ERFC.PRECISE in Collabora Office: Evaluate the Complementary Gaussian Integral
Use Collabora ERFC.PRECISE for complementary error-function values, understand negative inputs and form normal right-tail probabilities.
Verification status: See the evidence and test scope described in this guide. How formula examples are checked
Quick answer: =ERFC.PRECISE(1) has independently expected result approximately 0.157299207, matching the official help’s rounded value 0.157299.
Syntax and complement definition
=ERFC.PRECISE(LowerLimit)
LowerLimit is the starting point of the normalized Gaussian integral extending to infinity. The dedicated Collabora help describes this complementary integral and documents one required argument.
Mathematically erfc(x) is (2/SQRT(PI())) times the integral of EXP(-t^2) from x to infinity. It equals 1-erf(x). The normalization makes ERFC.PRECISE(0)=1; this does not mean the standard-normal probability above zero is one.
For negative x, erfc(x) exceeds one and approaches two as x decreases without bound. Those values are valid complementary-error-function outputs, not probabilities above 100%. A normal-tail conversion needs additional scaling described below.
Example 1: build a complementary table
Put −1, 0, 0.5, 1, 2 in A2:A6. Enter =ERFC.PRECISE(A2) in B2 and fill down. Independent targets are approximately 1.842700793, 1, 0.479500122, 0.157299207 and 0.004677735.
In C2 enter =ERF.PRECISE(A2) and fill down. In D2 use =B2+C2; the mathematical target is one in every row. The negative-input pair has one negative term and one term greater than one, so it still satisfies the identity.
Do not cap the complementary values at one. Such a cap would silently change the function and break its relation to the original Gaussian integral.
Example 2: compute a standard-normal right tail
For standardized z, the normal probability above z is =0.5*ERFC.PRECISE(z/SQRT(2)). At z=1 the independent target is approximately 0.158655254; at z=2 it is approximately 0.022750132.
Put 1 and 2 in F2:F3 and enter =0.5*ERFC.PRECISE(F2/SQRT(2)) in G2, then fill down. Using ERFC.PRECISE(z) directly would give the wrong argument scale and omit the half factor.
For z=0, the formula gives 0.5, the standard-normal upper half. This is a simple control that immediately catches a missing multiplication by one half.
Advanced application: calculate a two-sided tail
For a nonnegative threshold z, the standard-normal probability outside the interval from −z to z is =ERFC.PRECISE(z/SQRT(2)). At z=2 the independent result is approximately 0.045500264, twice the one-sided upper tail.
This identity describes a symmetric normal-model event. It does not, by itself, choose a statistical test or establish a valid p-value for an arbitrary experiment. The model, standardization and test assumptions must be justified separately.
Advanced application: avoid early rounding in a small complement
At x=5, the independent erfc value is approximately 1.537459794428×10^-12. The corresponding erf value is so close to one that rounding it to twelve or fewer decimal places before subtraction can destroy substantial relative information.
Compare a direct ERFC.PRECISE(5) cell with =1-ROUND(ERF.PRECISE(5);10). The latter deliberately rounds the near-one intermediate and mathematically targets zero at that display precision. This illustrates why intermediate rounding matters; it is not a native accuracy benchmark.
Store the unrounded result and apply number formatting for presentation. Increasing displayed decimals cannot recover information already discarded by an explicit ROUND formula.
Errors and troubleshooting
Preserve the sign of the argument and distinguish the complementary integral from a probability. Negative x producing a value above one is expected mathematically. If a normal tail is twice as large as expected, inspect the missing half factor; if it decays too quickly, inspect the missing SQRT(2) adjustment.
The PRECISE suffix does not promise arbitrary precision. Very large arguments can underflow in finite arithmetic, and the short dedicated help does not establish all error displays, coercion rules or tail tolerances. These independent controls do not replace native validation for numerically sensitive calculations.
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.ERFC.PRECISE and places the function outside the cited OpenFormula 1.3 standard. This format disclosure does not establish cross-product behavioral identity.