the same as an ordinary average or probability percentage without a separate interpretation.

For negative inputs, the usual mathematical error function is odd: erf(-x)=-erf(x). A reversed integration interval changes sign: ERF(2,1) is the negative of ERF(1,2) mathematically. These are properties of the mathematical definition; the concise ONLYOFFICE reference does not specify every floating-point or error case.

=ERF(lower_limit, [upper_limit])

Important distinction: =ERF(1) computes 0 → 1, whereas =ERF(1,0) computes 1 → 0 and therefore has the opposite mathematical sign. A second argument of zero is not the same as omitting it. ERF.PRECISE(x) is separately documented with one required argument; it is not a license to invent an optional upper bound for the precise variant. ERF.PRECISE.

1. Create a blank spreadsheet in an ONLYOFFICE Spreadsheet Editor edition you can identify. Use English formula language for the formulas below. Record your Desktop version or the actual Docs/server version and your region if you later report test results.
2. Enter the specified headers, then enter the table’s input values in the exact cells shown. Numeric inputs must be numeric cells (without quote marks).
3. Enter the formulas into the output cells exactly as shown, beginning with =. Use Formula → Function to find ERF or type the function directly. Fill down only through the named last row; do not accidentally include table headers.
4. Compare your displayed values against the independently computed expected column. For decimals, change display format or use numeric tolerance rather than expecting identical trailing digits.
5. If your result differs, record the formula, underlying cell type, software platform/version, displayed result, separator/locale settings and any error without overwriting the expected-value reference. ONLYOFFICE’s formula-entry and recalculation guide describes recalculating via the Formula tab, or F9 for the workbook.

For the one-argument experiment, put Lower bound in A1, ERF output in B1 and Expected in C1. Enter numeric bounds A2:A14 from the first table, enter =ERF(A2) in B2 and fill through B14, and type the listed expectations in C. For the two-argument experiment, enter Lower limit in E1, Upper limit in F1, ERF result in G1 and Expected integral in H1. Enter numeric bounds E2:F11 from the second table. Type =ERF(E2,F2) in G2 and fill through G11. For both, use a numeric tolerance of approximately 0.000001 on the underlying result (=ABS(B2-C2)<0.000001 for the first table, =ABS(G2-H2)<0.000001 for the second), rather than a text-string comparison.

Outputs above are rounded for display to nine decimals and were independently cross-checked with Python math.erf and high-precision mpmath.erf, not with any ONLYOFFICE runtime. Small negative values are meaningful and should not automatically be classified as errors.

For E2=-1, F2=1, the expected interval value exceeds 1; this is not automatically an error. The error function erf(x) itself has values between -1 and 1 for real x, but the difference erf(b)-erf(a) can lie between -2 and 2. In particular, ERF(-1,1) mathematically equals about 1.685401586.

Put a lower bound in E2, upper in F2. The one-argument difference formula =ERF(F2)-ERF(E2) mathematically equals the vendor-documented two-argument value =ERF(E2,F2). The test is especially useful for a reversed interval. Do not require exact digit-for-digit equality across separately rounded computations; compare within a numeric tolerance. The case E5=2, F5=1 illustrates sign reversal relative to E4=1, F4=2.

The mathematical identity erf(x)+erfc(x)=1 can be used to cross-check the one-argument result. The proposed formula =ERF(A2)+ERFC(A2) should be mathematically close to 1 for finite real inputs; no native editor result is claimed. A standard-normal cumulative probability requires a transformation Phi(z)=(1+erf(z/sqrt(2)))/2—do not incorrectly treat ERF(z) itself as the CDF. Use the vendor’s separately documented ERFC and SQRT for these derived worksheet formulas.

In a dimensionless one-dimensional diffusion model, a normalized distance-to-scale variable may appear inside an error function. Put your measured distances and the model’s characteristic length in separate numeric columns; compute the dimensionless ratio before calling ERF. Label the scale explicitly and do not convert a spreadsheet ERF output directly into a concentration without the model’s coefficients. The two-bound form is useful for comparing contributions over a bounded interval; reversed bounds intentionally give negative signed integrals. This section provides mathematics and worksheet design, not a validated laboratory workflow or vendor-provided worked example.

Do not invent an error value. Where a case is mathematically defined but the editor’s coercion/overflow handling is undocumented, record it as native behaviour unverified, not a guaranteed #VALUE!, #NUM! or other message.

ERFC is the complementary error function; ERF.PRECISE is a distinct, documented one-argument function rather than an alias for this two-bound signature; ERFC.PRECISE is another distinct catalogue entry. SQRT appears in the Gaussian scaling transformation. Exact native equivalence of legacy and PRECISE implementations is not asserted.

Officially documented: The current, unversioned English ONLYOFFICE Docs Spreadsheet Editor function page for ERF and Insert Function catalogue list ERF as an Engineering function. Checked 2026-10-13 (UTC). This supports the existence, purpose and signature of the function in the documented editor; it is not proof of identical behaviour in all past web integrations, all Desktop Editors builds, or mobile versions.

First-supported version: Not established by this research. The vendor maintains distinct Docs release history and Desktop Editors release history. Their availability does not, by itself, identify the first supported release of ERF. Desktop version compatibility: NOT NATIVELY TESTED; browser/web version compatibility: NOT NATIVELY TESTED; historical versions: UNKNOWN; imported workbook round-trip and specific file-format compatibility: NOT TESTED.

English formulas: Examples use an initial = and commas between arguments where necessary, following the official Insert Function instructions. Under File → Advanced Settings, the editor offers Formula Language, Region, and decimal/thousands separators (official Advanced Settings guide). Translated formula names, regional separators and localized decimal entry are not verified here. Do not blindly swap commas for semicolons or translate a function name unless checked in the actual target installation.

Evidence classification: Every result labelled expected is derived from independent mathematical or logical computation, never copied from an ONLYOFFICE screenshot or claimed to have been observed in a running editor. Native Desktop executions: 0. Native web executions: 0. Any error strings described as possible diagnostic are not observed output.