ERF.PRECISE Function in Google Sheets: Formula, Examples & Troubleshooting

=ERF.PRECISE(lower_bound, [upper_bound])

lower_bound is required. Despite its name, when it is the only argument, the integral runs from zero to that value. Adding upper_bound makes the first argument the interval’s lower endpoint. Google’s ERF.PRECISE catalog entry supplies this spelling and links to the ERF contract.

That cross-reference establishes the documented mathematical definition, not an independent native proof of identical internal algorithms, numerical precision, or every edge case. The word PRECISE is not evidence that an approximate decimal becomes exact arithmetic.

Enter this worksheet area:

1. Put the input numbers in A2:A5 as numeric cells.
2. Type =ERF.PRECISE(A2) in B2 and copy down to B5.
3. Display at least six decimal places to compare the nonzero values.

These values follow the mathematical error function: erf(x) is 2/sqrt(pi) times the integral of exp(-t²) from 0 to x. Its odd symmetry explains why the two ±1 outputs have equal magnitude and opposite signs. A negative output here is mathematically meaningful; it is not a negative probability.

The value at zero is a useful baseline check because the integration interval has zero width. It does not test performance at large or extreme inputs.

Put 0.5 in D2 and 1 in E2. In F2 enter:

=ERF.PRECISE(D2,E2)

Under Google’s documented two-bound contract, the expected result is approximately 0.322200915136668. Independently, it is erf(1) − erf(0.5), the difference between the table’s B4 and B3 values.

In F3 enter =ERF.PRECISE(E2)-ERF.PRECISE(D2). It has the same mathematical expectation. Comparing both forms in a target workbook is useful because the two-argument spelling has not been native-tested for this guide. It does not establish exact bit-for-bit equality at every magnitude.

For a standard normal variable, the model probability of lying between −z and z is erf(z/sqrt(2)). This is a mathematical transformation of the Gaussian integral; it is not a claim that the error function alone verifies a normal-distribution assumption.

Put 1, 2, and 3 in H2:H4. In I2 enter =ERF.PRECISE(H2/SQRT(2)) and copy down. Expected model fractions are approximately:

Use these only when the chosen statistical model is appropriate. A measured process can have skew, heavy tails, or shifts that make a normal-model tolerance calculation misleading. Keep the assumption separate from the observed data.

Google’s linked ERF page documents #VALUE! for nonnumeric bounds. The ERF.PRECISE entry delegates its description to that page; no separate native error observation is asserted here. First check input types and whether a copied number contains text or a locale-specific decimal separator.

The one-bound function approaches 1 for large positive inputs. Subtracting two already rounded displayed values can erase a small interval result. Retain the underlying values and use suitable numerical methods for extreme-tail work. No undocumented precision guarantee or threshold is invented here.

Do not confuse erf(x) with a standard-normal cumulative probability at x. The normal transformation needs the scale factor sqrt(2) and, for a one-sided cumulative probability, an additional shift and division. The symmetric-band example above states exactly which quantity is calculated.

Microsoft documents Excel ERF.PRECISE(x) with one argument. Google’s catalog explicitly lists an optional second argument. Therefore, the two-bound Google form is not justified by the Excel signature; the difference-of-two-one-bound expressions is the mathematical form to review when moving a workbook between products. Conversion has not been tested here.

Google’s current catalog documents this name. Its first introduction, last functioning release, and retirement are not established by the sources reviewed. No relationship with similarly named functions in other products is assumed beyond the cited syntax comparison.

Related published guides: SQRT and EXP.

Reviewed October 17, 2026: Google ERF.PRECISE catalog, Google ERF definition, and Microsoft ERF.PRECISE syntax.