ERF.PRECISE in Collabora Office: Calculate the Gaussian Error Integral
Use Collabora ERF.PRECISE with its single-limit syntax, verify odd symmetry and connect it carefully to normal probabilities.
Verification status: See the evidence and test scope described in this guide. How formula examples are checked
Quick answer: =ERF.PRECISE(1) has independently expected result approximately 0.842700793, matching the official help’s rounded value 0.842701.
Syntax and integral limits
=ERF.PRECISE(LowerLimit)
The argument label LowerLimit can be misleading if read in isolation: the dedicated Collabora help says the calculation runs from zero to the supplied limit. There is one argument, not a lower-and-upper pair in this dotted function’s documented syntax.
The independent mathematical definition is (2/SQRT(PI())) times the integral of EXP(-t^2) from zero to x. It is the Gaussian error function, not a generic spreadsheet error detector and not a probability of a worksheet formula being wrong.
For positive x the result is positive and below one; for negative x it is negative. Reversing the direction of integration accounts for the sign. The mathematical function is odd: erf(-x)=-erf(x).
Example 1: build a signed integral table
Put −1, 0, 0.5, 1, 2 in A2:A6. Enter =ERF.PRECISE(A2) in B2 and fill down. Independent expected results are approximately −0.842700793, 0, 0.520499878, 0.842700793 and 0.995322265.
A negative result is valid for a negative limit. Do not replace it with ABS unless your intended mathematical operation specifically calls for an unsigned area.
The function approaches one as its positive argument grows, but does not equal one at an arbitrary finite mathematical input. A rounded spreadsheet display can show 1.000000 even when the stored value is slightly smaller.
Example 2: integrate between two limits
To obtain the same normalized Gaussian integral from a to b, use =ERF.PRECISE(b)-ERF.PRECISE(a). For a=0.5 and b=1, the independent result is approximately 0.322200915.
Put a in D2 and b in E2, and use =ERF.PRECISE(E2)-ERF.PRECISE(D2) in F2. Reversing the limits reverses the sign. This difference retains the normalization factor 2/SQRT(PI()); it is not the unnormalized integral of EXP(-t^2).
For limits −1 and 1, the normalized difference is approximately 1.685401586. A result above one is possible for this two-limit normalized integral and should not be mislabeled as a probability.
Advanced application: recover a standard-normal probability
The standard-normal cumulative probability at z is (1+ERF.PRECISE(z/SQRT(2)))/2. The SQRT(2) adjustment and the division by two are both required.
At z=1, =(1+ERF.PRECISE(1/SQRT(2)))/2 has independently expected value approximately 0.841344746. ERF.PRECISE(1) itself is approximately 0.842700793 and is a different quantity despite its nearby numerical value.
For a positive z, the standard-normal probability between −z and z is ERF.PRECISE(z/SQRT(2)). With z=1, that central probability is approximately 0.682689492.
Advanced application: check a complementary pair
Mathematically ERF.PRECISE(x)+ERFC.PRECISE(x)=1. At x=1, the independent complementary value is approximately 0.157299207, and the sum targets one.
For large positive x, computing a very small complement as 1 minus a near-one rounded erf value can lose meaningful digits. A direct complementary function can be more suitable mathematically; this guide does not certify that every installed implementation achieves a particular tail accuracy.
Errors and troubleshooting
Use a numeric limit and preserve the sign. The function name’s PRECISE suffix identifies the documented function; it is not evidence of arbitrary precision, an accuracy comparison with every legacy implementation, or native testing.
If a normal probability is incorrect, check the missing SQRT(2), half-offset or division by two. If a two-limit result exceeds one, inspect which normalized integral was requested before assuming an error. Nonnumeric coercion and exact native error displays are not documented by the short source section and remain unverified.
Availability and verification
The exact function is documented in Collabora Office 26.04 desktop help. The snapshot was retrieved on 2026-10-13 and hash-verified on October 15, 2026. Desktop help is not proof of Online or mobile availability. First introduced release and last functioning version are unknown; the dedicated source does not establish them.
No native Collabora or WPS execution occurred. Numerical values are independent mathematical expectations, not certification of application errors or all numerical limits. Formulas use English names and semicolon separators.
The dedicated help identifies namespace COM.MICROSOFT.ERF.PRECISE and places the function outside the cited OpenFormula 1.3 standard. This format disclosure does not establish cross-product behavioral identity.