ERFC
Supported, behaves as documentedCategory: Engineering · Last tested 2026-09-01
Real compatibility results for the ERFC function: executed in Excel for the web, Google Sheets and LibreOffice Calc, with desktop Excel behavior from Microsoft’s official documentation (we do not run desktop Excel — Excel for the web is a different application and is executed separately). Syntax and links to that documentation are below.
Support matrix
| Engine | Documented | Live-tested | Verdict |
|---|---|---|---|
| Excel (desktop) | Yes | No — documented only | n/a |
| Excel for the web | — | Yes (recalc, 2026-09-01) | Supported, behaves as documented |
| Google Sheets | Yes | Yes (Drive import, 2026-08-31) | Supported, behaves as documented |
| LibreOffice Calc | Yes | Yes (25.8.7.3, 2026-08-31) | Supported, behaves as documented |
LibreOffice version history
We executed the same test cases under each LibreOffice release to show exactly when ERFC’s support changed — not documentation claims, real results.
| LibreOffice version | Verdict | Tested |
|---|---|---|
| 24.2.0.3 | Supported, behaves as documented | 2026-08-31 |
| 24.8.7.2 | Supported, behaves as documented | 2026-08-31 |
| 25.2.0.3 | Supported, behaves as documented | 2026-08-31 |
| 25.8.7.3 | Supported, behaves as documented | 2026-08-31 |
Executed test cases
Excel for the web (executed 2026-09-01 via OneDrive recalculation)
These values come from Excel for the web, not from desktop Excel. They are two different implementations of the calculation engine, and this run measured only the web one: the corpus was uploaded to OneDrive as .xlsx, recalculated by Excel for the web on open, and downloaded again for readback. Excel for the web is a rolling service with no pinnable version, so the run is identified by its date. Where a value here disagrees with the Expected column — which is Microsoft’s documentation of the desktop product — we cannot tell you whether the web engine diverges from the desktop one or the documentation is wrong about both, because we do not run desktop Excel.
| Formula | Description | Result | Expected | Verdict |
|---|---|---|---|---|
| =ROUND(ERFC(1),8) | Microsoft's documented worked example: the complementary error function of 1 | 0.15729921 | 0.15729921ProvenanceMicrosoft's page publishes '=ERFC(1)' with the result 0.15729921. Re-derived independently with mpmath at 50 decimal digits: erfc(1) = 0.15729920705028513066, which rounds to the published 0.15729921 at 8 dp. It is also exactly 1 - erf(1) = 1 - 0.84270079294971486934, the identity the two pages' own examples encode. |
Matched |
| =ERFC(0) | The complementary error function at zero | 1 | 1ProvenanceDerived from the documented definition, "Returns the complementary ERF function integrated between x and infinity": at x = 0 that is the whole normalized integral, which is exactly 1. Asserted without a ROUND() wrapper because the answer is an exact integer -- an engine that returns 0.9999999999 here has a normalization error the 8-decimal published example would hide. |
Matched |
| =ROUND(ERFC(1)+ERF(1),12) | ERFC and ERF sum to 1 at the same argument | 1 | 1ProvenanceDerived from the two pages read together: ERF(1) is documented as the error function integrated between 0 and 1, ERFC(1) as the complementary function integrated between 1 and infinity, so their sum is the complete integral, 1. Asserting the SUM catches a cancellation or normalization defect that the separately published 0.84270079 and 0.15729921 cannot. |
Matched |
| =ERFC("abc") | A non-numeric argument | #VALUE! | #VALUE!ProvenanceExcel documents: "If x is nonnumeric, ERFC returns the #VALUE! error value." |
Matched |
Google Sheets (executed 2026-08-31 via Drive import)
Google Sheets is a rolling service with no pinnable version, so this run is identified by its date. The corpus was imported to Drive as .xlsx, recalculated by Sheets, and exported back for readback.
| Formula | Description | Result | Expected | Verdict |
|---|---|---|---|---|
| =ROUND(ERFC(1),8) | Microsoft's documented worked example: the complementary error function of 1 | 0.15729921 | 0.15729921ProvenanceMicrosoft's page publishes '=ERFC(1)' with the result 0.15729921. Re-derived independently with mpmath at 50 decimal digits: erfc(1) = 0.15729920705028513066, which rounds to the published 0.15729921 at 8 dp. It is also exactly 1 - erf(1) = 1 - 0.84270079294971486934, the identity the two pages' own examples encode. |
Matched |
| =ERFC(0) | The complementary error function at zero | 1 | 1ProvenanceDerived from the documented definition, "Returns the complementary ERF function integrated between x and infinity": at x = 0 that is the whole normalized integral, which is exactly 1. Asserted without a ROUND() wrapper because the answer is an exact integer -- an engine that returns 0.9999999999 here has a normalization error the 8-decimal published example would hide. |
Matched |
| =ROUND(ERFC(1)+ERF(1),12) | ERFC and ERF sum to 1 at the same argument | 1 | 1ProvenanceDerived from the two pages read together: ERF(1) is documented as the error function integrated between 0 and 1, ERFC(1) as the complementary function integrated between 1 and infinity, so their sum is the complete integral, 1. Asserting the SUM catches a cancellation or normalization defect that the separately published 0.84270079 and 0.15729921 cannot. |
Matched |
| =ERFC("abc") | A non-numeric argument | #VALUE! | #VALUE!ProvenanceExcel documents: "If x is nonnumeric, ERFC returns the #VALUE! error value." |
Matched |
LibreOffice Calc 25.8.7.3 (tested 2026-08-31)
| Formula | Description | Result | Expected | Verdict |
|---|---|---|---|---|
| =ROUND(ERFC(1),8) | Microsoft's documented worked example: the complementary error function of 1 | 0.15729921 | 0.15729921ProvenanceMicrosoft's page publishes '=ERFC(1)' with the result 0.15729921. Re-derived independently with mpmath at 50 decimal digits: erfc(1) = 0.15729920705028513066, which rounds to the published 0.15729921 at 8 dp. It is also exactly 1 - erf(1) = 1 - 0.84270079294971486934, the identity the two pages' own examples encode. |
Matched |
| =ERFC(0) | The complementary error function at zero | 1 | 1ProvenanceDerived from the documented definition, "Returns the complementary ERF function integrated between x and infinity": at x = 0 that is the whole normalized integral, which is exactly 1. Asserted without a ROUND() wrapper because the answer is an exact integer -- an engine that returns 0.9999999999 here has a normalization error the 8-decimal published example would hide. |
Matched |
| =ROUND(ERFC(1)+ERF(1),12) | ERFC and ERF sum to 1 at the same argument | 1 | 1ProvenanceDerived from the two pages read together: ERF(1) is documented as the error function integrated between 0 and 1, ERFC(1) as the complementary function integrated between 1 and infinity, so their sum is the complete integral, 1. Asserting the SUM catches a cancellation or normalization defect that the separately published 0.84270079 and 0.15729921 cannot. |
Matched |
| =ERFC("abc") | A non-numeric argument | #VALUE! | #VALUE!ProvenanceExcel documents: "If x is nonnumeric, ERFC returns the #VALUE! error value." |
Matched |
Docs & syntax
- Excel (desktop): official documentation
- Google Sheets: official documentation
- LibreOffice Calc: official documentation