PlanMaker ERFC: Nonnegative Inputs and Complementary Tails

The PlanMaker 2026 manual, 2024 manual and 2021 manual were retrieved on October 15, 2026. They document this function in those manual families. They do not establish its original introduction or a last-working-version endpoint; both historical endpoints remain unverified. Support in every FreeOffice/mobile edition or individual desktop build is outside this check.

No native PlanMaker execution was performed. Expected values below are independently checked mathematical controls, not captured application results. Formulas use the English manual’s commas; verify localized names and separators in the installed product.

=ERFC(LowerLimit)

LowerLimit is the required lower integration limit. All three checked PlanMaker manual families explicitly restrict it to values greater than or equal to zero. Do not import another product’s negative-input support merely because the mathematical complementary error function can be extended there.

NIST’s complementary-error definition is erfc(x)=(2/√π) times the integral of exp(−t²) from x to infinity, equal mathematically to 1−erf(x). This normalization explains the independent expectations below. ERFC is not the ordinary reciprocal 1/ERF(x), and no second upper-limit argument is shown in the PlanMaker syntax.

The product reference gives the domain but does not identify an exact error code for a negative argument. This guide therefore says that negative inputs are outside the documented contract without inventing a native #NUM! or #VALUE! result.

Create TailControls with x in A1 and Complement in B1. Enter these nonnegative numbers in A2:A7 and fill B2 =ERFC(A2) through B7. Show at least twelve decimals for the ordinary controls.

In a copy change A5 from 1 to 0.75. Its expected complement becomes 0.288844366346. This increase is sensible because the lower integration limit has moved left, adding area to the remaining tail. It does not alter the other source values.

The value at zero is one, and positive inputs produce successively smaller positive mathematical tails. A display rounded to zero does not prove the underlying mathematical tail is exactly zero.

Put Zero_to_x in C1 and Total in D1. Fill C2 =ERF(A2) and D2 =B2+C2 through row 7. The expected C values are 0,0.276326390168,0.520499877813,0.842700792950,0.966105146475,0.995322265019. Each D has mathematical expectation 1.

This check uses the corresponding PlanMaker ERF contract at the same nonnegative input. It tests a relationship between outputs rather than proving native last-bit agreement or the safety of every algebraic rearrangement. If a total differs materially from one, check that the formulas point at the same A cell.

For x=3, =ERFC(3) has independent expectation 0.0000220904969986. For x=6, the corresponding tail is approximately 2.15197367125e-17. Scientific notation is more useful than twelve fixed decimals for the latter.

Mathematically =1-ERF(6) equals the same tail, but subtracting a value very close to one can destroy relative precision in finite arithmetic. Prefer a direct complementary-function formulation when the small tail itself is the quantity of interest, while separately testing the actual application’s accuracy. No claim is made here that PlanMaker’s ERFC implementation preserves a particular number of tail digits or that its ERF(6) rounds in a specified way.

The distinction is numerical conditioning, not a different mathematical definition. Do not convert a tiny positive result to a hard zero just because a chosen number format hides it.

For a mathematical standard normal variable Z and nonnegative z, the upper-tail mass is erfc(z/√2)/2. On NormalTail, enter 0,1,2,3 in F2:F5. Fill G2 =ERFC(F2/(2^0.5))/2 down.

The independent expectations are 0.500000000000,0.158655253931,0.022750131948,0.001349898032. The division by two matters: ERFC(0) is one, while a symmetric normal distribution has half its mass above zero. The √2 rescaling also matters because the normal-density exponent differs from the error-function exponent.

For a symmetric two-sided tail beyond ±2, =ERFC(2/(2^0.5)) has expected result 0.045500263896, twice the one-sided quantity. This is a model calculation, not a claim about a measured dataset or an automatic significance decision.

Check input units and standardization before interpreting a result as a probability. A raw measurement is not automatically a z-score. Use explicit finite numeric inputs: blanks, numeric text, Booleans, arrays and extreme magnitudes do not have a fully documented coercion or error matrix in the checked entry.

Record the PlanMaker build, edition, platform and language for native reproduction. Compare the supplied controls with sufficient precision, then test any small-tail accuracy requirement separately. The wider mathematical domain does not override PlanMaker’s nonnegative documented restriction, and a reference calculation is not a native execution record.